Effect of public awareness, behaviours and treatment on infection-age-structured of mathematical model for HIV/AIDS dynamics

Since the discovering of the HIV/AIDS epidemic, more people have been infected with the HIV/AIDS infection and several individuals have died of HIV/AIDS virus. In this research work, an infection-age-structured mathematical model for HIV/AIDS transmission dynamics is developed and investigated, taking into consideration the public awareness, Treatment and Sex behaviours. It is assumed that the infectious population is structured according to time and age of infection. We established the criteria for the existence and uniqueness of solution. An explicit formula for the effective reproduction number RE of the model is obtained. We showed that the disease-free-equilibrium (DFE) state is stable if RE1 and globally stable if RE>1 for X1