Analysis of HIV/AIDS Model with Nonlinear Incidence Function

O. A. Odebiyi, J. K. Oladejo, A. A. Yahaya and Elijah E.o
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O. A. Odebiyi: Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, PMB 4000, Ogbomoso, Oyo state
J. K. Oladejo: Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, PMB 4000, Ogbomoso, Oyo state
A. A. Yahaya: Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, PMB 4000, Ogbomoso, Oyo state
Elijah E.o: Department of Mathematics, P.M.B. 65, Minna, Niger state. PMB 4000, Ogbomoso, Oyo state

International Journal of Research and Innovation in Applied Science, 2024, vol. 9, issue 4, 317-341

Abstract: Human Immunodeficiency Virus – Acquired Immune Deficiency Syndrome HIV/AIDS stands as one of the most prevalent sexually transmitted disease globally and is regarded as one of the deadliest epidemic in human history. This study presents a mathematical model for understanding the dynamics of HIV/AIDS transmission, incorporating a saturated incidence rate. The model employs a system of ordinary differential equations, comprising various group of individuals including susceptible, asymptomatic infective, symptomatic infective, treated and AIDS class. The validity of the solution states affirms that the model is well-defined and holds epidemiological significance. The disease-free and endemic equilibrium states are identified, and their stability is analyzed using Routh Hurwitz criteria. Sensitivity analysis was carried out using normalized forward sensitivity index and result showed that the contact rate is the most sensitive parameter. However, it is observed from the numerical simulation that screening and treatment of the infective play a significant role in reducing the transmission of the disease. The outcome of the stability analysis for both disease-free and endemics equilibrium states indicates the potential for HIV/AIDS control.

Date: 2024
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