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Stability Analysis of SIR Model with Distributed Delay on Complex Networks.

Chuangxia Huang1,2, Jie Cao1, Fenghua Wen3

  • 1School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan 410114, China.

Plos One
|August 5, 2016
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Summary

This study analyzes the Susceptible-Infected-Removed (SIR) epidemic model with distributed delays and network complexity. Findings reveal disease spread depends on network structure and delays, influencing stability and convergence times.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Complex population networks exhibit heterogeneous contact patterns.
  • Distributed delays significantly influence epidemic dynamics.
  • Understanding disease spread requires integrating network topology and demographic factors.

Purpose of the Study:

  • To analytically study the Susceptible-Infected-Removed (SIR) epidemic model on complex networks.
  • To investigate the impact of distributed delays, demographics, and contact heterogeneity on epidemic stability.
  • To determine the factors governing the disease-free and endemic equilibria.

Main Methods:

  • Utilizing Lyapunov functional and Kirchhoff's matrix tree theorem for stability analysis.
  • Analyzing the basic reproduction number (R0) in relation to network topology and delay parameters.
  • Employing numerical simulations to validate analytical findings.

Main Results:

  • The basic reproduction number (R0) is determined by network topology, individual properties, and distributed time delay.
  • The system exhibits threshold behavior, with R0 dictating the stability of disease-free or endemic equilibria.
  • Distributed time delays affect the convergence time of contagion, with specific delay types showing faster or slower stabilization.

Conclusions:

  • The SIR model on complex networks is sensitive to network structure and delay characteristics.
  • Distributed delays play a crucial role in epidemic dynamics, influencing both stability and speed of spread.
  • The study provides a robust framework for understanding epidemic thresholds and temporal dynamics in heterogeneous populations.