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

2 Citations (Scopus)

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)1-21
Number of pages21
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - Apr 28 2018

Fingerprint

Immune Response
Local Stability
Global Stability
Infection
Dynamic Model
T Lymphocytes
Virus
Cell
Liapunov Functional
Renewal Equation
Basic Reproduction number
Mortality Rate
Immune System
Integral Equations
Verify
Numerical Simulation
Interaction
Model

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

Local and Global Stabilities of a Viral Dynamics Model with Infection-Age and Immune Response. / Pang, Jianhua; Chen, Jing; Liu, Zijian; Bi, Ping; Ruan, Shigui.

In: Journal of Dynamics and Differential Equations, 28.04.2018, p. 1-21.

Research output: Contribution to journalArticle

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