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Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

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  • Hendrik Baumann
  • Werner Sandmann

Abstract

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

Suggested Citation

  • Hendrik Baumann & Werner Sandmann, 2016. "Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-19, March.
    • Handle: RePEc:plo:pone00:0152144
    DOI: 10.1371/journal.pone.0152144
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    Cited by:

    1. Vincent Huang & James Unwin, 2019. "Markov Chain Models of Refugee Migration Data," Papers 1903.08255, arXiv.org.
    2. Antonio Gómez-Corral & Martín López-García & Maria Jesus Lopez-Herrero & Diana Taipe, 2020. "On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics," Mathematics, MDPI, vol. 8(10), pages 1-25, October.
    3. Amir Rastpour & Armann Ingolfsson & Burhaneddin Sandıkçı, 2022. "Algorithms for Queueing Systems with Reneging and Priorities Modeled as Quasi-Birth-Death Processes," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1693-1710, May.

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