随机抗生素耐药性模型的长期性行为  

Long Time Behavior of Stochastic Antibiotic Resistance Model

作　　者：陆桂菊 黄在堂 黄露秋 吕超 潘玉婷 LU Gui-ju;HUANG Zai-tang;HUANG Lu-qiu;LV Chao;PAN Yu-ting(School of Mathematics and Statistics,Nanning Normal University,Nanning 530299,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530299

出　　处：《南宁师范大学学报（自然科学版）》2020年第1期31-42,共12页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金(41665006,11561009);广西自然科学基金(2018GXNSFAA380240)。

摘　　要：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.

关 键 词：随机抗生素耐药性模型 灭绝性 持久性 不变概率测度 遍历性 

分 类 号：R37[医药卫生—病原生物学] O29[医药卫生—基础医学]