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Dynamic analysis of stochastic virus infection model with delay effect

Author

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  • Li, Dongxi
  • Zhao, Yue
  • Song, Shuling

Abstract

This paper mainly investigates the dynamic behavior of virus infection model with delay effect influenced by external noise. First, a mathematical model describing the evolution of virus under the influences of stochastic noise and delay effect is developed. And necessary conditions for extinction and weak persistence are derived by Ito’s formula. A new basic reproduction number R˜0 for virus infection model with delay effect to determine whether extinction or persistence is given. It is found that the delay parameter τ affects the new basic reproduction number R˜0, and the behavior of extinction and survival of virus. Besides, the threshold for extinction of stochastic model is smaller than the one of deterministic model. In the end, stochastic simulations are applied to illustrate and test the theoretical conclusions.

Suggested Citation

  • Li, Dongxi & Zhao, Yue & Song, Shuling, 2019. "Dynamic analysis of stochastic virus infection model with delay effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    • Handle: RePEc:eee:phsmap:v:528:y:2019:i:c:s0378437119308520
    DOI: 10.1016/j.physa.2019.121463
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    Cited by:

    1. Ma, Yuanlin & Yu, Xingwang, 2020. "The effect of environmental noise on threshold dynamics for a stochastic viral infection model with two modes of transmission and immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Igor Sazonov & Dmitry Grebennikov & Mark Kelbert & Andreas Meyerhans & Gennady Bocharov, 2020. "Viral Infection Dynamics Model Based on a Markov Process with Time Delay between Cell Infection and Progeny Production," Mathematics, MDPI, vol. 8(8), pages 1-21, July.

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