医院内抗生素耐药性传染的稳定性与Hopf分支  

Stability and Hopf Bifurcation about the Antibiotic Resistance with Infection in Nosocomial

作　　者：马佳辉[1] 薛亚奎[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2015年第3期261-267,共7页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10901145);山西省自然科学基金资助项目(2009011005-1和2012011002-1);山西省百人计划

摘　　要：研究了医院内感染的带有非线性发生率的抗生素耐药性的时滞传染病模型的稳定性.确定了疾病暴发的阈值R0,运用Lasalle-Liapunov不变集原理和Routh-Hurwitz判据得到了,当R0<1时无病平衡点是全局稳定的;当R0>1时,地方病平衡点存在且唯一,对于任意的τ≠0,总能得到在地方病平衡点处的Hopf分支存在的条件.最后通过数值模拟验证了结论的正确性.The stability of a delay infectious disease model about the antibiotic resistance with nonlinear incidence rate in hospitals was investigated.The threshold value R0 which determines the outbreak of infectious disease was found,Using Lasalle-Liapunov invariant set principle and Routh-Hurwitz criterion can draw such conclusions that when R0〈1,the disease-free equilibrium is globally asymptotically stable;If R0〉1,the endemic equilibriums of the model is exist and unique,for anyτ≠0the existence conditions for Hopf bifurcations at the endemic equilibrium always can be obtained.Finally a series of numerical simulations are presented to illustrate the mathematical findings.

关 键 词：时滞模型 非线性发生率 HOPF分支 抗生素耐药性 

分 类 号：O175[理学—数学]