AbstractAfter 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.Author summaryStochastic simulation of epidemics is crucial to a variety of tasks in public health, encompassing intervention evaluation, trend forecasting, and estimation of epidemic parameters, among others. In many situations, due to model complexity, time constraints, unavailability or unfamiliarity with existing software, or other reasons, agent-based models are used to simulate epidemic processes. However, many simulation algorithms are ad hoc, which may introduce unwanted or unnoticed approximations. We present a method to build approximate, agent-based models from mathematical descriptions of stochastic epidemic processes which will improve simulation speed and converge to exact simulation techniques in limiting cases. The simplicity and generality of our method should be widely applicable to various problems in mathematical epidemiology and its connection to other methods developed in chemical physics should inspire future work and elaboration.
Case Studies for a Markov Chain Approach to Analyze Agent-Based Models
