Optimal Control of HIV/AIDS Epidemic Model with Two Latent Stages, Vertical Transmission and Treatment

In this research, we discussed about optimal control of HIV/AIDS epidemic model with two latent stages, vertical transmission and treatment. In this model, the population is divided into five subpopulations, namely susceptible subpopulation, slow latent subpopulation, fast latent subpopulation, symptomatic subpopulation and AIDS subpopulation. The latent stage is divided into slow latent and fast latent stage depend on the condition of immune system which is different for each individual. Treatment (ART/antiretroviral) is given to infected individu in symptomatic stage. The rate of treatment from symptomatic stage to slow latent stage and to fast latent stage are set as u 1(t) and u 2(t) control variable, respectively. Here, the objective of optimal control is to minimize the number of infected as well as the cost of controls. The optimal control is obtained by applying Pontryagin's Principle. In the end, we show some numerical simulations by using Forward-Backward Sweep Method. Numerical simulation result show that the combination of u 1 and u 2 control is the most effective control to reduce the number of infected/symptomatic subpopulation with minimum cost of controls.