Dynamic analysis and optimal control of HIV/AIDS model with ideological transfer

This paper presents an HIV/AIDS model with ideological transfer in male susceptible individuals, and considers condoms and education as control measures. First, it gives the threshold R-0 of the model. Then it proves that the disease-free equilibrium is globally asymptotically stable when R-0 0 < 1 . Under different threshold conditions, the local stability of the boundary equilibria is given. The existence of the endemic equilibrium is also given. We also perform numerical simulations for different parameter values. Furthermore, when considering control measures, the simulation results show that effective and long-term use of condoms significantly reduce the number of infected individuals and education should be vigorously promoted when the epidemic is controllable. This result provides theoretical guidance for effective control the spread of HIV.