A MATHEMSTICAL MODEL OF HIV/AIDS EPIDEMIC IN THE PRESENCE OF IRRESPONSIBLE INFECTIVES

Abstract

In this thesis, a non-linear mathematical model is proposed and analyzed to study the effect of irresponsible infectives in the spread of HIV/AIDS in a variable size population. In considering the modeling dynamics, the population is 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 are assumed to be infected through sexual contact with infectives and all infectives develop AIDS at a constant rate. The stability theory of differential equations and computer simulations are used to analyze the model. The model analysis shows that the disease-free equilibrium is always locally asymptotically stable and in such a case the basic reproductive number Ro < 1 and the endemic equilibrium does not exist. The disease is thus eliminated from the system. If Ro > 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 infectives who are more likely not to take part in sexual interactions. A numerical simulation of the model is also used to investigate the influence of certain other parameters on the transmission dynamics of HIV/AIDS.