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The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis

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  • Zhou, Haihua
  • Song, Huijuan
  • Wang, Zejia

Abstract

In this paper, we consider a free boundary problem modeling tumor growth with angiogenesis and time delay in regulatory apoptosis. Two factors are introduced to cause tumor cell death: one is the apoptosis because of exceeding the natural lifespan, the other is the regulatory apoptosis with time delay. The existence, uniqueness and asymptotic behavior of solutions are investigated. The results show that the stabilities of stationary solutions are dramatically affected by such time delay in certain cases, and Hopf bifurcation occurs at some threshold values of time delay. Some numerical simulation results are incorporated supporting the analytical results. The impact of angiogenesis on the Hopf bifurcation is also numerically discussed.

Suggested Citation

  • Zhou, Haihua & Song, Huijuan & Wang, Zejia, 2022. "The effect of time delay in regulatory apoptosis on a tumor model with angiogenesis," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004295
    DOI: 10.1016/j.chaos.2022.112219
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    References listed on IDEAS

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    1. Zhou, Haihua & Wang, Zejia & Yuan, Daming & Song, Huijuan, 2021. "Hopf bifurcation of a free boundary problem modeling tumor growth with angiogenesis and two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Xu, Shihe, 2009. "Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2491-2494.
    3. Rihan, F.A. & Lakshmanan, S. & Maurer, H., 2019. "Optimal control of tumour-immune model with time-delay and immuno-chemotherapy," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 147-165.
    4. Rihan, F.A. & Abdel Rahman, D.H. & Lakshmanan, S. & Alkhajeh, A.S., 2014. "A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 606-623.
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