Modeling the Effects of Prevention and Early Diagnosis on HIV/AIDS Infection Diffusion

In this paper, a new model describing the human immunodeficiency virus (HIV)-acquired immuno deficiency syndrome (AIDS) epidemic spread is proposed. The improvement with respect to the known models has been driven by recent results obtained from historical data collection and the suggestions given by the World Health Organization: the characteristics of the virus diffusion, mainly by body fluids, imply the trivial fact that wise behaviors of healthy subjects and fast timely recognition of a new positive diagnosis should reduce the spread quite fast. Therefore, the set of susceptible subjects is divided into two categories: the wise people that, suitably informed, avoid dangerous behaviors, and the ones that, with irresponsible acts, could get the infection. The set of infected subjects is constituted by people who are still not aware of being infected (and therefore are responsible of the HIV spread), along with the subjects aware of being infected by HIV or AIDS. Inspired by the international guidelines suggestions, three controls are introduced, aiming both at the prevention and at the cure: an informative campaign, a test campaign, and an HIV/AIDS therapy action. Among them, the core of the control effort is a fast HIV diagnosis. The equilibrium points, their stability, and the influences of the introduced inputs to the system behavior are studied, yielding to preliminary statements for prospective works on suitable control design approaches.