Mathematical model of immune response to Hepatitis C virus (HCV) disease

Abstract

This paper presents a mathematical model that comprehensively analyzes the dynamics of Hepatitis C Virus (HCV) infection. The model based on a system of nonlinear differential equations captures the interactions between liver cells (hepatocytes), the Hepatitis C virus, immune cells, and cytokines dynamics. We establish the well-posedness of the model within a biologically feasible region. Using the next-generation method, we calculate the basic reproduction number, ${\Re }_0$, a threshold parameter that determines whether the infection will spread or die. A sensitivity analysis is also performed to identify the parameters that most significantly influence this number. We derive the conditions for the stability of disease-free and endemic equilibrium. The model is then used to investigate the system’s behavior under various scenarios: a weak immune response, the absence of T helper cell support, and a strong immune response. Our simulations show that the lack of interleukin-2 (IL-2) significantly affects the activation of cytotoxic T lymphocyte (CTLs). These results underscore the importance of including T helper cells, Interferon$-\gamma$ (IFN-$\gamma$) and IL-2 for an accurate representation of the dynamics of hepatitis C virus infection. Ultimately, this study deepens our understanding of the dynamics of HCV infection and simplifies how specific immune components shape the course of the disease.