PLoS ONE (Jan 2016)

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

  • Hendrik Baumann,
  • Werner Sandmann

DOI
https://doi.org/10.1371/journal.pone.0152144
Journal volume & issue
Vol. 11, no. 3
p. e0152144

Abstract

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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.