Tag Archives: Computational models

The Systematic Comparison of Agent-Based Policy Models – It’s time we got our act together!

By Mike Bithell and Bruce Edmonds

Model Intercomparison

The recent Covid crisis has led to a surge of new model development and a renewed interest in the use of models as policy tools. While this is in some senses welcome, the sudden appearance of many new models presents a problem in terms of their assessment, the appropriateness of their application and reconciling any differences in outcome. Even if they appear similar, their underlying assumptions may differ, their initial data might not be the same, policy options may be applied in different ways, stochastic effects explored to a varying extent, and model outputs presented in any number of different forms. As a result, it can be unclear what aspects of variations in output between models are results of mechanistic, parameter or data differences. Any comparison between models is made tricky by differences in experimental design and selection of output measures.

If we wish to do better, we suggest that a more formal approach to making comparisons between models would be helpful. However, it appears that this is not commonly undertaken most fields in a systematic and persistent way, except for the field of climate change, and closely related fields such as pollution transport or economic impact modelling (although efforts are underway to extend such systematic comparison to ecosystem models –  Wei et al., 2014, Tittensor et al., 2018⁠). Examining the way in which this is done for climate models may therefore prove instructive.

Model Intercomparison Projects (MIP) in the Climate Community

Formal intercomparison of atmospheric models goes back at least to 1989 (Gates et al., 1999)⁠ with the first atmospheric model inter-comparison project (AMIP), initiated by the World Climate Research Programme. By 1999 this had contributions from all significant atmospheric modelling groups, providing standardised time-series of over 30 model variables for one particular historical decade of simulation, with a standard experimental setup. Comparisons of model mean values with available data helped to reveal overall model strengths and weaknesses: no single model was best at simulation of all aspects of the atmosphere, with accuracy varying greatly between simulations. The model outputs also formed a reference base for further inter-comparison experiments including targets for model improvement and reduction of systematic errors, as well as a starting point for improved experimental design, software and data management standards and protocols for communication and model intercomparison. This led to AMIPII and, subsequently, to a series of Climate model inter-comparison projects (CMIP) beginning with CMIP I in 1996. The latest iteration (CMIP 6) is a collection of 23 separate model intercomparison experiments covering atmosphere, ocean, land surface, geo-engineering, and the paleoclimate. This collection is aimed at the upcoming 2021 IPCC process (AR6). Participating projects go through an endorsement process for inclusion, (a process agreed with modelling groups), based on 10 criteria designed to ensure some degree of coherence between the various models – a further 18 MIPS are also listed as currently active (https://www.wcrp-climate.org/wgcm-cmip/wgcm-cmip6). Groups contribute to a central set of common experiments covering the period 1850 to the near-present. An overview of the whole process can be found in (Eyring et al., 2016).

The current structure includes a set of three overarching questions covering the dynamics of the earth system, model systematic biases and understanding possible future change under uncertainty. Individual MIPS may build on this to address one or more of a set of 7 “grand science challenges” associated with the climate. Modelling groups agree to provide outputs in a standard form, obtained from a specified set of experiments under the same design, and to provide standardised documentation to go with their models. Originally (up to CMIP 5), outputs were then added to a central public repository for further analysis, however the output grew so large under CMIP6 that now the data is held dispersed over repositories maintained by separate groups.

Other Examples

Two further more recent examples of collective model  development may also be helpful to consider.

Firstly, an informal network collating models across more than 50 research groups has already been generated as a result of the COVID crisis –  the Covid Forecast Hub (https://covid19forecasthub.org). This is run by a small number of research groups collaborating with the US Centre for Disease Control and is strongly focussed on the epidemiology. Participants are encouraged to submit weekly forecasts, and these are integrated into a data repository and can be vizualized on the website – viewers can look at forward projections, along with associated confidence intervals and model evaluation scores, including those for an ensemble of all models. The focus on forecasts in this case arises out of the strong policy drivers for the current crisis, but the main point is that it is possible to immediately view measures of model performance and to compare the different model types: one clear message that rapidly becomes apparent is that many of the forward projections have 95% (and at some times, even 50%) confidence intervals for incident deaths that more than span the full range of the past historic data. The benefit of comparing many different models in this case is apparent, as many of the historic single-model projections diverge strongly from the data (and the models most in error are not consistently the same ones over time), although the ensemble mean tends to be better.

As a second example, one could consider the Psychological Science Accelerator (PSA: Moshontz et al 2018, https://psysciacc.org/). This is a collaborative network set up with the aim of addressing the “replication crisis” in psychology: many previously published results in psychology have proved problematic to replicate as a result of small or non-representative sampling or use of experimental designs that do not generalize well or have not been used consistently either within or across studies. The PSA seeks to ensure accumulation of reliable and generalizable evidence in psychological science, based on principles of inclusion, decentralization, openness, transparency and rigour. The existence of this network has, for example, enabled the reinvestigation of previous  experiments but with much larger and less nationally biased samples (e.g. Jones et al 2021).

The Benefits of the Intercomparison Exercises and Collaborative Model Building

More specifically, long-term intercomparison projects help to do the following.

  • Build on past effort. Rather than modellers re-inventing the wheel (or building a new framework) with each new model project, libraries of well-tested and documented models, with data archives, including code and experimental design, would allow researchers to more efficiently work on new problems, building on previous coding effort
  • Aid replication. Focussed long term intercomparison projects centred on model results with consistent standardised data formats would allow new versions of code to be quickly tested against historical archives to check whether expected results could be recovered and where differences might arise, particularly if different modelling languages were being used
  • Help to formalize. While informal code archives can help to illustrate the methods or theoretical foundations of a model, intercomparison projects help to understand which kinds of formal model might be good for particular applications, and which can be expected to produce helpful results for given desired output measures
  • Build credibility. A continuously updated set of model implementations and assessment of their areas of competence and lack thereof (as compared with available datasets) would help to demonstrate the usefulness (or otherwise) of ABM as a way to represent social systems
  • Influence Policy (where appropriate). Formal international policy organisations such as the IPCC or the more recently formed IPBES are effective partly through an underpinning of well tested and consistently updated models. As yet it is difficult to see whether such a body would be appropriate or effective for social systems, as we lack the background of demonstrable accumulated and well tested model results.

Lessons for ABM?

What might we be able to learn from the above, if we attempted to use a similar process to compare ABM policy models?

In the first place, the projects started small and grew over time: it would not be necessary, for example, to cover all possible ABM applications at the outset. On the other hand, the latest CMIP iterations include a wide range of different types of model covering many different aspects of the earth system, so that the breadth of possible model types need not be seen as a barrier.

Secondly, the climate inter-comparison project has been persistent for some 30 years – over this time many models have come and gone, but the history of inter-comparisons allows for an overview of how well these models have performed over time – data from the original AMIP I models is still available on request, supporting assessments concerning  long-term model improvement.

Thirdly, although climate models are complex – implementing a variety of different mechanisms in different ways – they can still be compared by use of standardised outputs, and at least some (although not necessarily all) have been capable of direct comparison with empirical data.

Finally, an agreed experimental design and public archive for documentation and output that is stable over time is needed; this needs to be done via a collective agreement among the modelling groups involved so as to ensure a long-term buy-in from the community as a whole, so that there is a consistent basis for long-term model development, building on past experience.

The need for aligning or reproducing ABMs has long been recognised within the community (Axtell et al. 1996; Edmonds & Hales 2003), but on a one-one basis for verifying the specification of models against their implementation, although (Hales et al. 2003) discusses a range of possibilities. However, this is far from a situation where many different models of basically the same phenomena are systematically compared – this would be a larger scale collaboration lasting over a longer time span.

The community has already established a standardised form of documentation in the ODD protocol. Sharing of model code is also becoming routine, and can be easily achieved through COMSES, Github or similar. The sharing of data in a long-term archive may require more investigation. As a starting project COVID-19 provides an ideal opportunity for setting up such a model inter-comparison project – multiple groups already have running examples, and a shared set of outputs and experiments should be straightforward to agree on. This would potentially form a basis for forward looking experiments designed to assist with possible future pandemic problems, and a basis on which to build further features into the existing disease-focussed modelling, such as the effects of economic, social and psychological issues.

Additional Challenges for ABMs of Social Phenomena

Nobody supposes that modelling social phenomena is going to have the same set of challenges that climate change models face. Some of the differences include:

  • The availability of good data. Social science is bedevilled by a paucity of the right kind of data. Although an increasing amount of relevant data is being produced, there are commercial, ethical and data protection barriers to accessing it and the data rarely concerns the same set of actors or events.
  • The understanding of micro-level behaviour. Whilst the micro-level understanding of our atmosphere is very well established, those of the behaviour of the most important actors (humans) is not. However, it may be that better data might partially substitute for a generic behavioural model of decision-making.
  • Agreement upon the goals of modelling. Although there will always be considerable variation in terms of what is wanted from a model of any particular social phenomena, a common core of agreed objectives will help focus any comparison and give confidence via ensembles of projections. Although the MIPs and Covid Forecast Hub are focussed on prediction, it may be that empirical explanation may be more important in other areas.
  • The available resources. ABM projects tend to be add-ons to larger endeavours and based around short-term grant funding. The funding for big ABM projects is yet to be established, not having the equivalent of weather forecasting to piggy-back on.
  • Persistence of modelling teams/projects. ABM tends to be quite short-term with each project developing a new model for a new project. This has made it hard to keep good modelling teams together.
  • Deep uncertainty. Whilst the set of possible factors and processes involved in a climate change model are well established, which social mechanisms need to be involved in any model of any particular social phenomena is unknown. For this reason, there is deep disagreement about the assumptions to be made in such models, as well as sharp divergence in outcome due to changes brought about by a particular mechanism but not included in a model. Whilst uncertainty in known mechanisms can be quantified, assessing the impact of those due to such deep uncertainty is much harder.
  • The sensitivity of the political context. Even in the case of Climate Change, where the assumptions made are relatively well understood and done on objective bases, the modelling exercise and its outcomes can be politically contested. In other areas, where the representation of people’s behaviour might be key to model outcomes, this will need even more care (Adoha & Edmonds 2017).

However, some of these problems were solved in the case of Climate Change as a result of the CMIP exercises and the reports they ultimately resulted in. Over time the development of the models also allowed for a broadening and updating of modelling goals, starting from a relatively narrow initial set of experiments. Ensuring the persistence of individual modelling teams is easier in the context of an internationally recognised comparison project, because resources may be easier to obtain, and there is a consistent central focus. The modelling projects became longer-term as individual researchers could establish a career doing just climate change modelling and importance of the work increasingly recognised. An ABM modelling comparison project might help solve some of these problems as the importance of its work is established.

Towards an Initial Proposal

The topic chosen for this project should be something where there: (a) is enough public interest to justify the effort, (b) there are a number of models with a similar purpose in mind being developed.  At the current stage, this suggests dynamic models of COVID spread, but there are other possibilities, including: transport models (where people go and who they meet) or criminological models (where and when crimes happen).

Whichever ensemble of models is focussed upon, these models should be compared on a core of standard, with the same:

  • Start and end dates (but not necessarily the same temporal granularity)
  • Covering the same set of regions or cases
  • Using the same population data (though possibly enhanced with extra data and maybe scaled population sizes)
  • With the same initial conditions in terms of the population
  • Outputting a core of agreed measures (but maybe others as well)
  • Checked against their agreement against a core set of cases, with agreed data sets
  • Reported on in a standard format (though with a discussion section for further/other observations)
  • well documented and with code that is open access
  • Run a minimum of times with different random seeds

Any modeller/team that had a suitable model and was willing to adhere to the rules would be welcome to participate (commercial, government or academic) and these teams would collectively decide the rules, development and write any reports on the comparisons. Other interested stakeholder groups could be involved including professional/academic associations, NGOs and government departments but in a consultative role providing wider critique – it is important that the terms and reports from the exercise be independent or any particular interest or authority.

Conclusion

We call upon those who think ABMs have the potential to usefully inform policy decisions to work together, in order that the transparency and rigour of our modelling matches our ambition. Whilst model comparison exercises of the kind described are important for any simulation work, particular care needs to be taken when the outcomes can affect people’s lives.

References

Aodha, L. & Edmonds, B. (2017) Some pitfalls to beware when applying models to issues of policy relevance. In Edmonds, B. & Meyer, R. (eds.) Simulating Social Complexity – a handbook, 2nd edition. Springer, 801-822. (A version is at http://cfpm.org/discussionpapers/236)

Axtell, R., Axelrod, R., Epstein, J. M., & Cohen, M. D. (1996). Aligning simulation models: A case study and results. Computational & Mathematical Organization Theory, 1(2), 123-141. https://link.springer.com/article/10.1007%2FBF01299065

Edmonds, B., & Hales, D. (2003). Replication, replication and replication: Some hard lessons from model alignment. Journal of Artificial Societies and Social Simulation, 6(4), 11. http://jasss.soc.surrey.ac.uk/6/4/11.html

Eyring, V., Bony, S., Meehl, G. A., Senior, C. A., Stevens, B., Stouffer, R. J., & Taylor, K. E. (2016). Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geoscientific Model Development, 9(5), 1937–1958. https://doi.org/10.5194/gmd-9-1937-2016

Gates, W. L., Boyle, J. S., Covey, C., Dease, C. G., Doutriaux, C. M., Drach, R. S., Fiorino, M., Gleckler, P. J., Hnilo, J. J., Marlais, S. M., Phillips, T. J., Potter, G. L., Santer, B. D., Sperber, K. R., Taylor, K. E., & Williams, D. N. (1999). An Overview of the Results of the Atmospheric Model Intercomparison Project (AMIP I). In Bulletin of the American Meteorological Society (Vol. 80, Issue 1, pp. 29–55). American Meteorological Society. https://doi.org/10.1175/1520-0477(1999)080<0029:AOOTRO>2.0.CO;2

Hales, D., Rouchier, J., & Edmonds, B. (2003). Model-to-model analysis. Journal of Artificial Societies and Social Simulation, 6(4), 5. http://jasss.soc.surrey.ac.uk/6/4/5.html

Jones, B.C., DeBruine, L.M., Flake, J.K. et al. To which world regions does the valence–dominance model of social perception apply?. Nat Hum Behav 5, 159–169 (2021). https://doi.org/10.1038/s41562-020-01007-2

Moshontz, H. + 85 others (2018) The Psychological Science Accelerator: Advancing Psychology Through a Distributed Collaborative Network ,  1(4) 501-515. https://doi.org/10.1177/2515245918797607

Tittensor, D. P., Eddy, T. D., Lotze, H. K., Galbraith, E. D., Cheung, W., Barange, M., Blanchard, J. L., Bopp, L., Bryndum-Buchholz, A., Büchner, M., Bulman, C., Carozza, D. A., Christensen, V., Coll, M., Dunne, J. P., Fernandes, J. A., Fulton, E. A., Hobday, A. J., Huber, V., … Walker, N. D. (2018). A protocol for the intercomparison of marine fishery and ecosystem models: Fish-MIP v1.0. Geoscientific Model Development, 11(4), 1421–1442. https://doi.org/10.5194/gmd-11-1421-2018

Wei, Y., Liu, S., Huntzinger, D. N., Michalak, A. M., Viovy, N., Post, W. M., Schwalm, C. R., Schaefer, K., Jacobson, A. R., Lu, C., Tian, H., Ricciuto, D. M., Cook, R. B., Mao, J., & Shi, X. (2014). The north american carbon program multi-scale synthesis and terrestrial model intercomparison project – Part 2: Environmental driver data. Geoscientific Model Development, 7(6), 2875–2893. https://doi.org/10.5194/gmd-7-2875-2014


Bithell, M. and Edmonds, B. (2020) The Systematic Comparison of Agent-Based Policy Models - It’s time we got our act together!. Review of Artificial Societies and Social Simulation, 11th May 2021. https://rofasss.org/2021/05/11/SystComp/


 

Should the family size be used in COVID-19 vaccine prioritization strategy to prevent variants diffusion? A first investigation using a basic ABM

By Gianfranco Giulioni

Department of Philosophical, Pedagogical and Economic-Quantitative Sciences, University of Chieti-Pescara, Italy

(A contribution to the: JASSS-Covid19-Thread)

When writing this document, few countries have made significant progress in vaccinating their population while many others still move first steps.

Despite the importance of COVID-19 adverse effects on society, there seems to be too little debate on the best option for progressing the vaccination process after the front-line healthcare personnel has been immunized.

The overall adopted strategies in the front-runner countries prioritize people using their health fragility, and age. For example, this strategy’s effectiveness is supported by Bubar et al. (2021), who provide results based on a detailed age-stratified Susceptible, Exposed, Infectious, Recovered (SEIR) model.

During the Covid infection outbreak, the importance of families in COVID diffusion was stressed by experts and media. This observation motivates the present effort, which investigates if considering family size among the vaccine prioritization strategy can have a role.

This document describes an ABM model developed with the intent of analyzing the question. The model is basic and has the essentials features to investigate the issue.

As highlighted by Squazzoni et al. (2020) a careful investigation of pandemics requires the cooperation of many scientists from different disciplines. To ease this cooperation and to the aim of transparency (Barton et al. 2020), the code is made publicly available to allow further developments and accurate parameters calibration to those who might be interested. (https://github.com/gfgprojects/abseir_family)

The following part of the document will sketch the model functioning and provide some considerations on families’ effects on vaccination strategy.

Brief Model Description

The ABSEIR-family model code is written in Java, taking advantage of the Repast Simphony modeling system (https://repast.github.io/).

Figure 1 gives an overview of the current development state of the model core classes.

Briefly, the code handles the relevant events of a pandemic:

  • the appearance of the first case,
  • the infection diffusion by contacts,
  • the introduction of measures for diffusion limitation such as quarantine,
  • the activation and implementation of the immunization process.

The distinguishing feature of the model is that individuals are grouped in families. This grouping allows considering two different diffusion speeds: fast among family members and slower when contacts involve two individuals from different families.

Figure 1: relationships between the core classes of the ABSEIR-family model and their variables and methods.

It is perhaps worth describing the evolution of an individual state to sketch the functioning of the model.

An individual’s dynamic is guided by a variable named infectionAge. In the beginning, all the individuals have this variable at zero. The program increases the infectionAge of all the individuals having a non zero value of this variable at each time step.

When an individual has contact with an infectious, s/he can get the infection or not. If infected, the individual enters the latency period, i.e. her/his infectionAge is set to 1 and the variable starts moving ahead with time, but s/he is not infectious. Individuals whose infectionAge is greater than the latency period length (ll ) become infectious.

At each time step, an infectious meets all her/his family members and mof randomly chosen non-family members. S/he passes on the infection with probability pif to family members and pof to non-family members. The infection can be passed on only if the contacted individual’s infectionAge equals zero and if s/he is not in quarantine.

The infectious phase ends when the infection is discovered (quarantine) or when the individual recovers i.e., the infectionAge is greater than the latency period length plus the infection length parameter (li).

At the present stage of development, the code does not handle the virus adverse post-infection evolution. All the infected individuals in this model recover. The infectionAge is set at a negative value at recovery because recovereds stay immune for a while (lr). Similarly, vaccination set the individual’s  infectionAge to a (high) negative value (lv).

At the present state of the pandemic evolution it is perhaps useful to use the model to get insights into how the family size could affect the vaccination process’s effectiveness. This will be attempted hereafter.

Highlighting the relevance of families size by an ad-hoc example

The relevance of family size in vaccination strategy can be shown using the following ad-hoc example.

Suppose there are two covid-free villages (say village A and B) whose health authorities are about to start vaccinations to avoid the disease spreading.

Villages are identical in the other aspects except for the family size distribution. Each village has 50 inhabitants, but village A has 10 families with five components each, while village B has two five members families and 40 singletons. Five vaccines arrive each day in each village.

Some additional extreme assumptions are made to make differences straightforward.

First, healthy family members are infected for sure by a member who contracted the virus. Second, each individual has the same number of contacts (say n) outside the family and the probability to pass  on the virus in external contacts is lower than 1. Symptoms take several days before showing up.

Now, the health authority are about to start the vaccination process and has to decide how to employ the available vaccines.

Intuition would suggest that Village B’s health authority should immunize large families first. Indeed, if case zero arrives at the end of the second vaccination day, the spread of the disease among the population should be limited because the virus can be passed on by external contacts only; and the probability of transmitting the virus in external contacts is lower than in the family.

But, should this strategy be used even by village A health authority?

To answer this question, we compare the family-based vaccination strategy with a random-based vaccination strategy. In a random-based vaccination strategy, we expect one members to be immunized in each family at the end of the second vaccination day. In the family-based vaccination strategy, two families are immunized at the end of the second vaccination day. Now, suppose one of the not-immunized citizens gets the virus at the end of day two. It is easy to verify there will be an infected more in the family-based strategy (all the five components of the family) than in the random-based strategy (4 components because one of them was immunized before). Furthermore, this implies that there will be n additional dangerous external contacts in the family-based strategy than in the random-based strategy.

These observations make us conclude that a random vaccination strategy will slow down the infection dynamics in village A while it will speed up infections in village B, and the opposite is true for the family-based immunization strategy.

Some simulation exercises

In this part of the document, the model described above will be used to compare further the family-based and random-based vaccination strategy to be used against the appearance of a new case (or variant) in a situation similar to that described in the example but with a more realistic setting.

As one can easily imagine, the family size distribution and COVID transmission risk in families are crucial to our simulation exercises. It is therefore important to gather real-world information for these phenomena. Fortunately, recent scientific contributions can help.

Several authors point out that a Poisson distribution is a good statistical model representing the family size distribution. This distribution is suitable because a single parameter characterizes it, i.e., its average, but it has the drawback of having a positive probability for zero value. Recently, Jarosz (2020) confirms the Poisson distribution’s goodness for modeling family size and shows how shifting it by one unit would be a valid alternative to solve the zero family size problem.

Furthermore, average family sizes data can be easily found using, for example, the OECD family database (http://www.oecd.org/social/family/database.htm).

The current version of the database (updated on 06-12-2016) presents data for 2015 with some exceptions. It shows how the average size of families in OECD countries is 2.46, ranging from Mexico (3.93) to Sweden (1.8).

The result in Metlay et al. (2021) guides the choice of the infection in the family parameter. They  provide evidence of an overall household infection risk of 10.1%

Simulation exercises consist in parameters sensitivity analysis with respect to the benchmark parameter set reported hereafter.

The simulation initialization is done by loading the family size distribution. Two alternative distributions are used and are tuned to obtain a system with a total number of individuals close to 20000. The two distributions are characterized by different average family sizes (afs) and are shown in figure 2.

Figure 2: two family size distributions used to initialize the simulation. Figures by the dots inform on the frequency of the corresponding size. Black square relates to the distribution with an average of 2.5; red circles relate to the distribution with an average of 3.5

The description of the vaccination strategy gives a possibility to list other relevant parameters. The immunization center is endowed with nv doses of vaccine at each time starting from time tv. At time t0, the state of one of the individuals is changed from susceptible to infected. This subject (case zero) is taken from a family having three susceptibles among their components.

Case zero undergoes the same process as all other following infected individuals described above.

The relevant parameters of the simulations are reported in table 1.

var description values reference
ni number of individuals ≅20000
afs average family size 2.5;3.5 OECD
nv number of vaccine doses available at each time 50;100;150
tv vaccination starting time 1
t0 case zero appearance time 10
ll length of latency 3 Buran et al 2021
li length of infectious period 5 Buran et al 2021
pif probability to infect a family member 0.1 Metlay et al 2021
pof probability to infect a non-family individual 0.01;0.02;0.03
mof number of non-family contacts of an infectious 10

Table 1: relevant parameters of the model.

We are now going to discuss the results of our simulation exercises. We focus particularly on the number of people infected up to a given point in time.

Due to the presence of random elements, each run has a different trajectory. We limit these effects as much as possible to allow ceteris paribus comparisons. For example, we keep the family size distribution equal across runs by loading the distributions displayed in figure 2 instead of using the run-time random number generator. Again, we set the number of non-family contacts (mof) equal for all the agents, although the code could set it randomly at each time step. Despite these randomness reductions, significant differences in the dynamics remain within the same parametrization because of randomness in the network of contacts.

To allow comparisons among different parametrizations in the presence of different evolution, we use the cross-section distributions of the total number of infected at the end of the infection process (i.e. time 200).

Figure 3 reports the empirical cumulative distribution function (ecdf) of several parametrizations. To easily read the figure, we put the different charts as in a plane having the average family size (afs) in the abscissa and the number of available vaccines (nv) in the ordinate. From above, we know two values of afs (i.e. 2.5 and 3.5) and three values of nv (i.e. 50, 100 and 150) are considered. Therefore figure 3 is made up of 6 charts.

Each chart reports ecdfs corresponding to the three different pof levels reported in table 1. In particular, circles denote edcfs for pof = 0.01, squares are for  pof = 0.02 and triangles for  pof = 0.03. At the end, choosing a parameters values triplet (afs, nv, pof), two ecdfs are identified. The red one is for the random-based, while the black one is for the family-based vaccination strategy. The family based vaccination strategy prioritizes families with higher number of members not yet infected.

Figure 3 shows mixed results: the random-based vaccination strategy outperforms the family-based one (the red line is above the balck one) for some parameters combinations while the reverse holds for others. In particular, the random-based tends to dominate the family-based strategy in case of larger family (afs = 3.5) and low and high vaccination levels (nv = 50 and 150). The opposite is true with smaller families at the same vaccination levels. The intermediate level of vaccination provides exceptions.

Figure 3: empirical cumulative distribution function of several parametrizations. The ecdfs is build by taking the number of infected people at period 200 of 100 runs with different random seed for each parametrization.

It is perhaps useful to highlight how, in the model, the family-based vaccination strategy stops the diffusion of a new wave or variant with a significant probability for smaller average family size and low and high vaccination levels (bottom-left and top-left charts) and for large average family size and middle level of vaccination (middle-right chart).

A conclusive note

At present, the model is very simple and can be improved in several directions. The most useful would probably be the inclusion of family-specific information. Setting up the model with additional information on each family member’s age or health state would allow overcoming the “universal mixing assumption” (Watts et al., 2020) currently in the model. Furthermore, additional vaccination strategy prioritization based on multiple criteria (such as vaccinating the families of most fragile or elderly) could be compared.

Initializing the model with census data of a local community could give a chance to analyze a more realistic setting in the wake of Pescarmona et al. (2020) and be more useful and understandable to (local) policy makers (Edmonds, 2020).

Developing the model to provide estimations for hospitalization and mortality is another needed step towards more sound vaccination strategies comparison.

Vaccinating by families could balance direct (vaccinating highest risk individuals) and indirect protection, i.e., limiting the probability the virus reaches most fragiles by vaccinating people with many contacts. It could also have positive economic effects relaunching, for example, family tourism. However, it cannot be implemented at risk of worsening the pandemic.

The present text aims only at posing a question. Further assessments following Squazzoni et al.’s (2020) recommendations are needed.

References

Barton, C.M. et al. (2020) Call for transparency of COVID-19 models. Science, 368(6490), 482-483. doi:10.1126/science.abb8637

Bubar, K.M. et al. (2021) Model-informed COVID-19 vaccine prioritization strategies by age and serostatus. Science 371, 916–921. doi:10.1126/science.abe6959

Edmonds, B. (2020) What more is needed for truly democratically accountable modelling? Review of Artificial Societies and Social Simulation, 2nd May 2020. https://rofasss.org/2020/05/02/democratically-accountable-modelling/

Jarosz, B. (2021) Poisson Distribution: A Model for Estimating Households by Household Size. Population Research and Policy Review, 40, 149–162. doi:10.1007/s11113-020-09575-x

Metlay J.P., Haas J.S., Soltoff A.E., Armstrong KA. Household Transmission of SARS-CoV-2. (2021) JAMA Netw Open, 4(2):e210304. doi:10.1001/jamanetworkopen.2021.0304

Pescarmona, G., Terna, P., Acquadro, A., Pescarmona, P., Russo, G., and Terna, S. (2020) How Can ABM Models Become Part of the Policy-Making Process in Times of Emergencies – The S.I.S.A.R. Epidemic Model. Review of Artificial Societies and Social Simulation, 20th Oct 2020. https://rofasss.org/2020/10/20/sisar/

Watts, C.J., Gilbert, N., Robertson, D., Droy, L.T., Ladley, D and Chattoe-Brown, E. (2020) The role of population scale in compartmental models of COVID-19 transmission. Review of Artificial Societies and Social Simulation, 14th August 2020. https://rofasss.org/2020/08/14/role-population-scale/

Squazzoni, F., Polhill, J. G., Edmonds, B., Ahrweiler, P., Antosz, P., Scholz, G., Chappin, É., Borit, M., Verhagen, H., Giardini, F. and Gilbert, N. (2020) Computational Models That Matter During a Global Pandemic Outbreak: A Call to Action. Journal of Artificial Societies and Social Simulation, 23(2):10. <http://jasss.soc.surrey.ac.uk/23/2/10.html>. doi: 10.18564/jasss.4298


Giulioni, G. (2020) Should the family size be used in COVID-19 vaccine prioritization strategy to prevent variants diffusion? A first investigation using a basic ABM. Review of Artificial Societies and Social Simulation, 15th April 2021. https://rofasss.org/2021/04/15/famsize/


 

The role of population scale in compartmental models of COVID-19 transmission

By Christopher J. Watts1,*, Nigel Gilbert2, Duncan Robertson3, 4, Laurence T. Droy5, Daniel Ladley6and Edmund Chattoe-Brown5

*Corresponding author, 12 Manor Farm Cottages, Waresley, Sandy, SG19 3BZ, UK, 2Centre for Research in Social Simulation (CRESS), University of Surrey, Guildford GU2 7XH, UK, 3School of Business and Economics, Loughborough University, Loughborough, UK, 4St Catherine’s College, University of Oxford, Oxford, UK, 5School of Media, Communication and Sociology, University of Leicester, UK, 6University of Leicester School of Business, University of Leicester, Leicester, LE17RH, UK

(A contribution to the: JASSS-Covid19-Thread)

Compartmental models of COVID-19 transmission have been used to inform policy, including the decision to temporarily reduce social contacts among the general population (“lockdown”). One such model is a Susceptible-Exposed-Infectious-Removed (SEIR) model developed by a team at the London School of Hygiene and Tropical Medicine (hereafter, “the LSHTM model”, Davies et al., 2020a). This was used to evaluate the impact of several proposed interventions on the numbers of cases, deaths, and intensive care unit (ICU) hospital beds required in the UK. We wish here to draw attention to behaviour common to this and other compartmental models of diffusion, namely their sensitivity to the size of the population simulated and the number of seed infections within that population. This sensitivity may compromise any policy advice given.

We therefore describe below the essential details of the LSHTM model, our experiments on its sensitivity, and why they matter to its use in policy making.

The LSHTM model

Compartmental models of disease transmission divide members of a population according to their disease states, including at a minimum people who are “susceptible” to a disease, and those who are “infectious”. Susceptible individuals make social contact with others within the same population at given rates, with no preference for the other’s disease state, spatial location, or social networks (the “universal mixing” assumption). Social contacts result in infections with a chance proportional to the fraction of the population who are currently infectious. Perhaps to reduce the implausibility of the universal mixing assumption, the LSHTM model is run for each of 186 county-level administrative units (“counties”, having an average size of 357,000 people), instead of a single run covering the whole UK population (66.4 million). Each county receives the same seed infection schedule: two new infections per day for 28 days. The 186 county time series are then summed to form a time series for the UK. There are no social contacts between counties, and the 186 county-level runs are independent of each other. Outputs from the model include total and peak cases and deaths, ICU and non-ICU hospital bed occupancy, and the time to peak cases, all reported for the UK as a whole.

Interventions are modelled as 12-week reductions in contact rates, and, in the first experiment, scheduled to commence 6 weeks prior to the peak in UK cases with no intervention. Further experiments shift the start of the intervention, and trigger the intervention upon reaching a given number of ICU beds, rather than a specific time.

Studying sensitivity to population size

The 186 counties vary in their population sizes, from Isles of Scilly (2,242 people) to West Midlands (2.9 million). We investigated whether the variation in population size led to differences in model behaviour. The LSHTM model files were cloned from https://github.com/cmmid/covid-UK , while the data analysis was performed using our own scripts posted at https://github.com/innovative-simulator/PopScaleCompartmentModels .

A graph showing Peak week infections against population size (on a log scale). The peak week looks increasing linear (with the log population scale), but there is a uniform increase in peak week with more seed infections.The figure above shows the results of running the LSHTM model with populations of various sizes, each point being an average of 10 repetitions. The time, in weeks, to the peak in cases forms a linear trend with the base-10 logarithm of population. A linear regression line fitted to these points gives Peak Week = 2.70 log10(Population) – 2.80, with R2 = 0.999.

To help understand this relationship, we then compared the seeding used by the LSHTM team, i.e. 2 infectious persons per day for 28 days, to two forms of reduced seeding, 1 per day for 28 days, and 2 per day for 14 days. Halving the seeding is similar in effect, but not identical to, doubling the population size.

Deterministic versions of other compartmental models of transmission (SIR, SEIR, SI) confirmed the relation between population size and time of occurrence to be a common feature of such models. See the R and Excel files at: https://github.com/innovative-simulator/PopScaleCompartmentModels .

For the simplest, the SI model, the stock of infectious people is described by the logistic function.I(t)=N/(1+exp(-u*C*(t-t*)))Here N is the population size, u susceptibility, and C the contact rate. If I(0)=s, the number of seed infections, then it can be shown that the peak in new infections, I(t*), occurs at timet*=ln(N/s-1)/(u*C)

Hence, for N/s >> 1, the time to peak cases, t*, correlates well with log10N/s.

As well as peak cases, analogous sensitivity was found for the timing of peaks in infections and hospital admissions, and for reaching critical levels, such as the hospital bed capacity as a proportion of the population. In contrast, the heights of peaks, and totals of cases, deaths and beds were constant percentages of population when population size was varied.

Why the unit of population matters

Davies et al. (2020a) make forecasts of both the level of peak cases and the timing of their occurrence. Despite showing that two counties can vary in their results (Davies et al., 2020a, p. 6), and mentioning in the supplementary material some effects of changing the seeding schedule (Davies et al., 2020b, p. 5), they do not mention any sensitivity to population size. But, as we have shown here, given the same number and timing of seed infections, the county with the smallest population will peak in cases earlier than the one with the largest. This sensitivity to population size affects the arguments of Davies et al. in several ways.

Firstly, Davies et al. produce their forecasts for the UK by summing county-level time series. But counties with out-of-sync peaks will sum to produce a shorter, flatter peak for the UK, than would have been achieved by synchronous county peaks. Thus the forecasts of peak cases for the UK are being systematically biased down.

Secondly, timing is important for the effectiveness of the interventions. As Davies et al. note in relation to their experiment on shifting the start time of the intervention, an intervention can be too early or too late. It is too early if, when it ends after 12 weeks, the majority of the population is still susceptible to any remaining infectious cases, and a serious epidemic can still occur. At the other extreme, an intervention can be too late if it starts when most of the epidemic has already occurred.

A timing problem also threatens if the intervention is triggered by the occupancy of ICU beds reaching some critical level. This level will be reached for the UK or average county later than for a small county. Thus the problem extends beyond the timing of peaks to affect other aspects of a policy supported by the model.

Our results imply that an intervention timed optimally for a UK-level, or average county-level, cases peak, as well as an intervention triggered by a UK-level beds occupancy threshold, may be less effective for counties with far-from-average sizes.

There are multiple ways of resolving these issues, including re-scaling seed infections in line with size of population unit, simulating the UK directly rather than as a sum of counties, and rejecting compartmental models in favour of network- or agent-based models. A discussion of the respective pros and cons of these alternatives requires a longer paper. For now, we note that compartmental models remain quick and cheap to design, fit, and study. The issues with Davies et al. (2020a) we have drawn attention to here highlight (1) the importance of adequate sensitivity testing, (2) the need for care when choosing at which scale to model and how to seed an infection, and (3) the problems that can stem from uniform national policy interventions, rather than ones targeted at a more local level.

References

Davies, N. G., Kucharski, A. J., Eggo, R. M., Gimma, A., Edmunds, W. J., Jombart, T., . . . Liu, Y. (2020a). Effects of non-pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in the UK: a modelling study. The Lancet Public Health, 5(7), e375-e385. doi:10.1016/S2468-2667(20)30133-X

Davies, N. G., Kucharski, A. J., Eggo, R. M., Gimma, A., Edmunds, W. J., Jombart, T., . . . Liu, Y. (2020b). Supplement to Davies et al. (2020b). https://www.thelancet.com/cms/10.1016/S2468-2667(20)30133-X/attachment/cee85e76-cffb-42e5-97b6-06a7e1e2379a/mmc1.pdf


Watts, C.J., Gilbert, N., Robertson, D., Droy, L.T., Ladley, D and Chattoe-Brown, E. (2020) The role of population scale in compartmental models of COVID-19 transmission. Review of Artificial Societies and Social Simulation, 14th August 2020. https://rofasss.org/2020/08/14/role-population-scale/


 

A Bibliography of ABM Research Explicitly Comparing Real and Simulated Data for Validation

By Edmund Chattoe-Brown

The Motivation

Research that confronts models with data is still sufficiently rare that it is hard to get a representative sense of how it is done and how convincing the results are simply by “background reading”. One way to advance good quality empirical modelling is therefore simply to make it more visible in quantity. With this in mind I have constructed (building on the work of Angus and Hassani-Mahmooei 2015) the first version of a bibliography listing all ABM attempting empirical validation in JASSS between 1998 and 2019 (along with a few other example) – which generates 68 items in all. Each entry gives a full reference and also describes what comparisons are made and where in the article they occur. In addition the document contains a provisional bibliography of articles giving advice or technical support to validation and lists three survey articles that categorise large samples of simulations by their relationships to data (which served as actual or potential sources for the bibliography).

With thanks to Bruce Edmonds, this first version of the bibliography has been made available as a Centre for Policy Modelling Discussion Paper CPM-20-216, which can be downloaded http://cfpm.org/discussionpapers/256.

The Argument

It may seem quite surprising to focus only on validation initially but there is an argument (Chattoe-Brown 2019) which says that this is a more fundamental challenge to the quality of a model than calibration. A model that cannot track real data well, even when its parameters are tuned to do so is clearly a fundamentally inadequate model. Only once some measure of validation has been achieved can we decide how “convincing” it is (comparing independent empirical calibration with parameter tuning for example). Arguably, without validation, we cannot really be sure whether a model tells us anything about the real world at all (no matter how plausible any narrative about its assumptions may appear). This can be seen as a consequence of the arguments about complexity routinely made by ABM practitioners as the plausibility of the assumptions does not map intuitively onto the plausibility of the outputs.

The Uses

Although these are covered in the preface to the bibliography in greater detail, such a sample has a number of scientific uses which I hope will form the basis for further research.

  • To identify (and justify) good and bad practice, thus promoting good practice.
  • To identify (and then perhaps fill) gaps in the set of technical tools needed to support validation (for example involving particular sorts of data).
  • To test the feasibility and value of general advice offered on validation to date and refine it in the face of practical challenges faced by analysis of real cases.
  • To allow new models to demonstrably outperform the levels of validation achieved by existing models (thus creating the possibility for progressive empirical research in ABM).
  • To support agreement about the effective use of the term validation and to distinguish it from related concepts (like verification) and potentially unhelpful (for example ambiguous or rhetorically loaded) uses

The Plan

Because of the labour involved and the diversity of fields in which ABM have now been used over several decades, an effective bibliography on this kind cannot be the work of a single author (or even a team of authors). My plan is thus to solicit (fully credited) contributions and regularly release new versions of the bibliography – with new co-authors as appropriate. (This publishing model is intended to maintain the quality and suitability for citation of the resulting document relative to the anarchy that sometimes arises in genuine communal authorship!) All of the following contributions will be gratefully accepted for the next revision (on which I am already working myself in any event)

  • References to new surveys or literature reviews that categorise significant samples of ABM research by their relationship to data.
  • References for proposed new entries to the bibliography in as much detail as possible.
  • Proposals to delete incorrectly categorised entries. (There are a small number of cases where I have found it very difficult to establish exactly what the authors did in the name of validation, partly as a result of confusing or ambiguous terminology.)
  • Proposed revisions to incorrect or “unfair” descriptions of existing entries (ideally by the authors of those pieces).
  • Offers of collaboration for a proposed companion bibliography on calibration. Ultimately this will lead to a (likely very small) sample of calibrated and validated ABM (which are often surprisingly little cited given their importance to the credibility of the ABM “project” – see, for example, Chattoe-Brown (2018a, 2018b).

References

Angus, Simon D. and Hassani-Mahmooei, Behrooz (2015) ‘“Anarchy” Reigns: A Quantitative Analysis of Agent-Based Modelling Publication Practices in JASSS, 2001-2012’, Journal of Artificial Societies and Social Simulation, 18(4), October, article 16. <http://jasss.soc.surrey.ac.uk/18/4/16.html> doi:10.18564/jasss.2952

Chattoe-Brown, Edmund (2018a) ‘Query: What is the Earliest Example of a Social Science Simulation (that is Nonetheless Arguably an ABM) and Shows Real and Simulated Data in the Same Figure or Table?’ Review of Artificial Societies and Social Simulation, 11 June. https://rofasss.org/2018/06/11/ecb/

Chattoe-Brown, Edmund (2018b) ‘A Forgotten Contribution: Jean-Paul Grémy’s Empirically Informed Simulation of Emerging Attitude/Career Choice Congruence (1974)’, Review of Artificial Societies and Social Simulation, 1 June. https://rofasss.org/2018/06/01/ecb/

Chattoe-Brown, Edmund (2019) ‘Agent Based Models’, in Atkinson, Paul, Delamont, Sara, Cernat, Alexandru, Sakshaug, Joseph W. and Williams, Richard A. (eds.) SAGE Research Methods Foundations. doi:10.4135/9781526421036836969


Chattoe-Brown, E. (2020) A Bibliography of ABM Research Explicitly Comparing Real and Simulated Data for Validation. Review of Artificial Societies and Social Simulation, 12th June 2020. https://rofasss.org/2020/06/12/abm-validation-bib/


 

The Policy Context of Covid19 Agent-Based Modelling

By Edmund Chattoe-Brown

(A contribution to the: JASSS-Covid19-Thread)

In the recent discussions about the role of ABM and COVID, there seems to be an emphasis on the purely technical dimensions of modelling. This obviously involves us “playing to our strengths” but unfortunately it may reduce the effectiveness that our potential policy contributions can make. Here are three contextual aspects of policy for consideration to provide a contrast/corrective.

What is “Good” Policy?

Obviously from a modelling perspective good policy involves achieving stated goals. So a model that suggests a lower death rate (or less taxing of critical care facilities) under one intervention rather than another is a potential argument for that intervention. (Though of course how forceful the argument is depends on the quality of the model.) But the problem is that policy is predominantly a political and not a technical process (related arguments are made by Edmonds 2020). The actual goals by which a policy is evaluated may not be limited to the obvious technical ones (even if that is what we hear most about in the public sphere) and, most problematically, there may be goals which policy makers are unwilling to disclose. Since we do not know what these goals are, we cannot tell whether their ends are legitimate (having to negotiate privately with the powerful to achieve anything) or less so (getting re-elected as an end in itself).

Of course, by its nature (being based on both power and secrecy), this problem may be unfixable but even awareness of it may change our modelling perspective in useful ways. Firstly, when academic advice is accused of irrelevance, the academics can only ever be partly to blame. You can only design good policy to the extent that the policy maker is willing to tell you the full evaluation function (to the extent that they know it of course). Obviously, if policy is being measured by things you can’t know about, your advice is at risk of being of limited value. Secondly, with this is mind, we may be able to gain some insight into the hidden agenda of policy by looking at what kind of suggestions tend to be accepted and rejected. Thirdly, once we recognise that there may be “unknown unknowns” we can start to conjecture intelligently about what these could be and take some account of them in our modelling strategies. For example, how many epidemic models consider the financial costs of interventions even approximately? Is the idea that we can and will afford whatever it takes to reduce deaths a blind spot of the “medical model?”

When and How to Intervene

There used to be an (actually rather odd) saying: “You can’t get a baby in a month by making nine women pregnant”. There has been a huge upsurge in interest regarding modelling and its relationship to policy since start of the COVID crisis (of which this theme is just one example) but realising the value of this interest currently faces significant practical problems. Data collection is even harder than usual (as is scholarship in general), there is a limit to how fast good research can ever be done, peer review takes time and so on. The question here is whether any amount of rushing around at the present moment will compensate for neglected activities when scholarship was easier and had more time (an argument also supported by Bithell 2018). The classic example is the muttering in the ABM community about the Ferguson model being many thousands of lines of undocumented C code. Now we are in a crisis, even making the model available was a big ask, let alone making it easier to read so that people might “heckle” it. But what stopped it being available, documented, externally validated and so on before COVID? What do we need to do so that next time there is a pandemic crisis, which there surely will be, “we” (the modelling community very broadly defined) are able to offer the government a “ready” model that has the best features of various modelling techniques, evidence of unfudgeable quality against data, relevant policy scenarios and so on? (Specifically, how will ABM make sure it deserves to play a fit part in this effort?) Apart from the models themselves, what infrastructures, modelling practices, publishing requirements and so on do we need to set up and get working well while we have the time? In practice, given the challenges of making effective contributions right now (and the proliferation of research that has been made available without time for peer review may be actively harmful), this perspective may be the most important thing we can realistically carry into the “post lockdown” world.

What Happens Afterwards?

ABM has taken such a long time to “get to” policy based on data that looking further than the giving of such advice simply seems to have been beyond us. But since policy is what actually happens, we have a serious problem with counterfactuals. If the government decides to “flatten the curve” rather than seek “herd immunity” then we know how the policy implemented relates to the model “findings” (for good or ill) but not how the policy that was not implemented does. Perhaps the outturn of the policy that looked worse in the model would actually have been better had it been implemented?

Unfortunately (this is not a typo), we are about to have an unprecedently large social data set of comparative experiments in the nature and timing of epidemiological interventions, but ABM needs to be ready and willing to engage with this data. I think that ABM probably has a unique contribution to make in “endogenising” the effects of policy implementation and compliance (rather than seeing these, from a “model fitting” perspective, as structural changes to parameter values) but to make this work, we need to show much more interest in data than we have to date.

In 1971, Dutton and Starbuck, in a worryingly neglected article (cited only once in JASSS since 1998 and even then not in respect of model empirics) reported that 81% of the models they surveyed up to 1969 could not achieve even qualitative measurement in both calibration and validation (with only 4% achieving quantitative measurement in both). As a very rough comparison (but still the best available), Angus and Hassani-Mahmooei (2015) showed that just 13% of articles in JASSS published between 2010 and 2012 displayed “results elements” both from the simulation and using empirical material (but the reader cannot tell whether these are qualitative or quantitative elements or whether their joint presence involves comparison as ABM methodology would indicate). It would be hard to make the case that the situation in respect to ABM and data has therefore improved significantly in 4 decades and it is at least possible that it has got worse!

For the purposes of policy making (in the light of the comments above), what matters of course is not whether the ABM community believes that models without data continue to make a useful contribution but whether policy makers do.

References

Angus, S. D. and Hassani-Mahmooei, B. (2015) “Anarchy” Reigns: A Quantitative Analysis of Agent-Based Modelling Publication Practices in JASSS, 2001-2012, Journal of Artificial Societies and Social Simulation, 18(4), 16. doi:10.18564/jasss.2952

Bithell, M. (2018) Continuous model development: a plea for persistent virtual worlds, Review of Artificial Societies and Social Simulation, 22nd August 2018. https://rofasss.org/2018/08/22/mb

Dutton, John M. and Starbuck, William H. (1971) Computer Simulation Models of Human Behavior: A History of an Intellectual Technology. IEEE Transactions on Systems, Man, and Cybernetics, SMC-1(2), 128–171. doi:10.1109/tsmc.1971.4308269

Edmonds, B. (2020) What more is needed for truly democratically accountable modelling? Review of Artificial Societies and Social Simulation, 2nd May 2020. https://rofasss.org/2020/05/02/democratically-accountable-modelling/


Chattoe-Brown, E. (2020) The Policy Context of Covid19 Agent-Based Modelling. Review of Artificial Societies and Social Simulation, 4th May 2020. https://rofasss.org/2020/05/04/policy-context/


 

What more is needed for Democratically Accountable Modelling?

By Bruce Edmonds

(A contribution to the: JASSS-Covid19-Thread)

In the context of the Covid19 outbreak, the (Squazzoni et al 2020) paper argued for the importance of making complex simulation models open (a call reiterated in Barton et al 2020) and that relevant data needs to be made available to modellers. These are important steps but, I argue, more is needed.

The Central Dilemma

The crux of the dilemma is as follows. Complex and urgent situations (such as the Covid19 pandemic) are beyond the human mind to encompass – there are just too many possible interactions and complexities. For this reason one needs complex models, to leverage some understanding of the situation as a guide for what to do. We can not directly understand the situation, but we can understand some of what a complex model tells us about the situation. The difficulty is that such models are, themselves, complex and difficult to understand. It is easy to deceive oneself using such a model. Professional modellers only just manage to get some understanding of such models (and then, usually, only with help and critique from many other modellers and having worked on it for some time: Edmonds 2020) – politicians and the public have no chance of doing so. Given this situation, any decision-makers or policy actors are in an invidious position – whether to trust what the expert modellers say if it contradicts their own judgement. They will be criticised either way if, in hindsight, that decision appears to have been wrong. Even if the advice supports their judgement there is the danger of giving false confidence.

What options does such a policy maker have? In authoritarian or secretive states there is no problem (for the policy makers) – they can listen to who they like (hiring or firing advisers until they get advice they are satisfied with), and then either claim credit if it turned out to be right or blame the advisers if it was not. However, such decisions are very often not value-free technocratic decisions, but ones that involve complex trade-offs that affect people’s lives. In these cases the democratic process is important for getting good (or at least accountable) decisions. However, democratic debate and scientific rigour often do not mix well [note 1].

A Cautionary Tale

As discussed in (Adoha & Edmonds 2019) Scientific modelling can make things worse, as in the case of the North Atlantic Cod Fisheries Collapse. In this case, the modellers became enmeshed within the standards and wishes of those managing the situation and ended up confirming their wishful thinking. An effect of technocratising the decision-making about how much it is safe to catch had the effect of narrowing down the debate to particular measurement and modelling processes (which turned out to be gravely mistaken). In doing so the modellers contributed to the collapse of the industry, with severe social and ecological consequences.

What to do?

How to best interface between scientific and policy processes is not clear, however some directions are becoming apparent.

  • That the process of developing and giving advice to policy actors should become more transparent, including who is giving advice and on what basis. In particular, any reservations or caveats that the experts add should be open to scrutiny so the line between advice (by the experts) and decision-making (by the politicians) is clearer.
  • That such experts are careful not to over-state or hype their own results. For example, implying that their model can predict (or forecast) the future of complex situations and so anticipate the effects of policy before implementation (de Matos Fernandes and Keijzer 2020). Often a reliable assessment of results only occurs after a period of academic scrutiny and debate.
  • Policy actors need to learn a little bit about modelling, in particular when and how modelling can be reliably used. This is discussed in (Government Office for Science 2018, Calder et al. 2018) which also includes a very useful checklist for policy actors who deal with modellers.
  • That the public learn some maturity about the uncertainties in scientific debate and conclusions. Preliminary results and critiques tend to be jumped on too early to support one side within polarised debate or models rejected simply on the grounds they are not 100% certain. We need to collectively develop ways of facing and living with uncertainty.
  • That the decision-making process is kept as open to input as possible. That the modelling (and its limitations) should not be used as an excuse to limit what the voices that are heard, or the debate to a purely technical one, excluding values (Aodha & Edmonds 2017).
  • That public funding bodies and journals should insist on researchers making their full code and documentation available to others for scrutiny, checking and further development (readers can help by signing the Open Modelling Foundation’s open letter and the campaign for Democratically Accountable Modelling’s manifesto).

Some Relevant Resources

  • CoMSeS.net — a collection of resources for computational model-based science, including a platform for publicly sharing simulation model code and documentation and forums for discussion of relevant issues (including one for covid19 models)
  • The Open Modelling Foundation — an international open science community that works to enable the next generation modelling of human and natural systems, including its standards and methodology.
  • The European Social Simulation Association — which is planning to launch some initiatives to encourage better modelling standards and facilitate access to data.
  • The Campaign for Democratic Modelling — which campaigns concerning the issues described in this article.

Notes

note1: As an example of this see accounts of the relationship between the UK scientific advisory committees and the Government in the Financial Times and BuzzFeed.

References

Barton et al. (2020) Call for transparency of COVID-19 models. Science, Vol. 368(6490), 482-483. doi:10.1126/science.abb8637

Aodha, L.Edmonds, B. (2017) Some pitfalls to beware when applying models to issues of policy relevance. In Edmonds, B. & Meyer, R. (eds.) Simulating Social Complexity – a handbook, 2nd edition. Springer, 801-822. (see also http://cfpm.org/discussionpapers/236)

Calder, M., Craig, C., Culley, D., de Cani, R., Donnelly, C.A., Douglas, R., Edmonds, B., Gascoigne, J., Gilbert, N. Hargrove, C., Hinds, D., Lane, D.C., Mitchell, D., Pavey, G., Robertson, D., Rosewell, B., Sherwin, S., Walport, M. & Wilson, A. (2018) Computational modelling for decision-making: where, why, what, who and how. Royal Society Open Science,

Edmonds, B. (2020) Good Modelling Takes a Lot of Time and Many Eyes. Review of Artificial Societies and Social Simulation, 13th April 2020. https://rofasss.org/2020/04/13/a-lot-of-time-and-many-eyes/

de Matos Fernandes, C. A. and Keijzer, M. A. (2020) No one can predict the future: More than a semantic dispute. Review of Artificial Societies and Social Simulation, 15th April 2020. https://rofasss.org/2020/04/15/no-one-can-predict-the-future/

Government Office for Science (2018) Computational Modelling: Technological Futures. https://www.gov.uk/government/publications/computational-modelling-blackett-review

Squazzoni, F., Polhill, J. G., Edmonds, B., Ahrweiler, P., Antosz, P., Scholz, G., Chappin, É., Borit, M., Verhagen, H., Giardini, F. and Gilbert, N. (2020) Computational Models That Matter During a Global Pandemic Outbreak: A Call to Action. Journal of Artificial Societies and Social Simulation, 23(2):10. <http://jasss.soc.surrey.ac.uk/23/2/10.html>. doi: 10.18564/jasss.4298


Edmonds, B. (2020) What more is needed for truly democratically accountable modelling? Review of Artificial Societies and Social Simulation, 2nd May 2020. https://rofasss.org/2020/05/02/democratically-accountable-modelling/


 

Understanding the current COVID-19 epidemic: one question, one model

By the CoVprehension Collective

(A contribution to the: JASSS-Covid19-Thread)

On the evening of 16th March 2020, the French president, Emmanuel Macron announced the start of a national lockdown, for a period of 15 days. It would be effective from noon the next day (17th March). On the 18th March 2020 at 01:11 pm, the first email circulated in the MicMac team, who had been working on the micro-macro modelling of the spread of a disease in a transportation network a few years. This email was the start of CoVprehension. After about a week of intense emulation, the website was launched, with three questions answered. A month later, there were about fifteen questions on the website, and the group was composed of nearly thirty members from French research institutions, in a varied pool of disciplines, all contributing as volunteers from their confined residence.

CoVprehension in principles

This rapid dynamic originates from a very singular context. It is tricky to analyse it given that the COVID-19 crisis is still developing. However, we can highlight a few fundamental principles leading the project.

The first principle is undeniably a principle of action. To become an actor of the situation first, but this invitation extends to readers of the website, allowing them to run the simulation and to change its parameters; but also more broadly by giving them suggestions on how to link their actions to this global phenomenon which is hard to comprehend. This empowerment also touches upon principles of social justice and, longer term, democracy in the face of this health crisis. By accompanying the process of social awareness, we aim to guide the audience towards a free and informed consent (cf. code of public health) in order to confront the disease. Our first principle is spelled out on theCoVprehension website in the form of a list of objectives that the CoVprehension collective set themselves:

  • Comprehension (the propagation of the virus, the actions put in place)
  • Objectification (giving a more concrete shape to this event which is bigger than us and can be overwhelming)
  • Visualisation (showing the mechanisms at play)
  • Identification (the essential principles and actions to put in place)
  • Do something (overcoming fears and anxieties to become actors in the epidemic)

The second founding principle is that of an interdisciplinary scientific collective formed on a voluntary basis. CoVprehension is self-organised and rests on three pillars: volunteering, collaborative work and the will to be useful during the crisis by offering a space for information, reflection and interaction with a large audience.

As a third principle, we have agility and reactivity. The main idea of the project is to answer questions that people ask, with short posts based on a model or data analysis. This can only be done if the delay between question and answer remains short, which is a real challenge given the complexity of the subject, the high frequency of scientific literature being produced since the beginning of the crisis, and the large number of unknowns and uncertainties which characterise it.

The fourth principle, finally, is the autonomy of groups which form to answer the questions. This allows a multiplicity of perspectives and points of view, sometimes divergent. This necessity draws on the acknowledgement by the European simulation community that a lack of pluralism is even more harmful to support public decision-making than a lack of transparency.

A collaborative organisation and an interactive website

The four principles have lead us, quite naturally, to favour a functioning organisation which exploits short and frequent retroactions and relies of adapted tools. The questions asked online through a Framasoft form are transferred to all CoVprehension members, while a moderator is in charge of replying to them quickly and personally. Each question is integrated into a Trello management board, which allows each member of the collective to pick the questions they want to contribute to and to follow their progression until publication. The collaboration and debate on each of the questions is done using VoIP application Discord. Model prototypes are mostly developed on the Netlogo platform (with some javascript exceptions). Finally, the whole project and website is hosted on GitHub.

The website itself (https://covprehension.org/en) is freely accessible online. Besides the posts answering questions, it contains a simulator to rerun and reproduce the simulations showcased in the posts, a page with scientific resources on the COVID-19 epidemic, a page presenting the project members and a link to the form allowing anyone to ask the collective a question.

On the 28th April 2020, the collective counted 29 members (including 10 women): medical doctors, researchers, engineers and specialists in the fields of computer science, geography, epidemiology, mathematics, economy, data analysis, medicine, architecture and digital media production. The professional statuses of the team members vary (from PhD student to full professor, from intern to engineer, from lecturer to freelancer) whereas their skills complement each other (although a majority of them are complex system modellers). The collective effort enables CoVprehension to scale up on information collection, sharing and updating. This is also fueled by debates during the first take on questions by small teams. Such scaling up would otherwise only be possible in large epidemiology laboratories with massive funding. To increase visibility, the content of the website, initially all in French, is being translated into English progressively as new questions are published.

Simple simulation models

When a question requires a model, especially so for the first questions, our choice has been to build simple models (cf. Question 0). Indeed, the objective of CoVprehension models is not to predict. It is rather to describe, to explain and to illustrate some aspects of the COVID-19 epidemic and its consequences on population. KISS models (“Keep It Simple, Stupid!” cf. Edmonds  & Moss 2004) for the opposition between simple and “descriptive” models) seem better suited to our project. They can unveil broad tendencies and help develop intuitions about potential strategies to deal with the crisis, which can then be also shared with a broad audience.

By choosing a KISS posture, we implicitly reject KIDS postures in such crisis circumstances. Indeed, if the conditions and processes modelled were better informed and known, we could simulate a precise dynamic and generate a series of predictions and forecasts. This is what N. Ferguson’s team did for instance, with a model initially developed with regards to the H5N1 flu in Asia (Ferguson et al., 2005). This model was used heavily to inform public decision-making in the first days of the epidemic in the United Kingdom. Building and calibrating such models takes an awfully long time (Ferguson’s project dates back from 2005) and requires teams and recurring funding which is almost impossible to get nowadays for most teams. At the moment, we think that uncertainty is too big, and that the crisis and the questions that people have do not always necessitate the modelling of complex processes. A large area of the space of social questions mobilised can be answered without describing the mechanisms in so much detail. It is possible that this situation will change as we get information from other scientific disciplines. For now, demonstrating that even simple models are very sensitive to many elements which remain uncertain shows that the scientific discourse could gain by remaining humble: the website reveals how little we know about the future consequences of the epidemic and the political decisions made to tackle it.

Feedback on the questions received and answered

At the end of April, twenty-seven questions have been asked to the CoVprehension collective, through the online form. Seven of them are not really questions (they are rather remarks and comments from people supporting the initiative). Some questions happen to have been asked by colleagues and relatives. The intended outreach has not been fully realised since the website seems to reach people who are already capable of looking for information on the internet. This was to be expected given the circumstances. Everyone who has done some scientific outreach knows how hard it is to reach populations who have not been been made aware of or are interested in scientific facts in the first place. Some successful initiatives (like “les petits débrouillards” or “la main à la pâte” in France) spread scientific knowledge related to recent publications in collaboration with researchers, but they are much better equipped for that (since they do not rely mostly on institutional portals like we do). This large selection bias in our audience (almost impossible to solve, unless we create some specific buzz… which we will then have to handle in terms of new question influx, which is not possible at the moment given the size of the collective and its organisation) means that our website has been protected from trolling. However, we can expect that it might be used within educational programs for example, where STEM teachers could make the students use the various simulators in a question and answer type of game.

Figure 1 shows that the majority of questions are taken by small interdisciplinary teams of two or three members. The most frequent collaborations are between geographers and computer scientists. They are often joined by epidemiologists and mathematicians, and recently by economists. Most topics require the team to build and analyse a simulation model in order to answer the question. The timing of team formations reflects the arrival of new team members in the early days of the project, leading to a large number of questions to be tackled simultaneously. Since April, the rhythm has slowed, reflecting also the increasing complexity of questions, models and answers, but also the marginal “cost” of this investment on the other projects and responsibilities of the researchers involved.

Visualisation of the questions tackled by Covprehension.

Figure 1. Visualisation of the questions tackled by Covprehension.

Initially, the website prioritised questions on simulation and aggregation effects specifically connected with the distribution models of diffusion. For instance, the first questions aimed essentially at showing the most tautological results: with simple interaction rules, we illustrated logically expected effects. These results are nevertheless interesting because while they are trivial to simulation practitioners, they also serve to convince profane readers that they are able to follow the logic:

  • Reducing the density of interactions reduces the spread of the virus and therefore: maybe the lockdown can alter the infection curve (cf. Question 2 and Question 3).
  • By simply adding a variable for the number of hospital beds, we can visualise the impact of lockdown on hospital congestion (cf. Question 7).

For more elaborate questions to be tackled (and to rationalise the debates):

  • Some alternative policies have been highlighted (the Swedish case: Question 13; the deconfinement: Question 9);
  • Some indicators with contradicting impacts have been discussed, which shows the complexity of political decisions and leads readers to question the relevance of some of these indicators (cf. Question 6);
  • The hypotheses (behavioural ones in particular) have been largely discussed, which highlights the way in which the model deviates from what it represents in a simplified way (cf. Question 15).

More than half of the questions asked could not be answered through modelling. In the first phase of the project, we personnally replied to these questions and directed the person towards robust scientific websites or articles where their question could be better answered. The current evolution of the project is more fundamental: new researchers from complementary disciplines have shown some interest in the work done so far and are now integrated into the team (including two medical doctors operating in COVID-19 centres for instance). This will broaden the scope of questions tackled by the team from now on.

Our work fits into a type of education to critical thinking about formal models, one that has long been known as necessary to a technical democracy (Stengers, 2017). At this point, the website can be considered both as a result by itself and as a pilot to function as a model for further initiatives.

Conclusion

Feedback on the CoVprehension project has mostly been positive, but not exempt from limits and weaknesses. Firstly, the necessity of a prompt response has been detrimental to our capacity to fully explore different models, to evaluate their robustness and look for unexpected results. Model validation is unglamorous, slow and hard to communicate. It is crucial nevertheless when assessing the credibility to be associated with models and results. We are now trying to explore our models in parallel. Secondly, the website may suggest a homogeneity of perspectives and a lack of debates regarding how questions are to be answered. These debates do take place during the assessment of questions but so far remain hidden from the readers. It shows indirectly in the way some themes appear in different answers treated from different angles by different teams (for example: the lockdown, treated in question 6, 7, 9 and 14). We consider the possibility of publishing alternative answers to a given question in order to show this possible divergence. Finally, the project is facing a significant challenge: that of continuing its existence in parallel with its members’ activities, with the number of members increasing. The efforts in management, research, editing, publishing and translation have to be maintained while the transaction costs are going up as the size and diversity of the collective increases, as the debates become more and more specific and happen on different platforms… and while new questions keep arriving!

References

Edmonds, B., & Moss, S. (2004). From KISS to KIDS–an ‘anti-simplistic’ modelling approach. In International workshop on multi-agent systems and agent-based simulation (pp. 130-144). Springer, Berlin, Heidelberg. doi:10.1007/978-3-540-32243-6_11

Ferguson, N. M., Cummings, D. A., Cauchemez, S., Fraser, C., Riley, S., Meeyai, A. & Burke, D. S. (2005). Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature, 437(7056), 209-214. doi:10.1038/nature04017

Stengers I. (2017). Civiliser la modernité ? Whitehead et les ruminations du sens commun, Dijon, Les presses du réel. https://www.lespressesdureel.com/EN/ouvrage.php?id=3497


the CoVprehension Collective (2020) Understanding the current COVID-19 epidemic: one question, one model. Review of Artificial Societies and Social Simulation, 30th April 2020. https://rofasss.org/2020/04/30/covprehension/


 

What can and cannot be feasibly modelled of the Covid-19 Pandemic

By Nick Gotts

(A contribution to the: JASSS-Covid19-Thread)

The place of modelling in informing policy has been highlighted by the Covid-19 pandemic. In the UK, a specific individual-based epidemiological model, that developed by Neil Ferguson of Imperial College London, has been credited with the government’s U-turn from pursuing a policy of building up “herd immunity” by allowing the Sars-CoV-2 virus to spread through the population in order to avoid a possible “second wave” next winter (while trying to limit the speed of spread so as to avoid overwhelming medical facilities, and to shield the most vulnerable), to a “lockdown” imposed in order to minimise the number of people infected. Ferguson’s model reportedly indicated several hundred thousand deaths if the original policy was followed, and this was judged unacceptable.

I do not doubt that the reversal of policy was correct – indeed, that the original policy should never have been considered – one prominent epidemiologist said he thought the report of it was “satire” when he first heard it (Hanage 2020). As Hanage says: “Vulnerable people should not be exposed to Covid-19 right now in the service of a hypothetical future”. But it has also been reported (Reynolds 2020) that Ferguson’s model is a rapid modification of one he built to study possible policy responses to a hypothetical influenza pandemic (Ferguson et al. 2006); and that (Ferguson himself says) this model consists of “thousands of lines of undocumented C”. That major policy decisions should be made on such a basis is both wrong in itself, and threatens to bring scientific modelling into disrepute – indeed, I have already seen the justified questioning of the UK government’s reliance on modelling used by climate change denialists in their ceaseless quest to attack climate science.

What can social simulation contribute in the Covid-19 crisis? I suggest that attempts to model the pandemic as a whole, or even in individual countries, are fundamentally misplaced at this stage: too little is known about the behaviour of the virus, and governments need to take decisions on a timescale that simply does not allow for responsible modelling practice. Where social simulation might be of immediate use is in relation to the local application of policies already decided on. To give one example, supermarkets in the UK (and I assume, elsewhere) are now limiting the number of shoppers in their stores at any one time, in an effort to apply the guidelines on maintaining physical distance between individuals from different households. But how many people should be permitted in a given store? Experience from traffic models suggests there may well be a critical point at which it rather suddenly becomes impossible to maintain distance as the number of shoppers increases – but where does it lie for a particular store? Could the goods on sale be rearranged in ways that allow larger numbers – for example, by distributing items in high demand across two or more aisles? Supermarkets collect a lot of information about what is bought, and which items tend to be bought together – could they shorten individual shoppers’ time in the store by improving their signage? (Under normal circumstances, of course, they are likely to want to retain shoppers as long as possible, and send them down as many aisles as possible, to encourage impulse buys.)

Agents in such a model could be assigned a list of desired purchases, speed of movement and of collecting items from shelves, and constraints on how close they come to other shoppers – probably with some individual variation. I would be interested to learn if any modelling teams have approached supermarket chains (or vice versa) with a proposal for such a model, which should be readily adaptable to different stores. Other possibilities include models of how police should be distributed over an area to best ensure they will see (and be seen by) individuals or groups disregarding constraints on gathering in groups, and of the “contagiousness” of such behaviour – which, unlike actual Covid-19 infection events, is readily observable. Social simulators, in summary, should look for things they can reasonably hope to do quickly and in conjunction with organisations that have or can readily collect the required data, not try to do what is way beyond what is possible in the time available.

References

Ferguson, N. M., Cummings, D. A., Fraser, C., Cajka, J. C., Cooley, P. C., & Burke, D. S. (2006). Strategies for mitigating an influenza pandemic. Nature, 442(7101), 448-452. doi:10.1038/nature04795

Hanage, W. (2020) I’m an epidemiologist. When I heard about Britain’s ‘herd immunity’ coronavirus plan, I thought it was satire. The Guardian, 2020-03-15. https://www.theguardian.com/commentisfree/2020/mar/15/epidemiologist-britain-herd-immunity-coronavirus-covid-19

Reynolds, C. (2020) Big Tech Fights Back: From Pandemic Simulation Code, to Immune Response. Computer Business Review 2020-03-15. https://www.cbronline.com/news/pandemic-simulation-code.


Gotts, N. (2020) What can and cannot be feasibly modelled of the Covid-19 Pandemic. Review of Artificial Societies and Social Simulation, 29th April 2020. https://rofasss.org/2020/04/29/feasibility/


 

The Danger of too much Compassion – how modellers can easily deceive themselves

By Andreas Tolk

(A contribution to the: JASSS-Covid19-Thread)

In 2017, Shermer observed that in cases where moral and epistemological considerations are deeply intertwined, it is human nature to cherry-pick the results and data that support the current world view (Shermer 2017). In other words, we tend to look for data justifying our moral conviction. The same is an inherent challenge for simulations as well: we tend to favour our underlying assumptions and biases – often even unconsciously – when we implement our simulation systems. If now others use this simulation system in support of predictive analysis, we are in danger of philosophical regress: a series of statements in which a logical procedure is continually reapplied to its own result without approaching a useful conclusion. As stated in an earlier paper of mine (Tolk 2017):

The danger of the simulationist’s regress is that such predictions are made by the theory, and then the implementation of the theory in form of the simulation system is used to conduct a simulation experiment that is then used as supporting evidence. This, however, is exactly the regress we wanted to avoid: we test a hypothesis by implementing it as a simulation, and then use the simulated data in lieu of empirical data as supporting evidence justifying the propositions: we create a series of statements – the theory, the simulation, and the resulting simulated data – in which a logical procedure is continually reapplied to its own result….

In particular in cases where moral and epistemological considerations are deeply intertwined, it is human nature to cherry-pick the results and data that support the current world view (Shermer 2017). Simulationists are not immune to this, and as they can implement their beliefs into a complex simulation system that now can be used by others to gain quasi-empirical numerical insight into the behavior of the described complex system, their implemented world view can easily be confused with a surrogate for real world experiments.

I am afraid that we may have fallen into such a fallacy in some of our efforts to use simulation to better understand the Covid-19 crisis and what we can do. This is for sure a moral problem, as at the end of our recommendations this is about human lives! And we assumed that the recommendations of the medical community for social distancing and other non pharmaceutical interventions (NPI) is the best we can do, as it saves many lives. So we built our models to clearly demonstrate the benefits of social distancing and other NPIs, which leads to danger of regress: we assume that NPIs are the best action, so we write a simulation to show that NPIs are the best action, and then we use these simulations to prove that NPIs are the best action. But can we actually use empirical data to support these assumptions? Looking closely at the data, the correlation of success – measured as flattening the curves – and the amount and strictness of the NPIs is not always observable. So we may have missed something, as our model-based predictions are not supported as we hope for, which is a problem: do we just collect the wrong data and should use something else to validate the models, or are the models insufficient to explain the data? And how do we ensure that our passion doesn’t interfere with our scientific objectivity?

One way to address this issue is diversity of opinion implemented as a set of orchestrated models, to use a multitude of models instead of just one. In another comment, the idea of using exploratory analysis to support decision making under deep uncertainty is mentioned. I highly recommend to have a look at (Marchau, Bloemen & Popper 2019) Decision Making Under Deep Uncertainty: From Theory to Practice. I am optimistic that if we are inclusive of a diversity of ideas – even if we don’t like them – and allow for computational evaluation of ALL options using exploratory analysis, we may find a way for better supporting the community.

References

Marchau, V. A., Walker, W. E., Bloemen, P. J., & Popper, S. W. (2019). Decision making under deep uncertainty. Springer. doi:10.1007/978-3-030-05252-2

Tolk, A. (2017, April). Bias ex silico: observations on simulationist’s regress. In Proceedings of the 50th Annual Simulation Symposium. Society for Computer Simulation International. ANSS ’17: Proceedings of the 50th Annual Simulation Symposium, April 2017 Article No.: 15 Pages 1–9. https://dl.acm.org/citation.cfm?id=3106403

Shermer, M. (2017) How to Convince Someone When Facts Fail – Why worldview threats undermine evidence. Scientific American, 316, 1, 69 (January 2017). doi:10.1038/scientificamerican0117-69


Tolk, A. (2020) The Danger of too much Compassion - how modellers can easily deceive themselves. Review of Artificial Societies and Social Simulation, 28th April 2020. https://rofasss.org/2020/04/28/self-deception/