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**Stability analysis of a non-linear HIV/AIDS epidemic model with vaccination and antiretroviral therapy.**
*(English)*
Zbl 1427.92057

Summary: In this paper, we like to propose and analyze a non-linear HIV/AIDS epidemic model with vaccination and antiretroviral therapy. For our convenient study we have divided the total populations into five classes such as susceptible class, unaware HIV infected class, aware HIV infected class, pre AIDS class and AIDS class respectively. For our present purpose we have taken only the disease spread through horizontal transmission into consideration. In this paper we have tried to develop a nonlinear HIV/AIDS mathematical model to study the transmission dynamics of HIV at four compartments of the populations with vaccination and antiretroviral therapy and to prove the positivity and boundedness of its solutions. In this paper we have added a treatment procedure i.e. antiretroviral therapy and tried to find out its effect. We have also analyzed the stability behaviour of the system. Finally we have found that vaccination and antiretroviral therapy is an effective way to control the disease transmission. The mathematical model solved numerically by using an iterative numerical recipe which supports the theoretical or analytical results.

### MSC:

92C60 | Medical epidemiology |

34D23 | Global stability of solutions to ordinary differential equations |

### Keywords:

HIV/AIDS epidemic model; antiretroviral therapy; basic reproduction number; stability; vaccination; numerical results
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\textit{D. Biswas} and \textit{S. Pal}, Int. J. Adv. Appl. Math. Mech. 5, No. 2, 41--50 (2017; Zbl 1427.92057)

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