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Oscillations and hysteresis in an epidemic model with information-dependent imperfect vaccination

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  • Buonomo, Bruno
  • Della Marca, Rossella

Abstract

We investigate a behavioral epidemic model including a partially effective vaccination at all ages. The vaccination is information-dependent, in the sense that the vaccination rate of susceptibles depends on the current and the past information available about the disease prevalence in the population. The weight given to the past history is described by an exponential kernel. The proposed model presents both the possibility of backward bifurcation and that of oscillations triggered by behavioral memory. Furthermore, a forward hysteresis scenario may take place where multiple endemic states are possible when the basic reproduction number P0 is greater than one. Finally, a stable endemic state may destabilize via Hopf bifurcation not only when P0>1 but also when P0<1, depending on the interplay between some relevant information-related parameters.

Suggested Citation

  • Buonomo, Bruno & Della Marca, Rossella, 2019. "Oscillations and hysteresis in an epidemic model with information-dependent imperfect vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 97-114.
    • Handle: RePEc:eee:matcom:v:162:y:2019:i:c:p:97-114
    DOI: 10.1016/j.matcom.2019.01.005
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    References listed on IDEAS

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    1. Maoxing Liu & Yuting Chang & Lixia Zuo, 2016. "Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-6, January.
    2. Huo, Hai-Feng & Yang, Peng & Xiang, Hong, 2018. "Stability and bifurcation for an SEIS epidemic model with the impact of media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 702-720.
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    Cited by:

    1. Giacomo Ascione, 2020. "On the Construction of Some Deterministic and Stochastic Non-Local SIR Models," Mathematics, MDPI, vol. 8(12), pages 1-28, November.
    2. Fatima Sulayman & Farah Aini Abdullah & Mohd Hafiz Mohd, 2021. "An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    3. Weiwei Wang & Futian Weng & Jianping Zhu & Qiyuan Li & Xiaolong Wu, 2023. "An Analytical Approach for Temporal Infection Mapping and Composite Index Development," Mathematics, MDPI, vol. 11(20), pages 1-16, October.

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