Article citationsMore>>

Diekmann, O., Heesterbeek, J.P.A. and Metz, J.A.J. (1990) On the Definition and the Computation of the Basic Reproduction Ratio R0 in Models for Infectious Diseases in Heterogeneous Populations. Journal of Mathematical Biology, 28, 365-382.

has been cited by the following article:

• TITLE: The Global Stability Analysis of a Mathematical Cellular Model of Hepatitis C Virus Infection with Non-Cytolytic Process

  AUTHORS: Alexis Nangue, Cyprien Fokoue, Raoue Poumeni

  KEYWORDS: HCV Model, Global Solutions, Non-Cytolytic Process, Invariant Set, Lyapunov Functions, Basic Reproduction Number, Equilibrium Points

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.7, July 24, 2019

  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 .