Stability Analysis of a delayed HIV/AIDS
Epidemic Model with Saturated Incidence

Debashis Biswas; Samares Pal

doi:https://doi.org/10.14445/22315373/IJMTT-V43P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 43 | Number 3 | Year 2017 | Article Id. IJMTT-V43P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V43P526

Stability Analysis of a delayed HIV/AIDS Epidemic Model with Saturated Incidence

Debashis Biswas, Samares Pal

Citation :

Debashis Biswas, Samares Pal, "Stability Analysis of a delayed HIV/AIDS Epidemic Model with Saturated Incidence," International Journal of Mathematics Trends and Technology (IJMTT), vol. 43, no. 3, pp. 222-231, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V43P526

Abstract

In this paper, we investigate the effect of time delay on an HIV/AIDS epidemic model with saturated incidence rate. We accept that the individuals are being recruited into sexually matured age group at a constant rate and incorporates time delay for one to become infected and the other become fullyblown. We assume that the disease spread only by sexually transmission.The model consists two equilibria, namely, a disease-free equilibrium and an endemic equilibrium. We calculate the basic reproduction number by using the next generation matrix. Mathematical analyses consecrated that the global dynamics of the spread of the HIV/AIDS infectious disease are totally determined by the basic reproduction number R0 . For the basic reproduction number R0 <1 , and 1 0 the disease-free equilibrium is locally asymptotically stable. Whether R0 >1 , and 1 0 the endemic equilibrium point is locally asymptotically stable. Finally; we find the numerical solution of the model which justify the analytical results.

Keywords

HIV/AIDS Epidemic model, Time Delay, Basic reproduction number, Stability, Saturated Incidence.

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