Abstract
In developing nations, the human immunodeficiency virus (HIV) infection, which can lead to acquired immunodeficiency syndrome (AIDS), has become a serious infectious disease. It destroys millions of people and costs incredible amounts of money to treat and control epidemics. In this research, we implemented a Legendre wavelet collocation scheme for the model of HIV infection and compared the new findings to previous findings in the literature. The findings demonstrate the precision and practicality of the suggested approach for approximating the solutions of HIV model. Additionally, establish an autonomous non-linear model for the transmission dynamics of healthy CD4 + T-cells, infected CD4 + T-cells and free particles HIV with a cure rate. Through increased human immunity, the cure rate contributes to a reduction in infected cells and viruses. Using the Routh-Hurwitz criterion, we determine the basic reproductive number and assess the stability of the disease-free equilibrium and unique endemic equilibrium of the model. Furthermore, numerical simulations of the novel model are presented using the suggested approach to demonstrate the efficiency of the key findings.