Stability and Sensitivity Analysis of HIV/AIDS Model with Saturated Incidence Rate

Abstract

HIV/AIDS, an extremely harmful sexually transmitted disease, has had a significant impact on worldwide health, establishing itself as one of the most lethal epidemics ever recorded. In this study, a mathematical model is used to analyze how HIV/AIDS spreads and grows, taking into account high incidence rates. The model uses a set of typical differential equations to group people into different categories based on their health status, including those who are vulnerable, those who have been vaccinated, those who are asymptomatic, those who are symptomatic, and those who have AIDS. The effectiveness of the solution indicates that the model is clearly outlined and has important implications for epidemiology. By utilizing the next-generation matrix method, we calculated the basic reproduction number. In order to evaluate the model's stability, a comprehensive examination was conducted on both the local and global stability of both the disease-free and endemic equilibrium points. This analysis provides a comprehensive understanding of the model’s behavior, shedding light on the conditions necessary for the disease to persist or die out. Numerical simulations focusing on these key parameters demonstrate that achieving a disease-free environment is attainable, albeit requiring targeted interventions to maintain stability. This study underscores the significance of understanding saturated incidence rates in modeling HIV/AIDS transmission dynamics. The results offer important information for policymakers and public health authorities, allowing them to create successful tactics for managing the transmission of HIV/AIDS.