Coinfection dynamics of heroin transmission and HIV infection in a single population

We propose a coinfection model of heroin abuse and HIV infection, to describe the joint spread through a single population. The unique disease-free equilibrium always exists and it is stable only if the basic reproduction numbers of heroin abuse and HIV infection are both less than 1. The semi-trivial equilibrium of HIV infection exists if the basic reproduction number of HIV infection is larger than 1 and it is locally stable if and only if the  invasion reproduction number heroin use  is less than 1. The semi-trivial  equilibrium of heroin abuse exists if the basic reproduction number of heroin abuse is larger than 1 and it is locally stable if and only if the  invasion reproduction number of HIV infection  is less than 1. When both semi-trivial  equilibria lose their stabilities, a coexistence equilibrium occurs. In the proof of the existence  of the coexistence equilibrium, we resort to operator theory and a fixed point theorem applied in a partially ordered set. Finally, we compare the model to US data and  some numerical simulations are carried out to illustrate and extend the theoretical results.

Joint work with Xi-Chao Duan and Xue-Zhi Li.