Epidemic control using stochastic and deterministic transmission models: performance comparison with and without parameter uncertainties

BackgroundThe spread of infectious diseases can be modeled using deterministic models assuming a continuous population or stochastic models assuming a discrete population. A stochastic model can be approximated by its deterministic counterpart under some conditions, however deterministic models are unable to captures effects pertaining to the discrete nature of populations, for instance epidemic extinction. We look into the choice of a model - deterministic or stochastic - from the perspective of decision making. We are interested in the influence of parameter uncertainties and of the quality of the estimates used to inform decisions. MethodWe consider an emerging disease in a closed population whose spread can be modeled by a stochastic SIR model or its deterministic version. Our objective is to minimize the cumulative number of symptomatic infected-days over the course of the epidemic by picking a vaccination policy out of three available options. We consider four decision making scenarios: based on the stochastic model or the deterministic model, and informed or under parameter uncertainty. We also consider different sample sizes covering parameter draws, stochastic model runs, or both depending on the scenario. We estimate the average performance of decision making in each scenario and for each sample size. ResultsThe model used for decision making has an influence on the picked policies. The best achievable performance is obtained with the stochastic model, knowing parameter values, and for a large sample size. For small sample sizes, the deterministic model can outperform the stochastic model due to stochastic effects, both in the informed and the uninformed cases. Starting with the deterministic model under uncertainty, resolving uncertainties brings more benefit than switching to the stochastic model in our example. ConclusionThis article illustrates the interplay between the choice of a type of model, parameter uncertainties, and sample sizes. It points to issues to be carefully considered when attempting to optimize a stochastic model.