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

doi:10.1007/s10473-022-0319-1

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 1141-1159.doi: 10.1007/s10473-022-0319-1

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

黄明湛¹, 刘守宗¹, 宋新宇¹, 邹秀芬²

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

收稿日期:2020-12-18 修回日期:2021-04-11 出版日期:2022-06-26 发布日期:2022-06-24
通讯作者: Xinyu SONG,E-mail:xysong88@163.com E-mail:xysong88@163.com
基金资助:
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.

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

Mingzhan HUANG¹, Shouzong LIU¹, Xinyu SONG¹, Xiufen ZOU²

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 Online:2022-06-26 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.

摘要/Abstract

摘要： 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.

关键词: Tumor-immune system, chemotherapy, stochastic impulsive model, extinction, persistence

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

中图分类号:

92C50

黄明湛, 刘守宗, 宋新宇, 邹秀芬. CONTROL STRATEGIES FOR A TUMOR-IMMUNE SYSTEM WITH IMPULSIVE DRUG DELIVERY UNDER A RANDOM ENVIRONMENT[J]. 数学物理学报, 2022, 42(3): 1141-1159.

Mingzhan HUANG, Shouzong LIU, Xinyu SONG, Xiufen ZOU. CONTROL STRATEGIES FOR A TUMOR-IMMUNE SYSTEM WITH IMPULSIVE DRUG DELIVERY UNDER A RANDOM ENVIRONMENT[J]. Acta mathematica scientia,Series A, 2022, 42(3): 1141-1159.

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

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

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