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

Federico Papa; Francesca Binda; Giovanni Felici; Marco Franzetti; Alberto Gandolfi; Carmela Sinisgalli; Claudia Balotta; Federico Papa; Francesca Binda; Giovanni Felici; Marco Franzetti; Alberto Gandolfi; Carmela Sinisgalli; Claudia Balotta

doi:10.3934/mbe.2018008

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 1: 181-207. doi: 10.3934/mbe.2018008

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

1.
Istituto di Analisi dei Sistemi ed Informatica 'A. Ruberti' -CNR, Roma, Italy
2.
Dipartimento di Scienze Biomediche e Cliniche 'L. Sacco', Sezione di Malattie Infettive e Immunopatologia, Università degli Studi di Milano, Milano, Italy

Received: 21 September 2016 Accepted: 06 December 2016 Published: 01 February 2018
MSC : Primary: 34D05, 37B25; Secondary: 92B05, 92D30

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 $2003 \div 2012$. 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.
- HIV epidemic,
- HAART,
- immigration,
- emigration,
- epidemic ODE models,
- stability of equilibrium points
Citation: Federico Papa, Francesca Binda, Giovanni Felici, Marco Franzetti, Alberto Gandolfi, Carmela Sinisgalli, Claudia Balotta. A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment[J]. Mathematical Biosciences and Engineering, 2018, 15(1): 181-207. doi: 10.3934/mbe.2018008

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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 $2003 \div 2012$. 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.

References

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