Optimal control of HCV transmission under liquoring.

Chronic hepatitis C virus (HCV) and alcohol are common causes of chronic liver diseases and both are recognized as major causes of liver disease worldwide. Each poses a major public and economic burden to society, and when the two co-exist they appear to have a synergistic effect in the progression of chronic liver disease. In this research, we developed a SIRS model of transmission of the hepatitis C virus (HCV) under effect of liquoring in six compartments: Susceptible, Low liquoring, High liquoring, Acute, Chronic and Recovered Individuals. The system of non-linear ordinary differential equations is formulated. Basic reproduction number R is computed using the next generation matrix approach. The stability of the model is worked out at the equilibrium point. Model analysis shows that the disease-free equilibrium point is both locally and globally asymptotically stable. Sensitivity analysis with respect to key parameters of R indicates that control strategies should target reduction of the amount of alcohol use amongst people with HCV as it prevents or delays HCV disease progression. The control in our model is in terms of rehabilitation center which helps people to divert from high liquoring to low liquoring. Numerical simulation has been carried out to show the impact of control on different compartment. This research shows the positive impact of rehabilitation on liquoring habits and subsequently on HCV transmission.