Optimal control analysis of hepatitis C virus with acute and chronic stages in the presence of treatment and infected immigrants

Abstract

In this paper, we consider a deterministic hepatitis C virus (HCV) model and study the impact of optimal control on the screening of immigrants and treatment of HCV on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles. First, we derived the condition in which disease-free equilibrium is locally asymptotically stable and established that a stable disease-free equilibrium can only be achieved in the absence of infective immigrants. Second, we investigated the impact of each control mechanism individually and the combinations of these strategies in the control of HCV. The costs associated with each of these strategies are also investigated by formulating the costs function problem as an optimal control problem, and we then use the Pontryagin's Maximum Principle to solve the optimal control problems. From the numerical simulations we found that the optimal combination of treatment of acute-infected and chronic-infected individuals control strategy produced the same results as the combination of the three strategies (combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals). By our model and these results, we suggest the treatment of acute-infected and chronic-infected individuals control strategy should be optimized where resources are scarce, because the implementation of the three strategies (combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals) would imply additional cost.