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

Haihua Zhou, Huijuan Song and Zejia Wang

Chaos, Solitons & Fractals, 2022, vol. 160, issue C

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.

Keywords: Tumor model; Free boundary problem; Angiogenesis; Time delay; Hopf bifurcation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004295

DOI: 10.1016/j.chaos.2022.112219

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