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Epidemic threshold and ergodicity of an SEIR model with vertical transmission under the telegraph noise

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  • Lan, Guijie
  • Song, Baojun
  • Yuan, Sanling

Abstract

An SEIR epidemic model incorporating both environmental and genetic factors is developed to investigate the impact of Markovian switching on the transmission dynamics of infectious diseases. Probabilistically, we show first that the basic reproduction number R0 is a sharp threshold for the disease transmission: when R0<1, the disease dies out almost surely; when R0>1, the disease is persistent. We then obtain that the Markov process derived from the model is positive Harris recurrence if R0>1, followed by the global attractivity of the Ω-limit set and the ergodicity of the Markov process. The theoretical results are applied to study the dynamics of rubella in China. This work has significantly simplified the analysis process in the existing literature. This research concludes that multiple waves of infections may be driven by the randomly environmental switching.

Suggested Citation

  • Lan, Guijie & Song, Baojun & Yuan, Sanling, 2023. "Epidemic threshold and ergodicity of an SEIR model with vertical transmission under the telegraph noise," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011961
    DOI: 10.1016/j.chaos.2022.113017
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    1. Ozili, Peterson & Arun, Thankom, 2020. "Spillover of COVID-19: Impact on the Global Economy," MPRA Paper 99317, University Library of Munich, Germany.
    2. Li, Xue-Zhi & Zhou, Lin-Lin, 2009. "Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 874-884.
    3. Michelle Holder & Janelle Jones & Thomas Masterson, 2021. "The Early Impact of Covid-19 on Job Losses among Black Women in the United States," Feminist Economics, Taylor & Francis Journals, vol. 27(1-2), pages 103-116, April.
    4. Li, Chun-Hsien, 2015. "Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 234-243.
    5. Korolev, Ivan, 2021. "Identification and estimation of the SEIRD epidemic model for COVID-19," Journal of Econometrics, Elsevier, vol. 220(1), pages 63-85.
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    Cited by:

    1. Lan, Guijie & Yuan, Sanling, 2023. "Geometric ergodicity and Ω-limit set of an SIRm epidemic model with regime switching," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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