Analysis of a time-delayed mathematical model for tumour growth with an almost periodic supply of external nutrients

Xu, Shihe; Meng, Bo; Zhang, Fangwei

doi:10.1080/17513758.2017.1386804

Cited by 6 publications

(1 citation statement)

References 23 publications

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“…These models are based on mass conservation laws and reaction‐diffusion processes for cell densities and nutrient concentrations within the tumor. Mathematical analysis of such models has drawn considerable attention, and many interesting results have been derived in literatures and references given there. Lowengrub et al provided a systematic survey of tumor model studies.…”

Section: Introductionmentioning

confidence: 99%

Linear stability for a free boundary tumor model with a periodic supply of external nutrients

Huang

Zhang

2018

Math Methods in App Sciences

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In this paper, we consider a free boundary tumor model with a periodic supply of external nutrients, so that the nutrient concentration satisfies = (t) on the boundary, where (t) is a positive periodic function with period T. A parameter in the model is proportional to the "aggressiveness" of the tumor.If 0 <̃< min 0≤t≤T (t), wherẽis a threshold concentration for proliferation, Bai and Xu [Pac J Appl Math. 2013;5;217-223] proved that there exists a unique radially symmetric T-periodic positive solution ( * (r, t), p * (r, t), R * (t)), which is stable for any > 0 with respect to all radially symmetric perturbations. 17 We prove that under nonradially symmetric perturbations, there exists a number * such that if 0 < < * , then the T-periodic solution is linearly stable, whereas if > * , then the T-periodic solution is linearly unstable.

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Section: Introductionmentioning

confidence: 99%