Abstract
The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We firstly prove the existence of local and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Secondly we show, by the construction of appropriate Lyapunov functions, that the uninfected equilibrium and the unique infected equilibrium of the mathematical model of HCV are globally asymptotically stable respectively when the threshold number and when .
Highlights
IntroductionAccording to [1] [2], approximately 200 million people worldwide are persistently infected with the hepatitis C virus (HCV) and are at risk of developing chronic liver disease, cirrhosis, and hepatocellular carcinoma
The aim of this work is to analyse the global dynamics of an extended mathematical model of Hepatitis C virus (HCV) infection in vivo with cellular proliferation, spontaneous cure and hepatocyte homeostasis
According to [1] [2], approximately 200 million people worldwide are persistently infected with the hepatitis C virus (HCV) and are at risk of developing chronic liver disease, cirrhosis, and hepatocellular carcinoma
Summary
According to [1] [2], approximately 200 million people worldwide are persistently infected with the hepatitis C virus (HCV) and are at risk of developing chronic liver disease, cirrhosis, and hepatocellular carcinoma. HCV infection represents a significant global public health problem. HCV establishes chronic hepatitis in 60% - 80% of infected adults [3]. A model of human immunodeficiency virus infection was adapted by Neumann et al [4] to study the kinetics of chronic HCV infection during treatment and some mathematical analysis was done by [5]. In this paper we are going to study global dynamics of an HCV infection mathematical model with full logistic terms, antivirus treatments and homeostasis phenomenon. Nangue [8] concerning a mathematical intracellular HCV infection model with therapy
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