南京师大学报（自然科学版）Issue(1)：1-7,7.
具有标准发生率和脉冲干扰的SIRS传染病模型分岔分析
The Bifurcation Analysis of an SIRS Epidemic Model with Standard Incidence and Impulsive Perturbations
摘要
Abstract
Birth pulse,vertical transmission,and pulse treatment are considered in an SIRS model. The dynamical behav-ior of an SIRS epidemic model with standard incidence is discussed by means of both theoretical and numerical ways. Firstly,by using Floquet theory,the existence and stability of the trivial solution,infection-free periodic solution,and epi-demic periodic solution are proved. Secondly,the Poincare map,center manifold theorem,and bifurcation theorem are used to discuss transcritical bifurcation and flip bifurcation.The numerical results,which are illustrated with an example, are in good agreement with the theoretical analysis. Finally,biological explanations and main conclusions are given.关键词
SIRS模型/标准发生率/跨临界分岔/flip分岔Key words
SIRS model/standard incidence/transcritical bifurcation/flip bifurcation分类
数理科学引用本文复制引用
蒋贵荣,林娇,刘苏雨..具有标准发生率和脉冲干扰的SIRS传染病模型分岔分析[J].南京师大学报（自然科学版）,2015,(1):1-7,7.基金项目
国家自然科学基金(11162004)、广西自然科学基金(2012GXNSFAA053006)、广西研究生教育创新计划项目(YCSZ2014143) （11162004）
