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Updated: Nov 1, 2025

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Mathematical analysis on an age-structured SIS epidemic model with nonlocal diffusion.

Hao Kang1, Shigui Ruan2

  • 1Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA.

Journal of Mathematical Biology
|June 26, 2021
PubMed
Summary

This study introduces an age-structured epidemic model incorporating nonlocal diffusion to understand disease spread through long-distance travel. The research identifies a spectral radius threshold for disease persistence, crucial for public health strategies.

Keywords:
Age-structureGlobal dynamicsMonotone and positive operatorsNonlocal diffusionPrincipal eigenvalueSIS modelSemigroup theory

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Mathematical Modeling

Background:

  • Geographic spread of infectious diseases is complex.
  • Long-distance travel significantly impacts disease transmission dynamics.
  • Existing models may not fully capture age structure and nonlocal spread.

Purpose of the Study:

  • To develop and analyze an age-structured epidemic model with nonlocal diffusion.
  • To investigate the conditions for disease endemicity and spread.
  • To identify key thresholds governing disease dynamics.

Main Methods:

  • Utilizing semigroup theory for model analysis.
  • Applying methods of monotone and positive operators.
  • Analyzing the spectral radius of an associated linear operator.

Main Results:

  • Established well-posedness of the proposed epidemic model.
  • Proved the existence and uniqueness of a nontrivial steady state (endemic state).
  • Determined the local and global stability of the endemic state and identified a spectral radius threshold.

Conclusions:

  • The model provides a framework for understanding age-structured disease spread with nonlocal diffusion.
  • The spectral radius serves as a critical threshold for disease persistence.
  • Findings are vital for predicting and managing infectious disease outbreaks influenced by travel.