A Mathematical Model of The Best Way to Control the Spread of HIV/AIDS, Taking into Account the Group of People Who are not Affected After Being Exposed to the Disease

Abstract

In this study, we created a mathematical model of how HIV/AIDS spreads over time that includes measures to stop transmission after contact. There are six important parts to the model: Susceptible, Exposed within three days, Exposed but Not Infected, Treatment, Pre-AIDS, and AIDS. To find the effective reproduction number, the next-generation operator method was used. The stability analysis showed that the model's disease-free equilibrium point is locally asymptotically stable when the reproduction number is less than one, and it has a unique endemic equilibrium when the reproduction number is greater than one. Both pre-contact preventive measures and anti-retroviral treatment (ART) control measures were added to the optimal control model. To make the best system, Pontryagin's maximum theory was used. Seven ways of controlling things were thought about. "The optimal application of Pre-contact preventive control measures" was found to be the most cost-effective way to keep things under control. People who use both pre-contact preventive and anti-retroviral therapy together were also able to control the virus better and more cheaply than people who used the other two control strategies together. MATLAB was used to simulate how the populations of different classes changed when each of these strategies was used. This was done to see how these control measures affected the virus.