Global Stability of Disease-Free Equilibrium for an Acute Hepatitis C Virus Transmission Dynamics Model

Abstract

Global stability of disease-free equilibrium (DFE) of a deterministic epidemiological model describes the state of no infection that can eventually be reached in the absence of intervention, suggesting that the system can be deliberately intervened. This paper presents a global stability analysis of DFE,  obtained from an acute hepatitis C virus (HCV) transmission dynamics model that incorporates the dynamic effectors: immune response, hepatocytes proliferation and spontaneous clearance of the virus. The analysis was accomplished with calculated from the model system of equations at using the Metzler matrix method. With the parameter threshold, being a determining factor of the transmission of HCV infection, both the analytical results and simulation results have established the conditions for global stability of DEF. Precisely, the results show that the basic reproductive number,   remains below unity, , despite initial values of the state variables. Thus, there should be a timely strategic intervention to eradicate the disease by ensuring that the basic reproductive number is strictly less than unity.