Mathematical Analysis of HIV/AIDS Model with Treatment Factor
Abstract
This study presents a mathematical model of HIV/AIDS transmission using a system of differential equations known as the SEIAT model, which classifies the population into Susceptible, Exposed, Infected, AIDS-infected, and Treated compartments. The model incorporates treatment as a key control strategy in managing the disease spread. Analytical methods were employed to examine the existence of equilibrium points, and the basic reproduction number ( ) was derived using the next-generation matrix approach. Both local and global stability analyses were carried out to determine the conditions under which HIV/AIDS persists or dies out in the population. Numerical simulations supported the analytical results and provided insights into the model’s dynamic behavior. Sensitivity analysis was also conducted to assess the influence of various parameters on . The results revealed that reducing the contact rate between susceptible and infected individuals, as well as increasing treatment rates, significantly lowers the basic reproduction number and curtails the spread of the disease. Based on these findings, it is recommended that public health interventions prioritize reducing risky contact behavior and expanding access to effective treatment programs as vital strategies for controlling HIV/AIDS transmission.
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References
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