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Spreading disease: integro-differential equations old and new.

Jan Medlock1, Mark Kot

  • 1Department of Applied Mathematics, University of Washington, PO Box 352420, Seattle, WA 98195-2420, USA. medlock@amath.washington.edu

Mathematical Biosciences
|July 2, 2003
PubMed
Summary

This study compares two disease spread models. Dispersal of infectious individuals can accelerate or decelerate epidemic traveling waves based on transmission rates, unlike non-local contact models.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Mathematical Modeling

Background:

  • Understanding epidemic spread is crucial for public health interventions.
  • Spatial spread of infectious diseases can be modeled using various mathematical approaches.
  • Mollison's model provides a framework for diseases with non-local transmission.

Purpose of the Study:

  • To compare an integro-differential equation model of disease spread via dispersal with Mollison's non-local contact model.
  • To analyze the impact of transmission rates on the speed of epidemic traveling waves in both models.
  • To approximate the traveling wave shapes using analytical techniques.

Main Methods:

  • Formulation of an integro-differential equation for disease spread by dispersal.

Related Experiment Videos

  • Comparison with Mollison's model for non-local disease spread.
  • Analysis of traveling wave phenomena for symmetric kernels with moment generating functions.
  • Approximation of traveling wave shapes using piecewise linearization and regular perturbation schemes.

    • Main Results:

    • Spreading infectives result in faster traveling waves at low transmission rates.
    • Spreading infectives result in slower traveling waves at high transmission rates.
    • The speed of epidemic spread is dependent on the transmission rate and the model used.

    Conclusions:

    • The mechanism of disease spread (dispersal vs. non-local contact) significantly influences epidemic wave speed.
    • Transmission rates play a critical role in determining whether dispersal accelerates or decelerates spatial epidemic spread.
    • Approximation methods provide insights into the shape of traveling waves for these epidemic models.