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Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

Téo Granger1, Thomas M Michelitsch1, Michael Bestehorn2

  • 1Sorbonne Université, Institut Jean le Rond d'Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris, Cedex 05, France.

Entropy (Basel, Switzerland)
|May 24, 2024
PubMed
Summary

This study models epidemic spreading using random walkers on complex networks, finding that walker mortality reduces disease spread (RM < R0). The model accurately predicts outcomes on strongly connected networks, with broader applications in various dynamic systems.

Keywords:
compartment model with mortalityepidemic spreadingmemory effectsrandom graphsrandom walks

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Area of Science:

  • Complex Systems Science
  • Epidemiology
  • Network Science

Background:

  • Epidemic spreading in complex networks is crucial for understanding disease dynamics.
  • Existing models often lack vector-based transmission and walker mortality.
  • This study introduces a novel multiple random walker approach for vector-borne disease modeling.

Purpose of the Study:

  • To develop and analyze a mathematical model for epidemic spreading using multiple random walkers on complex networks.
  • To investigate the impact of walker mortality on disease transmission dynamics.
  • To compare model predictions with simulations across different network topologies (BA, ER, WS).

Main Methods:

  • Utilized a multiple random walker approach on Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) networks.
  • Developed stochastic evolution equations for compartmental populations (Susceptible, Infected, Dead).
  • Employed linear stability analysis to derive basic reproduction numbers (RM, R0) and analyze equilibrium states.

Main Results:

  • Derived basic reproduction numbers RM (with mortality) and R0 (without mortality), proving RM < R0.
  • Demonstrated that walker mortality significantly reduces epidemic spread.
  • Observed good agreement between mean-field and simulation results for strongly connected networks, with deviations in weakly connected structures or high mortality scenarios.

Conclusions:

  • The multiple random walker model provides a robust framework for studying vector-borne diseases with walker mortality.
  • Walker mortality is a critical factor in modulating epidemic dynamics.
  • The model's applicability extends beyond epidemiology to chemical reactions, contaminant spread, and fire propagation.