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Epidemic spreading with migration in networked metapopulation.

Ning-Ning Wang1, Ya-Jing Wang2, Shui-Han Qiu1,3

  • 1School of Systems Science, Beijing Normal University, Beijing 100875, China.

Communications in Nonlinear Science & Numerical Simulation
|January 17, 2022
PubMed
Summary

Networked metapopulation models reveal that while migration doesn't directly boost epidemic spread, it can shift populations to endemic states, increasing disease impact. This was validated using Wuhan COVID-19 data.

Keywords:
COVID-19EpidemicsMetastable stateMigrationNetworked metapopulation

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Network Science

Background:

  • Epidemic dynamics are significantly influenced by human migration patterns.
  • Traditional metapopulation models often assume uniform mixing, which may not accurately reflect real-world population structures and interactions.
  • Understanding the interplay between contact networks and inter-population migration is crucial for accurate epidemic forecasting.

Purpose of the Study:

  • To develop and analyze a networked metapopulation SIR model that incorporates both individual contact networks and inter-population migration.
  • To investigate how migration dynamics affect epidemic spreading and stability in interconnected populations.
  • To validate the model using empirical data from the Wuhan COVID-19 outbreak.

Main Methods:

  • Construction of an N-seat intertwined SIR model using network mean-field theory and the gravity law of migration.
  • Derivation of the basic reproduction number ( ) for the proposed model.
  • Development of a non-Markovian Node-Search algorithm for statistical simulations.
  • Validation using empirical data from 94 Chinese cities during the Wuhan epidemic.

Main Results:

  • Migration does not directly increase the epidemic's basic reproduction number ( ).
  • Migration can drive susceptible populations from a disease-free equilibrium to an endemic equilibrium when is sufficiently high.
  • This transition, facilitated by migration, expands the geographical influence of the epidemic.
  • Analysis suggests that Chinese government interventions, including contact tracing and testing, potentially averted at least 4 million COVID-19 cases during the initial wave.

Conclusions:

  • Networked metapopulation models provide a more realistic framework for studying epidemic spreading than uniform mixing models.
  • Migration acts as a critical factor in disease persistence and geographical expansion by altering population states.
  • Non-pharmaceutical interventions remain highly effective in controlling epidemic spread, even after the relaxation of travel restrictions.