Contact-dependent infection and mobility in the metapopulation SIR model from a birth–death process perspective

Abstract

Given the widespread impact of COVID-19, modeling and analysis of epidemic propagation has been critical to epidemic prevention and control. However, previous studies have overlooked the significant influence of individual heterogeneity in behavior and physiology, including contact-dependent infection and migration on epidemic propagation. In this paper, we propose two metapopulation SIR models from individual and population perspectives. The first individual model introduces individual contact-dependent infection considering activity potential and infection rate, which leads to the derivation of the basic reproduction number R0 of our model. The birth–death process, used in the second population model, is represented by a compound Poisson process flow and Poisson process decomposition, respectively, to depict population mobility among subpopulations. In simulations, the number of individuals in each state and the converged number are illustrated to demonstrate the impact of various parameters. The relationship between the basic reproduction number R0 and various parameters is also demonstrated. Furthermore, the validity of our model is also confirmed on a real clinical report dataset of COVID-19 disease.