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

Guijie Lan, Baojun Song, Sanling Yuan

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish
Article number113017
JournalChaos, Solitons and Fractals
Volume167
DOIs
StatePublished - Feb 2023

Keywords

  • Attractor
  • Piecewise deterministic Markov process
  • Stochastic SEIR epidemic model
  • Threshold
  • Ω-limit set

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