Mathematics analysis of the effect of public health educational campaigns, screening and therapy on HIV/AIDS transmission

Abstract

In this paper, a deterministic mathematical models are formulated and analyzed to assess the effect of the public health educational campaigns, screening, and therapy on the dynamics of HIV/AIDS. The information causes a change in behavior resulting in three susceptible classes. We calculate the effective reproduction number using the next-generation matrix method. It has been shown that the disease-free equilibrium point is locally asymptotically stable when the effective reproduction number is less than unity. Sensitivity analysis of effective reproduction number with respect to the model parameters were carried out. The most sensitive parameter on the effective reproduction number is the contact rate of susceptible to unaware HIV infective followed by the screening rate and the least sensitive parameter is the progression rate of screened infective to full-blown AIDS. Numerical simulations and sensitivity analysis are carried out to support the analytical results and to determine the parameters influencing the dynamics of the disease.