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Hopf bifurcation analysis of a tumor virotherapy model with two time delays

Author

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  • Li, Hui-zhong
  • Liu, Xiang-dong
  • Yan, Rui
  • Liu, Cheng

Abstract

Oncolytic virotherapy is gradually applied in clinical trial, which provides a new potential approach to cancer treatment. Tumor volume doubling time (TVDT) is so short that the infection delay caused by oncolytic virus should be considered in the modeling of virotherapy. A DDE model is constructed by adding two infection delays based on an ODE model that describes the dynamics of cancer cells, tumor cells, immune cells and oncolytic viruses. According to the different values of two delays, three cases of the model are discussed to investigate the stability and bifurcation of both the virus-free equilibrium and the positive equilibrium. Finally, some numerical simulations are performed to verify the obtained theoretical conclusions based on clinical trial data.

Suggested Citation

  • Li, Hui-zhong & Liu, Xiang-dong & Yan, Rui & Liu, Cheng, 2020. "Hopf bifurcation analysis of a tumor virotherapy model with two time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    • Handle: RePEc:eee:phsmap:v:553:y:2020:i:c:s037843712030073x
    DOI: 10.1016/j.physa.2020.124266
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    References listed on IDEAS

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    1. Kim, Kwang Su & Kim, Sangil & Jung, Il Hyo, 2018. "Hopf bifurcation analysis and optimal control of Treatment in a delayed oncolytic virus dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 1-16.
    2. Wang, Xia & Song, Xinyu & Tang, Sanyi & Rong, Libin, 2016. "Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 87-103.
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    Cited by:

    1. Wang, Jingnan & Shi, Hongbin & Xu, Li & Zang, Lu, 2022. "Hopf bifurcation and chaos of tumor-Lymphatic model with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Amine, Saida & Hajri, Youssra & Allali, Karam, 2022. "A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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