Stability and Hopf bifurcation analysis for an HIV infection model with Beddington–DeAngelis incidence and two delays

  • Hui MiaoEmail author
  • Chengjun Kang
Original Research


In this paper, we investigate the dynamical properties for a model of delayed differential equations which describes a virus–immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. The model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria for the CTL immune response model has been studied.


HIV infection model Equilibrium Local and global stability Lyapunov functional Hopf bifurcation 

Mathematics Subject Classification (2010)

93D05 93D20 37G99 



The authors are very grateful to the reviewers for their careful reading and helpful suggestions that greatly improved the presentation of this paper. This work was supported by the Youth Research Fund for the Shanxi University of Finance and Economics (Grant no. QN-2018007), starting Fund for the Shanxi University of Finance and Economics doctoral graduates research (Grant nos. Z18116 and Z24024), the Youth Research Fund for the Shanxi basic research project (2015021025), the National Natural Science Foundation of China (Grant nos. 11771373 and 11661076) and the Natural Science Foundation of Xinjiang (Grant no. 2016D03022).


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.School of Applied MathematicsShanxi University of Finance and EconomicsTaiyuanPeople’s Republic of China

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