A simple model of HIV epidemic in Italy: the role of the anti-retroviral treatment

In the present paper we propose a simple ODE model to describe the evolution of HIV epidemic in Italy. The model considers a single population of susceptibles, without distinction of high-risk groups within the general population, and accounts for the presence of immigration, modelling its effects on both the general demography and the dynamics of the infected subpopulations. To represent the intra-host disease progression, the untreated infected population is distributed over four compartments in cascade according to the CD4 counts. A further compartment is added to represent infected people under antiretroviral therapy. The values of the model parameters not reported in the literature are assessed by fitting available epidemiological data over the decade 2003 ÷ 2013. Predictions until year 2025 are computed, showing the benefits of the earlier eligibility of patients to the initiation of antiretroviral therapy. Analytical results about properties of the model in its time-invariant form are provided, in particular the global stability of the equilibrium points is established either in the absence and in the presence of infected among immigrants.