Table of Contents
Journal of Computational Medicine
Volume 2014, Article ID 654050, 18 pages
http://dx.doi.org/10.1155/2014/654050
Research Article

Transmission Dynamics of Hepatitis C with Control Strategies

Department of Mathematics, Lahore University of Management Sciences, Lahore 54792, Pakistan

Received 29 October 2013; Revised 6 December 2013; Accepted 17 December 2013; Published 13 February 2014

Academic Editor: Darryl D. D'Lima

Copyright © 2014 Adnan Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 , the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for . Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on . In addition, we have presented the numerical simulations to investigate the influence of different important parameters on . 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.