Impulsive SUI epidemic model for HIV/AIDS with chronological age and infection age

This paper develops an impulsive SUI model of human immunodeficiency virus/acquired immunodeficiency syndrome(HIV/AIDS) epidemic for the first time to study the dynamic behavior of this model. The SUI model is described by impulsive partial differential equations. First, the well-posedness of the model is attained by the method of characteristic lines and iterative method. Secondly, the basic reproduction number R0(q,T) of the epidemic which depends on the impulsive HIV-finding period T and the HIV-finding proportion q is obtained by mathematical analysis. Our result shows that HIV/AIDS epidemic can be theoretically eradicated if we can have the suitable HIV-finding proportion q and the impulsive HIV-finding period T   such that R0(q,T)<1R0(q,T)<1. We also conjecture that the infection-free periodic solution of the SUI model is unstable when R0(q,T)>1R0(q,T)>1.