脉冲免疫控制肿瘤生长模型的动力学性质  

Dynamic Properties of Tumor Growth Control Models with Impulsive Immunization

作　　者：王晶囡[1] 杨占文[2] 吕静[1] 蒋卫华[3] 张艳桥[4] 

机构地区：[1]哈尔滨理工大学应用数学系,黑龙江哈尔滨150080 [2]哈尔滨工业大学理学研究中心,黑龙江哈尔滨150001 [3]哈尔滨工业大学数学系,黑龙江哈尔滨150001 [4]哈尔滨医科大学附属肿瘤医院消化内科,黑龙江哈尔滨150081

出　　处：《生物数学学报》2016年第3期327-334,共8页Journal of Biomathematics

基　　金：黑龙江省教育厅项目(12541168);中央高校基本科研业务费专项经费资助(项目资助编号:HIT.IBRS EM.201332);黑龙江省青年科学基金项目(QC2014C003)

摘　　要：本文建立了一个具周期脉冲免疫控制肿瘤生长的微分方程模型,主要用来描述在固定时间段、瞬时注入的免疫效应细胞对肿瘤生长的影响.运用脉冲微分方程的比较定理和Floquet乘子理论,分析了模型的动力学性质,得到解的有界性与无肿瘤周期解的存在条件,数值模拟支持所得到的理论结果.最后,在数值上比较了常值输入和脉冲输入免疫效应细胞的疗效,展示了后者在控制肿瘤细胞生长方面具有优势.In this paper,we establish the differential equation model of controlling tumor growth with impulsive immunization,which is used to describe the effect of instantaneous injection of immune-effector cells in the fixed time interval on tumor growth.Using the comparison theorem of impulsive differential equation and the Floquet multipliers theory,we analyze the dynamic properties of the model,and obtain the boundedness of solutions and the existence conditions of periodic solutions without tumor.Some numerical simulations are performed to support the obtained theoretical results.Finally,we compare the treatment effects between the constant injection and the impulsive injection of immune-effector cells by numerical simulations,which shows that the impulsive injection has advantages in controlling the tumor cells growth.

关 键 词：肿瘤生长模型 周期解 脉冲控制 

分 类 号：O175.1[理学—数学] O193[理学—基础数学]