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Formulation of a new sir Model with Non-local Mobility.

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  • 1Department of Mathematics and Statistics, Eastern Kentucky University, 521 Lancaster Ave, Richmond, Kentucky, 40475, USA.

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|October 22, 2025
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Summary

This study introduces a novel Susceptible-Infectious-Recovered (SIR) model that includes particle mobility to better understand pandemic dynamics. The new model analyzes long-term behavior and introduces a mobility-based reproduction number, enhancing epidemiological predictions.

Keywords:
Dynamic spatial modelingEpidemic modelingMobilitySIR model

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Traditional Susceptible-Infectious-Recovered (SIR) models are foundational in epidemiology.
  • These models typically do not account for the spatial mobility of individuals.
  • Real-world pandemic propagation is significantly influenced by population movement.

Purpose of the Study:

  • To develop a novel dynamical SIR model incorporating nonlocal spatial motion.
  • To analyze the long-term behavior and dynamics of pandemic propagation considering mobility.
  • To introduce and compare a new mobility-based reproduction number with the classical one.

Main Methods:

  • Development of a mobility-based SIR model for three distinct particle types.
  • Analysis of the long-term behavior of the dynamic system.
  • Computation of first and second moments.
  • Introduction and comparison of a new reproduction number (R 0 m) with the classical (R 0).
  • Rigorous examination of intermittency within the enhanced model.

Main Results:

  • The study provides a framework for understanding pandemic dynamics that integrates spatial mobility.
  • A new reproduction number (R 0 m) is proposed, offering insights beyond traditional SIR models.
  • Analysis reveals the impact of spatial motion on system behavior and intermittency.

Conclusions:

  • The developed mobility-based SIR model offers a more realistic representation of pandemic spread.
  • Incorporating mobility enhances the understanding of epidemiological dynamics and disease transmission.
  • The findings contribute to improved pandemic preparedness and control strategies by considering population movement.