Homotopy Analysis of Explicit Solutions in a Chronic Hepatitis C Virus Model

Abstract

Mathematical analysis of nonlinear models in epidemiology has gen- erated a deep interest in gaining insights into the mechanisms that underlie hepatitis C virus (HCV) infections. In this article, we provide a study of a chronic HCV infection model with immune response, incorporating the effect of dendritic cells (DC) and cytotoxic T lymphocytes (CTL). Considering very recent developments in the literature related to the Homotopy Analysis Method (HAM), we calculate the explicit series solutions of the HCV model, focusing our analysis on a particu- lar set of dynamical variables. An optimal homotopy analysis approach is used to improve the computational efficiency of HAM by means of appropriate values for a convergence control parameter, which greatly accelerates the convergence of the series solutions. The approximated analytical solutions, with the variation of a parameter representing the expansion rate of CTL, are used to compute density plots, which allow us to discuss additional dynamical features of the model.