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Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model.

Tina Verma1, Arvind Kumar Gupta1

  • 1Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, 140001, Punjab, India.

Communications in Nonlinear Science & Numerical Simulation
|June 21, 2021
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Summary
This summary is machine-generated.

This study models infectious disease spread using a network of connected populations. Coupling patches synchronizes disease dynamics, leading to stable states and novel rhythmic patterns like Oscillation Death.

Keywords:
Amplitude deathBirhythmicityCouplingOscillation deathPatchesRhythmogenesisSEIR modelStability

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Infectious disease persistence and extinction are influenced by population connectivity and movement.
  • Rapid disease spread, as seen with COVID-19, highlights the link between population networks and epidemiology.
  • Empirical evidence shows infected individuals dispersing among distinct population patches.

Purpose of the Study:

  • To develop and analyze a network-based Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model.
  • To investigate how diffusive coupling between population patches affects disease dynamics and stability.
  • To explore emergent rhythmic phenomena like birhythmicity and rhythmogenesis in coupled epidemic systems.

Main Methods:

  • Developed a SEIR epidemic model with populations divided into interconnected patches.
  • Applied mean-field diffusive coupling to link these patches.
  • Analyzed synchronization, stability, and bifurcations (Hopf, transcritical) of disease equilibria.

Main Results:

  • Coupling unstable epidemiological classes leads to synchronization and stable states.
  • The model exhibits novel rhythmic processes: birhythmicity and rhythmogenesis.
  • Stability of Disease Free/Endemic Equilibria is achieved via Oscillation Death (OD) and Amplitude Death (AD).
  • Different steady states arise for identical and non-identical patch epidemiology, with transitions via bifurcations.

Conclusions:

  • Network structure and diffusive coupling are crucial for understanding infectious disease dynamics.
  • Coupled epidemic models can generate complex rhythmic behaviors beyond simple synchronization.
  • Mechanisms like Oscillation Death and Amplitude Death play a role in disease stabilization.