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

PLoS ONE. 2016;11(3):e0152144 DOI 10.1371/journal.pone.0152144

 

Journal Homepage

Journal Title: PLoS ONE

ISSN: 1932-6203 (Online)

Publisher: Public Library of Science (PLoS)

LCC Subject Category: Medicine | Science

Country of publisher: United States

Language of fulltext: English

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AUTHORS

Hendrik Baumann
Werner Sandmann

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Editorial Board

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Time From Submission to Publication: 24 weeks

 

Abstract | Full Text

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.