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Stochastic effects of the tumor‐T cell immune model
Author(s) -
Wang Jingnan,
Wang Huadi
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7255
Subject(s) - cytotoxic t cell , tumor cells , extinction (optical mineralogy) , mathematics , immune system , immunology , biology , cancer research , genetics , paleontology , in vitro
To investigate the effects of environmental factors on the tumor growth and the T cell growth, we establish a stochastic tumor‐immune model consisting of cytotoxic T cells and helper T cells. By using the Itô formula and the strong law of large numbers, we prove the existence of globally unique positive solution and obtain the sufficient conditions of the extinction and the weak persistence of tumor cells and T cells. Moreover, according to our obtained theoretical results, we perform some numerical simulations to show that different noise intensities lead to different states of tumor cells, cytotoxic T cells and helper T cells, including extinction and weak persistence, which can be useful for the prevention and control of tumor deterioration and for explaining tumor escape phenomena of clinical medicine.