A Global Stability Analysis of a Susceptible-Infected-Removed-Prevented-Controlled Epidemic Model

Abstract

A mathematical model of HIV transmission dynamics is proposed and analysed. The population is partitioned into five compartments of susceptible S ( t ), Infected I ( t ), Removed R (t), Prevented U ( t ) and the Controlled W ( t ). Each of the compartments comprises of cohort of individuals. Five systems of nonlinear equations are derived to represent each of the compartments. The general stability of the disease free equilibrium (DFE) and the endemic equilibrium states of the linearized model are established using the linear stability analysis (Routh-Hurwitz) method which is found to be locally asymptotically stable when the infected individuals receive ART and use the condom. The reproduction number is also derived using the idea of Diekmann and is found to be strictly less than one. This means that the epidemic will die out.