一类具有转移和治疗机制的随机结核病模型的平稳分布与灭绝

Stationary Distribution and Extinction of a Stochastic Tuberculosis Model with Immigration and Treatment Mechanism

考虑一类具有转移和治疗机制的肺结核传播模型在随机扰动下的动力学行为.首先,通过Lyapunov分析方法得到该模型正解的存在和唯一性;然后利用Has’minskii理论证明该模型存在唯一的平稳分布;最后通过随机分析方法得到该模型疾病消失的条件.

We considered a dynamic behavior of a class of tuberculosis transmission model with immigration and treatment mechanism under random perturbations.Firstly,the existence and uniqueness of a positive solution of the model were obtianed by Lyapunov analysis method.Secondly,it was proved that the model had unique stationary distribution by using Has’minskii theory.Finally,the conditions for extinction of the disease were obtained by stochastic analysis method.