Mathematical analysis of an extended cellular model of the Hepatitis C Virus infection with non-cytolytic process

Autor:	Nangue, Alexis, Fokoue, Cyprien, Poumeni, Raoue
Rok vydání:	2019
Předmět:	Mathematics - Dynamical Systems Quantitative Biology - Populations and Evolution 92B99 34D23 92D25 37C75 93DXX
Druh dokumentu:	Working Paper
Popis:	The aims of this work is to analyse of the global stability of the extended model of hepatitis C virus(HCV) infection with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We first give general information about hepatitis C. Secondly, We prove the existence of local, maximal and global solutions of the model and establish some properties of this solution as positivity and asymptotic behaviour. Thirdly we show, by the construction of an appropriate Lyapunov function, that the uninfected equilibrium and the unique infected equilibrium of the model of HCV are globally asymptotically stable respectively when the threshold number $\mathcal{R}_{0}<1-\frac{q}{d_{I}+q}$ and when $\mathcal{R}_{0}>1$. Finally, some numerical simulations are carried out using Maple software confirm these theoretical results. Comment: 48 PAGES
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.02561 Zobrazit plný text záznamu View this record from Arxiv