一类SEIR传染病模型的稳定性及最优控制策略

Stability and Optimal Control Strategy for a Class of SEIR Infectious Disease Model

考虑了具有常数输入及易感者与潜伏者存在双线性特征的一类SEIR模型,分析了两类平衡点的稳定性:当R0≤1时,无病平衡点全局渐近稳定;当R0>1时,地方病平衡点全局渐进稳定;引入控制决策变量,设定系统满足的性能指标,根据最优控制理论的极小值原理,得到了满足控制约束条件的最优控制策略.算列表明,本文算法是可行且有效的.

A class of SEIR infectious disease model is considered which have the constant input and the dual line feature for the susceptible and the exposed.The stability of two equilibrium are analyzed:if R0≤1,then Disease Free Equilibrium(DFE)is global asymptotically stable,while if R0>1,the Endemic Equilibrium(EE)is global asymptotically stable;The control strategy variance is introduced,the performance index is set for the system,utilizing Minimum Principle based on optimal control theory,the optimal control strategy which satisfy the constraint condition is achieved.The simulating examples demonstrate that the presented method is feasible and effective.