Global analysis of a mathematical model for Hepatitis C virus transmissions

•A new mathematical model is proposed to describe the dynamics of HCV infection transmissions.•Both of primary infection and re-infections are considered in the model.•Two thresholds of basic reproduction number R0 and control reproduction number Rc are derived.

In this paper, a mathematical model is proposed and analyzed for Hepatitis C virus (HCV) infection transmissions. In this model, both of chronic primary infection and possibility of reinfection are considered. Two thresholds of basic reproduction number R0 and control reproduction number Rc are derived. We get the sufficient conditions for the existence of infection-free equilibrium and endemic equilibrium. The sufficient conditions for the local and global stability of the equilibria are also obtained. Some numerical simulations are performed to prove the theoretical results. At last, some discussions are presented.