Epidemic Persistence: Equilibria and Stability Analysis of Spread Process Dynamics over Networks, with Asymptomatic Carriers and Heterogeneous Model Parameters

Abstract

We present an analysis of epidemiological compartment models that explicitly capture the dynamics of asymptomatic but infectious individuals. Our models can be viewed as an extension to classic SIR models, to which a distinct Asymptomatic compartment is added. We discuss both a group compartment model capturing a Susceptible-Asymptomatic-Infected-Recovered-Susceptible (SAIRS) epidemic process, and also introduce and evaluate SAIRS dynamics evolving over networks. We investigate equilibria and stability properties that include both disease-free and endemic equilibria states for these models, providing sufficient conditions for convergence to these equilibria. Model parameter estimation results based on local test-site and Peoria county clinic data are given, and a number of simulations illustrating the effects of asymptomatic-infected individuals and network structure on the spread and/or persistence of the disease are presented.