Mathematics Faculty Articles

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

Document Type

Article

Publication Date

4-28-2018

Publication Title

Journal of Dynamics and Differential Equations

Keywords

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

ISSN

1040-7294

First Page

1

Last Page

21

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.

Comments

©Springer Science+Business Media, LLC, part of Springer Nature 2018

Additional Comments

National Natural Science Foundation of China grant #s: 11401117, 11401060, 11401217, 11771168; Improvement Project for Young Teachers of Guangxi Province grant #: KY2016YB246; NSF grant #: DMS-1412454

DOI

10.1007/s10884-018-9663-1

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