随机抗生素耐药性模型的长期性行为

Long Time Behavior of Stochastic Antibiotic Resistance Model

该文主要研究了具有Beddington DeAngelis发生率的随机抗生素耐药性模型的持久性和遍历性.首先,利用鞅不等式、不变控制集和Portmanteau定理等知识,证明了随机抗生素耐药性模型的不变概率测度的存在唯一性.其次,运用强大数定理、李代数、支撑理论和Feller性质等知识,得到模型的解在总变差范数中收敛于稳定分布,即细菌持久性.最后,证明了模型的解过程的遍历性.

This paper mainly studies the persistence and ergodicity of a stochastic antibiotic resistance model with Beddington DeAngelis incidence.First,through martingale inequality,invariant control set and portmanteau theorem,etc,we proved the existence and uniqueness of the invariant probability measure of stochastic antibiotic resistance model.Secondly,by strong number theorem,Lie algebra,support theory and Feller property,the solution of the model converges to a stationary distribution in the total variation norm,the convergence speed is bounded,in other words,the bacteria is permanent.Furthermore,the ergodicity of the solution process of the model is proved.