具有固定时刻脉冲治疗策略的肿瘤免疫模型的定性分析

Qualitative Analysis of a Tumor-Immune Model with Impulsive Control Strategies at Fixed Times

提出肿瘤免疫模型刻画不同时刻采用药物治疗与免疫治疗策略控制肿瘤的过程.利用微小幅度扰动法,获得在肿瘤灭绝周期解对应的不动点处的雅可比矩阵的特征值,然后得到肿瘤灭绝周期解局部稳定的充分条件.进一步,运用常微分方程解的比较技巧,探究系统具有肿瘤存在周期解的持久性条件.最后,通过数值模拟分析治疗周期对系统的动力学行为的影响.

A tumor-immune model for describing the processes of chemotherapy and immunotherapy at different fixed times was proposed.By using the small amplitude perturbation method,the eigenvalues of the Jacobian matrix at the fixed point corresponding to the tumor-free periodic solution was obtained and then the sufficient condition of its local stability was given.Moreover,the permanence of the system with at least one tumor-present periodic solution was investigated using the comparison techniques of the solutions of ordinary differential equations.Finally,the effects of the therapeutic period on the dynamical behaviors of the system were analyzed by means of numerical simulations.