Stability analysis of an HIV/AIDS model with saturated incidence

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 S (t) , asymptomatic infective I1 (t) , symptomatic infective I2 (t) , treated T (t) and AIDS A(t) 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 and Descartes rule of signs. Sensitivity analysis was carried out using normalized forward sensitivity index and result showed that the contact rate is the most sensitive parameter. Existence of backward bifurcation analysis is equally carried out. More so, 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.