Modelling the spread of HIV/AIDS epidemic in the presence of irresponsible infectives

Abstract

In this study, a non-linear mathematical model was proposed and analyzed to study the effect of irresponsible infectives in the spread of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) in a variable size population. The population was divided into four subclasses, of susceptibles (HIV negatives who can contract the disease), irresponsible infectives (people who are infected with the virus but do not know or live irresponsible life styles) , responsible infectives (HIV positives who know they are infected and are careful) and full-blown AIDS patients. Susceptibles were assumed to be infected through sexual contact with infectives and all infectives develop AIDS at a constant rate. Stability analysis and numerical simulations of the resulting model are presented. The model analysis shows that the disease-free equilibrium is always locally asymptotically stable and in such a case the basic reproductive number R₀<1 and the endemic equilibrium does not exist. The disease is thus eliminated from the system. If R₀>1, the endemic equilibrium exists and the disease remains in the system. It is shown that the endemicity of the disease is reduced when irresponsible infectives become responsible.

Keywords: Vertical transmission, stability, simulation, irresponsible infectives