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Additional information on theory and case studies discussed in Context-dependent representation of within- and between-model uncertainty: aggregating probabilistic predictions in infectious disease epidemiology

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Mathematical modelling is used during disease outbreaks to compare control interventions. Using multiple models, the best method to combine model recommendations is unclear. Existing methods weight model projections, then rank control interventions using the combined projections, presuming model outputs are directly comparable. However, the way each model represents the epidemiological system will vary. We apply electoral vote-processing rules to combine model-generated rankings of interventions. Combining rankings of interventions, instead of combining model projections, avoids assuming that projections are comparable as all comparisons of projections are made within each model. We investigate four rules: First-past-the-post, Alternative Vote (AV), Coombs Method and Borda Count. We investigate rule sensitivity by including models that favour only one action or including those that rank interventions randomly. We investigate two case studies: the 2014 Ebola outbreak in West Africa (37 compartmental models) and a hypothetical foot-and-mouth disease outbreak in UK (four individual-based models). The Coombs Method was least susceptible to adding models that favoured a single action, Borda Count and AV were most susceptible to adding models that ranked interventions randomly. Each rule chose the same intervention as when ranking interventions by mean projections, suggesting that combining rankings provides similar recommendations with fewer assumptions about model comparability.This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.

Temporal variations in quantities of logistical factors affecting control efforts on infected premises (IPs) during the 2001 foot-and-mouth epidemic in the UK. Top panel: Mean size of IPs across report dates. Middle panels: Mean levels of control demand on culling and disposal responses to IPs across report dates. Bottom panel: Mean value of farm density within a 5km radius from IPs across report dates.

Mean daily delays to culling (purple) and disposal (green) over report dates, simulated as a function of farm size, control demand, and policy timeframes (time-dependent response).

Mean observed and predicted response delays on infected premises (IPs) grouped by farm size, control demand, and case report dates. IPs are separated into two size classes: farms that contain more than 500 livestock (red) and those with smaller populations (blue). Their response times are aggregated by the level of control demand, with the means calculated for each group (dots). From the same covariate values of farm size and control demand, delays are also simulated using the method of inverse probability integral transform. 1000 simulation replicates are run for each IP setting and their means are similarly aggregated and averaged by group (circles and lines). Note that the simulations of disposal delays on IPs reported prior to 1 April (c) depend only on farm size due to the insignificant effect of control demand (see Tables 1 and S2). The corresponding distribution of control demand is shown in each panel. Dashed line marks the 24 hours period.