Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STABILITY PROPERTIES OF A DELAYED VIRAL INFECTION MODEL WITH LYTIC IMMUNE RESPONSE

  • Song, Fang (School of Electronics and Information Engineering, Tongji University) ;
  • Wang, Xia (College of Mathematics and Information Science, Xinyang Normal University) ;
  • Song, Xinyu (College of Mathematics and Information Science, Xinyang Normal University)
  • Received : 2010.08.10
  • Accepted : 2010.10.19
  • Published : 2011.09.30
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Abstract

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

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References

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