OPTIMAL CONTROL OF HIV/AIDS-TB CO-INFECTION MODEL WITH HEALTH EDUCATION AND TREATMENT

HIV-TB co-infection is common and harmful, and is still a challenge to global public health. We propose an HIV-TB co-infection model with health education and treatment to seek the optimal strategy to control the diseases. The HIV-sub model, TB sub-model and HIV-TB co-infection model are analyzed, respectively. We obtain reproduction numbers, disease-free equilibria and endemic equilibria of two sub-models and analyze their stabilities. For the full model, the disease-free equilibrium is globally asymptotically stable under certain conditions. An optimal control problem is formulated by introducing five time-dependent controls, which are increasing the education rate for susceptible individuals, improving the educated individuals' sense of self-protection and increasing treatment rate for HIV, TB and dual infected individuals, respectively, into the full model. Its optimal solution is obtained by Pontryagin's minimum principle. We compare the number of infected individuals with and without optimal control using numerical simulations. Finally, we conduct a numerical simulation with different combinations of the five controls, which shows that combining all the five controls simultaneously is the best strategy to control the diseases. This result also indicates the necessity of strengthening health education for people under treatment.