免疫响应系统的全局稳定性

The Global Stability of the Immune-response System

研究了免疫响应系统无病平衡点和正平衡点的全局稳定性问题.通过构造合适的Lyapunov函数,得到了该系统各个平衡点的全局稳定性条件.结果表明,该系统当只有一个平衡点—无病平衡点时,其必然是全局稳定的;当参数变化导致出现新的平衡点—地方病平衡点时,它也必然是全局稳定的.理论和数值结果非常吻合,表明推导的结果是正确的.该结果的生理意义非常清楚,表明了治疗对此系统的动力学影响是关键性的,对患者的康复是非常重要的.

The global stability of the disease-free equilibrium and the epidemic equilibrium in the immune-response system is studied.By constructing the appropriate Lyapunov functions,the conditions of the global stability of both the equilibria are obtained.The obtained results show that the disease-free equilibrium must be globally stable if it is the only one,but as the parameter c varies,the epidemic equilibrium will be born and must be globally stable.The theoretical results are in good agreement with those from...