Mathematical modelling of HCV infectiology in a community with inflow of infected immigrants

Abstract

This paper examines the HCV infectiology in a community with inflow of infected immigrants. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. The disease free produced stable equilibrium for the threshold parameter less than unity (R0<1), while the backward bifurcation for endemic equilibrium is unstable and the forward bifurcation for endemic equilibrium at is stable. A recovered individual loses immunity and become immediately susceptible again. However the disease becomes more endemic due to the presence of infected immigrants in the community. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the HCV infectiology in a community with inflow of infected immigrants.