Dynamic analysis of a fractional-order delayed model for hepatitis B virus with CTL immune response

Ruiqing Shi; Ting Lu; Cuihong Wang

doi:10.1016/j.virusres.2019.197841

Dynamic analysis of a fractional-order delayed model for hepatitis B virus with CTL immune response

Virus Res. 2020 Feb:277:197841. doi: 10.1016/j.virusres.2019.197841. Epub 2019 Dec 27.

Authors

Ruiqing Shi¹, Ting Lu², Cuihong Wang³

Affiliations

¹ School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China. Electronic address: shirq1979@163.com.
² School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China. Electronic address: 1300757652@qq.com.
³ School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China. Electronic address: sxwangcuihong@163.com.

PMID: 31887328
DOI: 10.1016/j.virusres.2019.197841

Abstract

In this paper, a fractional-order delayed model with Holling II functional response and CTL immune response is constructed to describe the transmission of hepatitis B virus. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of three equilibriums are obtained. Thirdly, the stability of three equilibriums are investigated. In addition, some sufficient conditions for the occurrence of Hopf bifurcation near the endemic equilibrium are demonstrated by using time delay as the bifurcation parameter. After that, some numerical simulations are performed to verify the theoretical prediction. At last, a brief discussion is presented to end this paper.

Keywords: Basic reproduction number; CTL immuneresponse; Fractional-order; Hepatitis B virus; Hopf bifurcation.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Basic Reproduction Number
Computer Simulation
Hepatitis B virus / immunology*
Humans
Immunity, Cellular*
Models, Theoretical*
T-Lymphocytes, Cytotoxic / immunology*
Time Factors