A Fractional-Order Model for HIV Dynamics in a Two-Sex Population
Human Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost comple...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2018/6801475 |
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| author | Fatmawati Endrik Mifta Shaiful Mohammad Imam Utoyo |
| author_facet | Fatmawati Endrik Mifta Shaiful Mohammad Imam Utoyo |
| author_sort | Fatmawati |
| collection | DOAJ |
| description | Human Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost complete influence across the country. A mathematical model approach of HIV/AIDS dynamic is needed to predict the spread of the diseases in the future. In this paper, we presented a fractional-order model of the spread of HIV and AIDS diseases which incorporates two-sex population. The fractional derivative order of the model is in the interval (0,1]. We compute the basic reproduction number and prove the stability of the equilibriums of the model. The sensitivity analysis also is done to determine the important factor controlling the spread. Using the Adams-type predictor-corrector method, we then perform some numerical simulations for variation values of the order of the fractional derivative. Finally, the effects of various antiretroviral therapy (ART) treatments are studied and compared with numerical approach. |
| format | Article |
| id | doaj-art-45800a1ed28f4ae2b33563507c13fe0e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-45800a1ed28f4ae2b33563507c13fe0e2025-02-03T05:48:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252018-01-01201810.1155/2018/68014756801475A Fractional-Order Model for HIV Dynamics in a Two-Sex PopulationFatmawati0Endrik Mifta Shaiful1Mohammad Imam Utoyo2Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, IndonesiaDepartment of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, IndonesiaHuman Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost complete influence across the country. A mathematical model approach of HIV/AIDS dynamic is needed to predict the spread of the diseases in the future. In this paper, we presented a fractional-order model of the spread of HIV and AIDS diseases which incorporates two-sex population. The fractional derivative order of the model is in the interval (0,1]. We compute the basic reproduction number and prove the stability of the equilibriums of the model. The sensitivity analysis also is done to determine the important factor controlling the spread. Using the Adams-type predictor-corrector method, we then perform some numerical simulations for variation values of the order of the fractional derivative. Finally, the effects of various antiretroviral therapy (ART) treatments are studied and compared with numerical approach.http://dx.doi.org/10.1155/2018/6801475 |
| spellingShingle | Fatmawati Endrik Mifta Shaiful Mohammad Imam Utoyo A Fractional-Order Model for HIV Dynamics in a Two-Sex Population International Journal of Mathematics and Mathematical Sciences |
| title | A Fractional-Order Model for HIV Dynamics in a Two-Sex Population |
| title_full | A Fractional-Order Model for HIV Dynamics in a Two-Sex Population |
| title_fullStr | A Fractional-Order Model for HIV Dynamics in a Two-Sex Population |
| title_full_unstemmed | A Fractional-Order Model for HIV Dynamics in a Two-Sex Population |
| title_short | A Fractional-Order Model for HIV Dynamics in a Two-Sex Population |
| title_sort | fractional order model for hiv dynamics in a two sex population |
| url | http://dx.doi.org/10.1155/2018/6801475 |
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