Transmission dynamics of HIV/AIDS with screening and non-linear incidence

We formulate and analyze a deterministic mathematical model of transmission dynamics of HIV/AIDS with screening using non-linear incidence. The model divides the population into four subclasses that are susceptibles, infectives who do not know their HIV status. infectives who know their HIV status and those with full blown AIDS. The model assumes that susceptibles become infected via sexual contacts with both types of infectives and all infectives move with a constant rate to develop AIDS. Also it is assumed that individuals will die due to disease after reaching the full blown AIDS stage. The model is analyzed using the stability theory of differential equations and numerical simulations. The effect of screening of unaware infectives and the effect of non-linear incidence parameters are investigated. Qualitative results show that the model has two equilibria; the disease-free equilibrium which is locally asymptotically stable whenever the basic reproduction number is less than unity and the endemic equilibrium that is locally and globally asymptotically stable providedthat the basic reproduction number is greater than unity. Furthemore, when the basic reproduction number is equal to unity, forward bifurcation occurs. Numerical results suggest that screening of unaware infectives has the effect of reducing transmission dynamics of HIV/AIDS. Also, using non-linear incidence parameters, it is noted that transmission dynamics will be lowered when infectives after becoming aware of their infection do not take part in sexual interaction; that is behavioural changes is a key in reducing the transmission. Thus, educational program with respect to behavioural changes should be given to all infectives.