A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

Fatmawati, Endrik Mifta Shaiful and Mohammad Imam Utoyo

International Journal of Mathematics and Mathematical Sciences, 2018, vol. 2018, 1-11

Abstract:

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 . 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.

Date: 2018
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6801475

DOI: 10.1155/2018/6801475

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