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Dynamic analysis of the recurrent epidemic model

1 Department of Mathematics, Shaanxi University of Science and Technology, Xi’an, 710021, P.R. China
2 School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, P.R. China
3 Department of Applied Mathematics, The University of Western Ontario, London, N6A 5B7, Canada

Special Issues: Non-smooth biological dynamical systems and applications

In this work, an SIRS model with age structure is proposed for recurrent infectious disease by incorporating temporary immunity and delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the global stability of disease free equilibrium, the local stability of endemic equilibrium, and the existence of Hopf bifurcation. Both non-periodic and periodic behaviors are possible when the disease persists in population, where time delay plays an important role. Numerical examples are provided to illustrate our theoretical results.
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Keywords age-structured model; recurrent epidemic; C0-semigroup; asymptotical stability; Hopf bifurcation

Citation: Hui Cao, Dongxue Yan, Ao Li. Dynamic analysis of the recurrent epidemic model. Mathematical Biosciences and Engineering, 2019, 16(5): 5972-5990. doi: 10.3934/mbe.2019299


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This article has been cited by

  • 1. Hui Cao, Xiaoyan Gao, Jianquan Li, Dongxue Yan, Zongmin Yue, The bifurcation analysis of an SIRS epidemic model with immunity age and constant treatment, Applicable Analysis, 2019, 1, 10.1080/00036811.2019.1698728

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