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Computational and Applied Mathematics

, Volume 37, Issue 3, pp 3780–3805 | Cite as

Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response

  • Hui Miao
  • Zhidong Teng
  • Xamxinur Abdurahman
  • Zhiming Li
Article
  • 88 Downloads

Abstract

In this paper, the dynamical behaviors for a five-dimensional virus infection model with diffusion and two delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and a general incidence function are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion, intracellular delay and production delay are obtained by the numerical simulations.

Keywords

Virus infection model Delay Adaptive immune response Diffusion General incidence function Global stability 

Mathematics Subject Classification

34D40 35Q92 92B05 

Notes

Acknowledgements

This work was supported by the Natural Science Foundation of Shanxi University of Finance and Economics (Starting Fund for the Shanxi University of Finance and Economics doctoral graduates research, Grant No. Z18116), the National Natural Science Foundation of China (Grant nos. 11771373 and 11661076), the Natural Science Foundation of Xinjiang (Grant no. 2016D03022) and the Doctorial Subjects Foundation of the Ministry of Education of China (Grant no. 2013651110001).

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • Hui Miao
    • 1
  • Zhidong Teng
    • 2
  • Xamxinur Abdurahman
    • 2
  • Zhiming Li
    • 2
  1. 1.School of Applied MathematicsShanxi University of Finance and EconomicsTaiyuanPeople’s Republic of China
  2. 2.College of Mathematics and System SciencesXinjiang UniversityUrumqiPeople’s Republic of China

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