Analysis of a mathematical model of transmission dynamics of HIV/AIDS with saturated incidence rate

Abstract

In this study, a mathematical model for the HIV/AIDS epidemic is developed and analyzed to gain insight into the current and past states of HIV/AIDS and other epidemiological features that cause the progression from HIV to full-blown AIDS. The existence and uniqueness of the model show that the solutions exist and are unique. The basic reproduction number is the average number of new secondary infections generated by a single infected individual during the infectious period, which is established using the next-generation matrix method. The analysis shows that the disease-free equilibrium is locally asymptotically stable whenever the threshold quantity is less than unity, i.e., R₀ < 1, and is otherwise epidemic. The sensitivity of parameters with respect to the basic reproduction number shows that parameters with a positive index will increase the basic reproduction number; for example, the effective contact rate must not exceed 0.39 to avoid an endemic stage. Numerical analysis of the work shows the importance of the memory term; it also indicates that control measures targeted at the history of any disease and immunity boosts should be adopted to prevent HIV from leading to full-blown AIDS.