Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment with Saturated Incidence Function

The Human Immunodeficiency Virus (HIV) remains a significant global health challenge, with millions of people worldwide living with the virus. Despite advances in treatment and prevention, the disease continues to spread, underscoring the need for a deeper understanding of its transmission dynamics. This study presents a mathematical model of HIV transmission dynamics, incorporating a saturation term to capture the complex interactions among susceptible, infected, AIDS, and treated populations. The validity of the solution confirms that the model is well-defined and holds epidemiological significance. The basic reproduction number is obtained using the next-generation matrix approach. To assess the stability of the model, we conducted a thorough analysis of the local and global stability of both the disease-free and endemic equilibria. This analysis provides a comprehensive understanding of the model’s behavior, illuminating the conditions necessary for the disease to persist or die out. A sensitivity analysis is conducted to identify key parameters influencing the model’s behavior. Numerical simulations are then performed to further explore the dynamics of the system. Our results highlight the importance of targeted interventions to control the spread of the disease, thereby informing public health policy and intervention strategies.