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Spreading Properties for SIR Models on Homogeneous Trees.

Christophe Besse1, Grégory Faye2

  • 1CNRS, UMR 5219, Institut de Mathématiques de Toulouse, 31062, Toulouse Cedex, France.

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Summary
This summary is machine-generated.

This study models epidemic spread on trees. Higher interaction strength can prevent disease transmission, revealing new epidemic dynamics beyond simple lattices.

Keywords:
Discrete reaction–diffusion equationsEpidemic invasionHomogeneous treeSIR modelSpreading speed

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Epidemic modeling is crucial for understanding disease spread.
  • Homogeneous trees offer a structured network for studying transmission dynamics.
  • Previous models often simplify network structures, limiting insights into complex interactions.

Purpose of the Study:

  • To investigate the impact of tree degree and interaction strength on SIR-type epidemic spreading.
  • To identify novel spreading properties emerging in tree networks compared to linear lattices.
  • To determine the conditions under which epidemic spread is inhibited in these structured populations.

Main Methods:

  • Development of a SIR-type epidemic model on a homogeneous tree network.
  • Analysis of epidemic spreading as a function of tree degree, basic reproduction number, and interaction strength.
  • Comparison of model behavior on trees with varying degrees to lattice-based models.

Main Results:

  • For degree one, the model mirrors SIR models on integer lattices with discrete diffusion.
  • For degrees greater than two, unique spreading behaviors emerge.
  • A critical interaction strength was identified, above which epidemic spread is impossible on the tree.

Conclusions:

  • Tree structure significantly influences epidemic spreading dynamics.
  • Interaction strength is a critical factor that can halt disease transmission in structured populations.
  • The model provides new insights into epidemic control strategies in network settings.