一类时滞免疫反应系统动力学行为仿真

研究一类时滞免疫反应系统在机体清除靶细胞能力对浆细胞增长有影响的情形下的动力学行为,用时滞微分理论证明系统正平衡点的稳定性与时滞的关系,给出其稳定判定方法。在模型解基础上,用仿真方法研究部分参数变化对系统动力学行为的影响,给出了免疫系统呈现不同动力学行为的参数范围,实现免疫系统动态特性的仿真。结果表明,对于给定时滞,免疫反应系统的动力学行为不敏感地依赖于抗体清除抗原速率,而敏感地依赖于抗原繁殖系数。

Dynamical Behavior Simulation for Immune Reaction System with Time Delays

The dynamical behavior of a class of immune reaction systems with time delays was investigated under the condition that plasma cells increase was influenced by ability of organ eliminating target cells. In terms of delay differential equation theory, the connection between positive equilibrium stability and time delays was proved, and the stable criterion of the model was proposed. Based on numerical solutions of the model, the dynamical behavior affected by partial parametric variation was studied via simulation. Parameter setting was concluded when immune systems showed various dynamical behaviors, and simulation results for the dynamical property of immune systems were achieved. It is shown that, for a given delay, the dynamical behavior of immune reaction systems depends sensitively on antigenic propagation coefficients, instead of the speed rate of antigenic elimination.