Transmission Dynamics of Hepatitis C with Control Strategies

Abstract

We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R 0 ≤ 1 , the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R 0 > 1 . Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R 0 . In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R 0 . Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.