Modelling the effect of risky sexual behaviour on the spread of HIV/AIDS

A nonlinear mathematical model to study the effect of risky sexual behaviour on the spread of HIV/AIDS in a population with variable size structure is proposed and analyzed. The model divides the population into four subclasses that are susceptibles, infectives with high sexual activity level, infectives with low sexual activity level and AIDS population. The model exhibits two eqilibria namely, the disease-free and the endemic equilibrium. It is shown that the endemic equilibrium is locally asymptotically stable and is globally asymptotically stable under certain conditions showing that the disease becomes endemic. We found a threshold value, depending on the infection rates, of the proportion of infectives with high sexual activity level below which the epidemic does not sustain in the population. It is also shown that as the number of infectives with high sexual activity level increases, the number of AIDS individuals also increases. Numerical analysis of the model is also performed to investigate the influence of certain key parameters on the spread of the disease and to support the analytical results.