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Analysis of a Viral Infection Model with Delayed Nonlytic Immune Response

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  • Mengye Chen
  • Liang You
  • Jie Tang
  • Shasha Su
  • Ruiming Zhang

Abstract

We investigate the dynamical behavior of a virus infection model with delayed nonlytic immune response. By analyzing corresponding characteristic equations, the local stabilities of two boundary equilibria are established. By using suitable Lyapunov functional and LaSalle’s invariance principle, we establish the global stability of the infection-free equilibrium. We find that the infection free equilibrium is globally asymptotically stable when , and the infected equilibrium without immunity is local asymptotically stable when . Under the condition we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity . We show that the time delay can change the stability of and lead to the existence of Hopf bifurcations. The stabilities of bifurcating periodic solutions are studied and numerical simulations to our theorems are provided.

Suggested Citation

  • Mengye Chen & Liang You & Jie Tang & Shasha Su & Ruiming Zhang, 2015. "Analysis of a Viral Infection Model with Delayed Nonlytic Immune Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-11, May.
    • Handle: RePEc:hin:jnddns:235420
    DOI: 10.1155/2015/235420
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