Local and Global Stabilities of a Viral Dynamics Model with Infection-Age and Immune Response

Jianhua Pang, Jing Chen, Zijian Liu, Ping Bi, Shigui Ruan

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

In this paper, we construct an infection-age model to study the interaction between viruses and the immune system within the host. In the model, the mortality rate of infected cells, the rate that cytotoxic T lymphocytes (CTL) kill infected cells, the rate that infected cells produce new virus, and the CTL proliferate rate may depend on the infection-age. The basic reproduction number and the threshold for the existence of steady states are obtained. Local stability of both the infection-free and infection steady states is studied by analyzing the linearized systems. Global stability of the infection-free steady state is obtained by investigating a renewal integral equation and global stability of the infection steady state is obtained by constructing a Liapunov functional. Numerical simulations are presented to verify the theoretical results.

Original languageEnglish (US)
Pages (from-to)793-813
Number of pages21
JournalJournal of Dynamics and Differential Equations
Volume31
Issue number2
DOIs
StatePublished - Jun 1 2019

Keywords

  • Age-structured model
  • Integrated solution
  • Liapunov functional
  • Local and global stabilities
  • Viral dynamics

ASJC Scopus subject areas

  • Analysis

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