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 ...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.展开更多
In this paper, we propose a semi-continuous dynamical system to study the cooperative system with feedback control. Based on geometrical analysis and the analogue of Poincare criterion, the existence and stability of ...In this paper, we propose a semi-continuous dynamical system to study the cooperative system with feedback control. Based on geometrical analysis and the analogue of Poincare criterion, the existence and stability of the positive order one periodic solutions are given. Numerical results are carried out to illustrate the feasibility of our main results.展开更多
基金supported by the National Natural Science Foundation of China(12071407,11901502)Training plan for young backbone teachers in Henan Province(2019GGJS157)+3 种基金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)Nanhu Scholars Program for Young Scholars of XYNU。
文摘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.
基金Supported by the National Natural Science Foundation of China(11671346,11501489,11371306,11301453)Supported by the Department of Education of Henan Province(14B110034)+1 种基金Supported by the Nanhu Scholars Program of XYNU,Foundation and Frontier Project of Henan(152300410019)Supported by the Youth Teacher Foundation of XYNU(2016GGJJ-14)
文摘In this paper, we propose a semi-continuous dynamical system to study the cooperative system with feedback control. Based on geometrical analysis and the analogue of Poincare criterion, the existence and stability of the positive order one periodic solutions are given. Numerical results are carried out to illustrate the feasibility of our main results.