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Global Properties Of A Model Of Immune Effector Responses To Viral Infections

Author

Listed:
  • XIA WANG

    (Department of Mathematics, Xinyang Normal University, Xinyang 464000 Henan, P. R. China)

  • XINYU SONG

    (Department of Mathematics, Xinyang Normal University, Xinyang 464000 Henan, P. R. China;
    College of Mathematics and Information Science, Henan University, Kaifeng 475001 Henan, P. R. China)

Abstract

This article proposes a mathematical model which has been used to investigate the importance of lytic and non-lytic immune responses for the control of viral infections. By means of Lyapunov functions, the global properties of the model are obtained. The virus is cleared if the basic reproduction numberR0≤ 1and the virus persists in the host ifR0> 1. Furthermore, ifR0> 1and other conditions hold, the immune-free equilibriumE0is globally asymptotically stable. The equilibriumE1exists and is globally asymptotically stale if the CTL immune response reproductive numberR1 1. The equilibriumE2exists and is globally asymptotically stable ifR1> 1andR2 1andR2> 1.

Suggested Citation

  • Xia Wang & Xinyu Song, 2007. "Global Properties Of A Model Of Immune Effector Responses To Viral Infections," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 495-503.
    • Handle: RePEc:wsi:acsxxx:v:10:y:2007:i:04:n:s0219525907001252
    DOI: 10.1142/S0219525907001252
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