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Multiple recurrent outbreak cycles in an autonomous epidemiological model due to multiple limit cycle bifurcation

发布者:澳门新葡8455最新网站   发布时间:2018-06-13  浏览次数:61



系列学术活动之(32

题    目:

Multiple recurrent outbreak cycles in an autonomous epidemiological                

model due to multiple limit cycle bifurcation

摘    要:

Multiple recurrent outbreak cycles have been commonly observed in infectious

diseases such as measles and chicken pox. This complex outbreak dynamics in

epidemiologicals is rarely captured by deterministic models. In this talk,  we present a simple 2-dimensional SI epidemiological model and propose that the coexistence of multiple attractors attributes to the complex outbreak  patterns. We first determine the conditions on parameters for the existence of an isolated center, then properly perturb the model to generate Hopf bifurcation and obtain limit cycles around the center. We further analytically  prove that the maximum number of the coexisting limit cycles is three, and provide a corresponding set of parameters for the existence of the three limit cycles. Simulation results demonstrate the case with the maximum  coexisting attractors, which contains one stable disease free equilibrium and two stable endemic periodic solutions separated by one unstable periodic solution. Therefore, different disease outcomes can be predicted by a single

nonlinear deterministic model based on different initial data.

报 告 人:

郁培,教授,加拿大西安大略大学

时    间:

201861508:30-10:00

地    点:

明义-204

报告人概况:

郁培,加拿大西安大略大学(western university, canada)教授,博士生导师,常微分方程与动力系统领域著名专家,在非线性和混沌动力系统、稳定性理论和分支理论、微分方程的计算问题、生物数学以及物理和工程系统的应用问题等做出了杰出的工作。曾获安大略省长杰出研究奖,和合编辑在《siam review》等杂志发表近200篇论文以及springer等出版社出版了多部专著,其中《normal forms, melnikov functions and bifurcation of limit cycles》被列为applied mathematical sciences181册,2012年在springer出版。郁培教授任《journal of applied analysis and computation》、《international journal of bifurcation and chaos》与《communications in nonlinear science and numerical simulation》等国际知名杂志编委。







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