title: Random migration processes between two stochastic epidemic centers.
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.
authors.affiliation: Swansea University, Bay Campus, Fabian Way, SA1 8EN, UK. Electronic address: i.sazonov@swansea.ac.uk.
authors.forename: Igor
authors.initials: I
authors.lastname: Sazonov
authors.affiliation: National Research University Higher School of Economics, Moscow, R.F., Swansea University, Singleton Park, Swansea SA2 8PP, UK. Electronic address: m.kelbert@swansea.ac.uk.
authors.forename: Mark
authors.initials: M
authors.lastname: Kelbert
authors.affiliation: Swansea University Medical School, Singleton Park, Swansea SA2 8PP, UK. Electronic address: m.b.gravenor@swansea.ac.uk.
authors.forename: Michael B
authors.initials: MB
authors.lastname: Gravenor
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D003198:Computer Simulation; D058872:Epidemics / Q000706:statistics & numerical data*; D063426:Human Migration / Q000706:statistics & numerical data; D006801:Humans; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D011156:Population Density; D011336:Probability; D013269:Stochastic Processes
keywords: Epidemic modeling; Markov chains; Network interactions; Population dynamics; Stochastic processes