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Random migration processes between two stochastic epidemic centers.

Igor Sazonov1, Mark Kelbert2, Michael B Gravenor3

  • 1Swansea University, Bay Campus, Fabian Way, SA1 8EN, UK.

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Summary
This summary is machine-generated.

This study models epidemic spread in connected populations using Markov chains. Separating resident and visitor movement is crucial for understanding outbreak patterns and improving epidemic modeling in complex networks.

Keywords:
Epidemic modelingMarkov chainsNetwork interactionsPopulation dynamicsStochastic processes

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Stochastic epidemic models are essential for understanding disease transmission.
  • Coupled population centers with migration present complex dynamics.
  • Markov chains offer a robust framework for modeling both epidemic and migration processes.

Purpose of the Study:

  • To analyze epidemic dynamics in interconnected populations with random migration.
  • To investigate the impact of initial parameters, population sizes, and coupling on outbreak patterns.
  • To highlight the significance of differentiating between resident and visitor movement.

Main Methods:

  • Modeling epidemic and migration as Markov chains.
  • Deriving explicit formulae for migration process probability distributions.
  • Employing analytical and numerical methods for analysis.
  • Developing and testing a mean field approximation and an approximate method for highly populated centers.

Main Results:

  • Explicit formulae for migration probability distributions were derived.
  • Outbreak patterns were shown to depend significantly on initial parameters, population sizes, and coupling.
  • The separate consideration of resident and visitor movement proved important.
  • A mean field approximation and a novel approximate method for large centers were developed and validated.

Conclusions:

  • Accurate epidemic modeling requires distinguishing between resident and visitor populations.
  • The derived methods provide tools for analyzing epidemic spread in complex, coupled networks.
  • The study offers insights into the influence of migration patterns on disease dynamics.