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Spatial patterns in a discrete-time SIS patch model.

L J S Allen1, Y Lou, A L Nevai

  • 1Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA.

Journal of Mathematical Biology
|June 13, 2008
PubMed
Summary
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Infectious disease spread depends on habitat risk, connectivity, and movement. High-risk areas always sustain disease, while low-risk areas may become disease-free with reduced movement.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Spatial Ecology

Background:

  • Infectious disease dynamics are influenced by spatial factors.
  • Understanding how habitat characteristics and population movement affect disease spread is crucial.

Purpose of the Study:

  • To investigate the combined effects of spatial heterogeneity, habitat connectivity, and movement rates on infectious disease spatial patterns.
  • To analyze a discrete-time SIS patch model to understand disease persistence and spatial distribution.

Main Methods:

  • Formulation and analysis of a discrete-time SIS patch model.
  • Characterization of patches as low-risk or high-risk based on local disease parameters.
  • Analysis of endemic equilibrium (EE) and disease-free equilibrium (DFE) under varying mobility rates.

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Main Results:

  • Disease persistence differs between low-risk and high-risk habitats.
  • In low-risk habitats, disease persists below a mobility threshold; in high-risk habitats, it always persists.
  • The endemic equilibrium approaches a spatially inhomogeneous disease-free equilibrium as susceptible mobility decreases.

Conclusions:

  • Habitat risk (low vs. high) significantly impacts disease persistence and spatial patterns.
  • Sufficient conditions for disease eradication in high-risk patches can be determined by transmission, recovery, connectivity, and infected movement rates.
  • The model provides insights into disease dynamics in heterogeneous environments.