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Random migration processes between two stochastic epidemic centers / Igor Sazonov, Mark Kelbert, Michael Gravenor

Mathematical Biosciences, Volume: 274, Pages: 45 - 57

Swansea University Authors: Igor Sazonov, Michael Gravenor

DOI (Published version): 10.1016/j.mbs.2016.01.011

Abstract

We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of...

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Published in: Mathematical Biosciences
Published: 2016
Online Access: http://www.sciencedirect.com/science/article/pii/S0025556416000225
URI: https://cronfa.swan.ac.uk/Record/cronfa26751
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Abstract: We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically.
Keywords: Epidemic modeling; Population dynamics; Markov chains; Stochastic processes; Network interactions
College: College of Engineering
Start Page: 45
End Page: 57