Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (3): 1141-1159.doi: 10.1007/s10473-022-0319-1

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CONTROL STRATEGIES FOR A TUMOR-IMMUNE SYSTEM WITH IMPULSIVE DRUG DELIVERY UNDER A RANDOM ENVIRONMENT

Mingzhan HUANG1, Shouzong LIU1, Xinyu SONG1, Xiufen ZOU2   

  1. 1. College of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China;
    2. School of Mathematics and Statistics, Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, China
  • Received:2020-12-18 Revised:2021-04-11 Published:2022-06-24
  • Contact: Xinyu SONG,E-mail:xysong88@163.com E-mail:xysong88@163.com
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (12071407, 11901502), Training plan for young backbone teachers in Henan Province (2019GGJS157), Foundation of Henan Educational Committee under Contract (21A110022), Program for Science & Technology Innovation Talents in Universities of Henan Province (21HASTIT026), Scientific and Technological Key Projects of Henan Province (212102110025) and Nanhu Scholars Program for Young Scholars of XYNU.

Abstract: This paper mainly studies the stochastic character of tumor growth in the presence of immune response and periodically pulsed chemotherapy. First, a stochastic impulsive model describing the interaction and competition among normal cells, tumor cells and immune cells under periodically pulsed chemotherapy is established. Then, sufficient conditions for the extinction, non-persistence in the mean, weak and strong persistence in the mean of tumor cells are obtained. Finally, numerical simulations are performed which not only verify the theoretical results derived but also reveal some specific features. The results show that the growth trend of tumor cells is significantly affected by the intensity of noise and the frequency and dose of drug deliveries. In clinical practice, doctors can reduce the randomness of the environment and increase the intensity of drug input to inhibit the proliferation and growth of tumor cells.

Key words: Tumor-immune system, chemotherapy, stochastic impulsive model, extinction, persistence

CLC Number: 

  • 92C50
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