Effect of Heterogeneity and Mobility on a Model for Propagation of Epidemics

Abstract:

The SIR (Susceptible-Infected-Response) model is an important mathematical model for epidemic propagation. The model predicts the parameters describing epidemics such as the crowd immunity, half-decay time, and cumulative infection fraction with only one important parameter, the rescaled reproduction number Ro.  However, the model assumes that the population is homogeneous. As we have seen with the Sars-Cov2 epidemic, the United States is heterogenous population with different politics, cultures, and regions that will interact differently to the epidemic. The goal of this project is to incorporate heterogeneity into this model and determine how various degrees of heterogeneity will affect said measurements. A computer program was written to simulate a modified SIR model which allows for a population with varying levels of heterogeneity/mobility. With the highest levels of mobility, the results of the SIR model are reproduced. By varying the mobility of the population, we can simulate the results for the non-homogeneous case while also varying the other parameters that characterize the population. MATLAB scripts were also created to process to simulation data and provide the user with measurements that describe the various stages of the epidemic.