Uncertainty Quantification for the Stochastic Modeling of Influenza Propagation: How Many Simulation Runs is Enough

The aim of the study is to properly quantify the uncertainty associated with the stochastic epidemic process of influenza propagation reproduced by the multiagent model. To distinguish the output error caused by the epistemic nature of the disease propagation process and the one caused by too few simulation runs, we analyse the dynamics of the coefficient of variation relying on Lorscheid method of the sample size estimation. We demonstrate the performance of the method using a simulation of influenza propagation in a synthetic population of one of the major Russian city – Samara ($\mathbf{1 0 \%}$ sample). The results show that although the value of $\Delta c_{V}$ does not converge to zero for any of the regarded epidemic parameters (incidence peak height, incidence peak day, total cases), the analysis of $\Delta c_{V}$ may shed some light on the optimal number of the simulation runs which helps save computer time without sacrificing the quality of the variation assessment of epidemic indicators.

I. Introduction

Mathematical models based on statistical, machine learning or mechanistic approaches constitute an essential part of decision support systems in healthcare. Despite the fast evolution of modern forecasting techniques, the most widely used models are SEIR models described by the systems of differential equations. Their numerous advantages, such as simplicity and ease of interpretation, are however accompanied by a big drawback: being deterministic, they are unable to capture the inherent stochasticity of the epidemic process, which is an important factor to consider, especially at the beginning of the outbreak. The alternative approach, which is the second most popular, is multiagent modeling, which was created to address this issue. Modeled epidemic curves generated by repetitive simulation runs of a multiagent model help make an interval assessment of the epidemic parameters.