Condition for Global Stability for a SEIR Model Incorporating Exogenous Reinfection and Primary Infection Mechanisms

Abstract

A mathematical model incorporating exogenous reinfection and primary progression infection processes is proposed. Global stability is examined using the geometric approach which involves the generalization of Poincare-Bendixson criterion for systems of $n$ -ordinary differential equations. Analytical results show that for a Susceptible-Exposed-Infective-Recovered (SEIR) model incorporating exogenous reinfection and primary progression infection mechanisms, an additional condition is required to fulfill the Bendixson criterion for global stability. That is, the model is globally asymptotically stable whenever a parameter accounting for exogenous reinfection is less than the ratio of background mortality to effective contact rate. Numerical simulations are also presented to support theoretical findings.