 Epidemic threshold and ergodicity of an SEIR model with vertical transmission under the telegraph noiseGuijie Lan, Baojun Song and Sanling Yuan Chaos, Solitons & Fractals, 2023, vol. 167, issue C 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. Keywords: Stochastic SEIR epidemic model; Piecewise deterministic Markov process; Threshold; Ω-limit set; Attractor (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922011961 DOI: 10.1016/j.chaos.2022.113017 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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