A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment
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 emigrat...
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AIMS Press
2018-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018008 |
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| author | Federico Papa Francesca Binda Giovanni Felici Marco Franzetti Alberto Gandolfi Carmela Sinisgalli Claudia Balotta |
| author_facet | Federico Papa Francesca Binda Giovanni Felici Marco Franzetti Alberto Gandolfi Carmela Sinisgalli Claudia Balotta |
| author_sort | Federico Papa |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-57d91fb5a6b44e3492f3c63fd75d143c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-01-01 |
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| spelling | doaj-art-57d91fb5a6b44e3492f3c63fd75d143c2025-01-24T02:40:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-01-0115118120710.3934/mbe.2018008A simple model of HIV epidemic in Italy: The role of the antiretroviral treatmentFederico Papa0Francesca Binda1Giovanni Felici2Marco Franzetti3Alberto Gandolfi4Carmela Sinisgalli5Claudia Balotta6Istituto di Analisi dei Sistemi ed Informatica 'A. Ruberti' -CNR, Roma, ItalyDipartimento di Scienze Biomediche e Cliniche 'L. Sacco', Sezione di Malattie Infettive e Immunopatologia, Università degli Studi di Milano, Milano, ItalyIstituto di Analisi dei Sistemi ed Informatica 'A. Ruberti' -CNR, Roma, ItalyDipartimento di Scienze Biomediche e Cliniche 'L. Sacco', Sezione di Malattie Infettive e Immunopatologia, Università degli Studi di Milano, Milano, ItalyIstituto di Analisi dei Sistemi ed Informatica 'A. Ruberti' -CNR, Roma, ItalyIstituto di Analisi dei Sistemi ed Informatica 'A. Ruberti' -CNR, Roma, ItalyDipartimento di Scienze Biomediche e Cliniche 'L. Sacco', Sezione di Malattie Infettive e Immunopatologia, Università degli Studi di Milano, Milano, ItalyIn 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018008hiv epidemichaartimmigrationemigrationepidemic ode modelsstability of equilibrium points |
| spellingShingle | 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 Mathematical Biosciences and Engineering hiv epidemic haart immigration emigration epidemic ode models stability of equilibrium points |
| title | A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment |
| title_full | A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment |
| title_fullStr | A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment |
| title_full_unstemmed | A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment |
| title_short | A simple model of HIV epidemic in Italy: The role of the antiretroviral treatment |
| title_sort | simple model of hiv epidemic in italy the role of the antiretroviral treatment |
| topic | hiv epidemic haart immigration emigration epidemic ode models stability of equilibrium points |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018008 |
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