Principled simulation of agent-based models in epidemiology

Abstract

After more than a century of sustained work by mathematicians, biologists, epidemiologists, probabilists, and other experts, dynamic models have become a vital tool for understanding and describing epidemics and disease transmission systems. Such models fulfill a variety of crucial roles including data integration, estimation of disease burden, forecasting trends, counterfactual evaluation, and parameter estimation. These models often incorporate myriad details, from age and social structure to inform population mixing patterns, commuting and migration, and immunological dynamics, among others. This complexity can be daunting, so many researchers have turned to stochastic simulation using agent-based models. Developing agent-based models, however, can present formidable technical challenges. In particular, depending on how the model updates state, unwanted or even unnoticed approximations can be introduced into a simulation model. In this article, we present computational methods for approximating continuous time discrete event stochastic processes based on a discrete time step to speed up complicated simulations which also converges to the true process as the time step goes to zero. Our stochastic models is constructed via hazard functions, and only those hazards which are dependent on the state of other agents (such as infection) are approximated, whereas hazards governing dynamics internal to an agent (such as immune response) are simulated exactly. By partitioning hazards as being either dependent or internal, a generic algorithm can be presented which is applicable to many models of contagion processes, with natural areas of extension and optimization.