Mathematical Biosciences and Engineering

2019, Issue 5: 5972-5990. doi: 10.3934/mbe.2019299
Research article Special Issues

Dynamic analysis of the recurrent epidemic model

• Received: 28 February 2019 Accepted: 11 June 2019 Published: 27 June 2019
• 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.

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

Related Papers:

• 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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