HIV/AIDS epidemic fractional-order model |
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| Authors: | Zain Ul Abadin Zafar Kashif Rehan M Mushtaq |
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| Institution: | 1. Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan;2. Faculty of Information Technology, University of Central Punjab, Lahore, Pakistanzainzafar@ucp.edu.pk;4. Department of Mathematics, University of Engineering and Technology, KSK Campus, Lahore, Pakistan |
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| Abstract: | In this paper a non-linear mathematical model with fractional order ?, 0 < ? ≤ 1 is presented for analyzing and controlling the spread of HIV/AIDS. Both the disease-free equilibrium E0 and the endemic equilibrium E* are found and their stability is discussed using the stability theorem of fractional order differential equations. The basic reproduction number R0 plays an essential role in the stability properties of our system. When R0 < 1 the disease-free equilibrium E0 is attractor, but when R0 > 1, E0 is unstable and the endemic equilibrium (EE) E* exists and it is an attractor. Finally numerical Simulations are also established to investigate the influence of the system parameter on the spread of the disease. |
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| Keywords: | HIV/AIDS Model fractional derivatives stability predictor–corrector method Grunwald-Letnikov |
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