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Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate

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Abstract

An infection-age structured epidemic model with a nonlinear incidence rate is investigated. We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model. By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations, we show that the SIR (susceptible-infected-recovered) epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11471044 and 11371058) and the Fundamental Research Funds for the Central Universities. The authors are grateful to the referees for their valuable comments and suggestions which helped us to improve the presentation of the paper.

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  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    ZhiHua Liu & Rong Yuan

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  1. ZhiHua Liu
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  2. Rong Yuan
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Correspondence to ZhiHua Liu.

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Liu, Z., Yuan, R. Zero-Hopf bifurcation for an infection-age structured epidemic model with a nonlinear incidence rate. Sci. China Math. 60, 1371–1398 (2017). https://doi.org/10.1007/s11425-016-0371-8

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  • DOI: https://doi.org/10.1007/s11425-016-0371-8

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