In the present paper we propose a simple time-varying 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 and emigration, modelling their 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 per capita exit rate from treatment, due to voluntary interruption or failure of therapy, is assumed variable with time. The values of the model parameters not reported in the literature are assessed by fitting available epidemiological data over the decade 2003 ÷ 2012. Predictions until year 2025 are computed, enlightening the impact on the public health of the early initiation of the antiretroviral therapy. The benefits of this change in the treatment eligibility consist in reducing the HIV incidence rate, the rate of new AIDS cases, and the rate of death from AIDS. 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.

A Simple model of HIV epidemic in Italy: The role of the antiretroviral treatment / F. Papa, F. Binda, G. Felici, M. Franzetti, A. Gandolfi, C. Sinisgalli, C. Balotta. - In: MATHEMATICAL BIOSCIENCES AND ENGINEERING. - ISSN 1547-1063. - 15:1(2018 Feb 01), pp. 181-207. ((Intervento presentato al convegno International Conference on Mathematical and Computational Epidemiology of Infectious Diseases : The Interplay between Models and Public Health Policies tenutosi a Erice nel 2015 [10.3934/mbe.2018008].

A Simple model of HIV epidemic in Italy: The role of the antiretroviral treatment

Binda, Francesca;Franzetti, Marco;Balotta, Claudia
2018-02-01

Abstract

In the present paper we propose a simple time-varying 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 and emigration, modelling their 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 per capita exit rate from treatment, due to voluntary interruption or failure of therapy, is assumed variable with time. The values of the model parameters not reported in the literature are assessed by fitting available epidemiological data over the decade 2003 ÷ 2012. Predictions until year 2025 are computed, enlightening the impact on the public health of the early initiation of the antiretroviral therapy. The benefits of this change in the treatment eligibility consist in reducing the HIV incidence rate, the rate of new AIDS cases, and the rate of death from AIDS. 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.
Emigration; Epidemic ODE models; HAART; HIV epidemic; Immigration; Stability of equilibrium points; Modeling and Simulation; Agricultural and Biological Sciences (all); Computational Mathematics; Applied Mathematics
Settore MED/17 - Malattie Infettive
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/561689
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