Qualitative investigation of cytolytic and noncytolytic immune response in an HBV model

Alford, John G.; McCoy, Stephen A.

doi:10.2140/involve.2020.13.455

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Qualitative investigation of cytolytic and noncytolytic immune response in an HBV model

John G. Alford and Stephen A. McCoy

Vol. 13 (2020), No. 3, 455–474

DOI: 10.2140/involve.2020.13.455

Abstract

We investigate a mathematical model of infection by the hepatitis B virus (HBV) that includes cytolytic and noncytolytic immune response. The model exhibits a variety of steady-state solutions depending on parameter values, including nonunique and unique equilibrium solutions and periodic behavior. The disease-free equilibrium $E_{f}$ and the positive-disease equilibrium $E_{d}$ are examined. The basic reproduction ratio $R_{0}$ is computed in order to examine the uniqueness and local asymptotic stability of equilibria and to understand the model’s biological implications for HBV dynamics.

Keywords

mathematical model, hepatitis B viral dynamics, immune response

Mathematical Subject Classification 2010

Primary: 92C60

Milestones

Received: 26 October 2019

Revised: 12 March 2020

Accepted: 14 March 2020

Published: 14 July 2020

Communicated by Martin J. Bohner

Authors

John G. Alford
Department of Mathematics and Statistics Sam Houston State University Huntsville, TX United States

Stephen A. McCoy
Department of Mathematics University of Tennessee Knoxville, TN United States

Vol. 13, No. 3, 2020