Global stability of an SAIRS epidemic model with vaccinations, transient immunity and treatment

Abstract

We consider an SAIRS epidemic model with vaccinations and treatment, where asymptomatic and symptomatic infectious individuals are considered in the transmission of the disease. We found the basic reproduction number, ℛ0 and using ℛ0, we conducted global stability analysis. We proved when ℛ0<1, the disease-free equilibrium is globally stable. If ℛ0>1, the disease-free equilibrium in unstable and a unique endemic equilibrium exists. We explored the global stability of the endemic equilibrium and noticed it is globally stable under certain conditions. Moreover, we then considered a special case of the SAIRS model, the SAIR model. We proved the disease-free equilibrium is globally stability when ℛ0<1 and the endemic equilibrium is globally stable when ℛ0>1. Next, we numerically simulated our analytical results and plotted these for various cases. Finally, we performed sensitivity analysis to tell us how each parameter in the system affects disease transmission.