![]() The results obtained show the effectiveness and strength of the applied L1 scheme. ![]() Further, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to observe the impact of the arbitrary order derivative. HIV can be transmitted through unprotected sexual intercourse (vaginal, anal or oral). Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. During the acute HIV infection stage, the level of HIV in the blood is very high, which greatly increases the risk of HIV transmission. The virus attacks and destroys the infection-fighting CD4 cells (CD4 T lymphocyte) of the immune system. On the basis of R 0, the disease progress can be determined i.e., the population is free from the disease if R 0 1. In the acute stage of infection, HIV multiplies rapidly and spreads throughout the body. The threshold quantity namely basic reproduction number R 0 is calculated and analyzed for the disease status. Moreover, model equilibria are determined, and their stability analysis are considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle's invariant principle. Positivity and boundedness of the solution and the stability conditions of the fractional-order system are determined. The fractional derivatives are taken in Caputo sense and the numerical solution of the model is obtained by L1 scheme which involves the memory trace that can capture and integrate all past activity. The focus is on the spread of HIV by female sex workers through prostitution, because in the present world sexual transmission is the major cause of the HIV transmission. The model describes the spread of HIV disease in a system consisting of a population of susceptible males and the female sex workers. This paper considers a fractional-order HIV epidemic model with the inclusion of prostitution in the population and its consequences on the disease transmission. Many campaigns have been put into place, and people have been made aware of the various effects of the disease. HIV is a topic that has been greatly discussed and researched due to its impact on human population.
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