Dynamical Behaviors of the Tumor-Immune System in a Stochastic Environment
| Autor: | Xiaoyue Li, Chenggui Yuan, Guoting Song, Yang Xia |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Comparison theorem
Physics Immunogen Quantitative Biology::Tissues and Organs Applied Mathematics Probability (math.PR) Ergodicity chemical and pharmacologic phenomena 01 natural sciences Quantitative Biology::Cell Behavior 010101 applied mathematics Immune system FOS: Mathematics Cytotoxic T cell Invariant measure 0101 mathematics Environmental noise Biological system Mathematics - Probability |
| Zdroj: | SIAM Journal on Applied Mathematics. 79:2193-2217 |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/19m1243580 |
| Popis: | This paper investigates dynamic behaviors of the tumor-immune system perturbed by environmental noise. The model describes the response of the cytotoxic T lymphocyte (CTL) to the growth of an immunogenic tumour. The main methods are stochastic Lyapunov analysis, comparison theorem for stochastic differential equations (SDEs) and strong ergodicity theorem. Firstly, we prove the existence and uniqueness of the global positive solution for the tumor-immune system. Then we go a further step to study the boundaries of moments for tumor cells and effector cells and the asymptotic behavior in the boundary equilibrium points. Furthermore, we discuss the existence and uniqueness of stationary distribution and stochastic permanence of the tumor-immune system. Finally, we give several examples and numerical simulations to verify our results. Comment: arXiv admin note: text overlap with arXiv:q-bio/0602015 by other authors |
| Databáze: | OpenAIRE |
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