On the Stability of Endemic Equilibrium State of HIV/AIDS Model with Irresponsible Infective Immigrants

ABSTRACT

In this paper, a non–linear mathematical model is proposed to study the effects of irresponsible infected immigrants on the spread of HIV/AIDS in a heterogeneous population with a constant recruitment of susceptible receptors. Theequilibrium points, stability analysis, and numerical solution on the model are presented. The Routh–Hurwitz stability condition was employed to examine the stability of the disease– free equilibrium and Next Generation matrix was adopted to generate the Basic Reproduction Number. Also, the endemic equilibrium is stable as it satisfies the Bellman and Cooke’s condition for stability. It is realised that at the disease–free equilibrium, the model is stable when the basic reproduction number 0 R 1 and unstable otherwise. The condition for stability of the model near the endemic equilibrium state is presented. Numerical solution reveals that the presence of infective immigrants into the population significantly affects the spread of the disease. The analysis further shows that strict immigration policies such as screening and reduction in the number of immigrants into a given population, and behavioural change of all classes of individuals should be considered in efforts aimed at controlling the spread of the disease.