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On cognitive epidemic models: spatial segregation versus nonpharmaceutical interventions.

Guodong Liu1,2, Hao Wang3, Xiaoyan Zhang1

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Summary

The Fokker-Planck law better models cognitive dispersal in epidemic models than Fick's law. Nonpharmaceutical interventions can eliminate disease regionally, impacting final infection size.

Keywords:
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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Statistical Mechanics

Background:

  • Reaction-diffusion models are crucial for understanding disease spread in heterogeneous environments.
  • Cognitive dispersal influences epidemic dynamics, necessitating advanced modeling approaches.
  • Nonlocal infection mechanisms and individual movement patterns impact disease transmission.

Purpose of the Study:

  • To compare Fick's law and Fokker-Planck law in modeling cognitive dispersal within SEIR epidemic models.
  • To analyze the impact of different dispersal strategies on disease spread and spatial patterns.
  • To investigate the effectiveness of nonpharmaceutical interventions in controlling epidemics.

Main Methods:

  • Application of Fick's law and Fokker-Planck law to two reaction-diffusion SEIR epidemic models.
  • Analysis of threshold dynamics using basic reproduction numbers.
  • Numerical simulations to explore spatial segregation and intervention effects.

Main Results:

  • The Fokker-Planck law provides a more accurate description of individual diffusion, considering varied dispersal strategies.
  • Spatial segregation patterns differ based on diffusion model (random vs. symmetric) and nonlocal infection radius.
  • Nonpharmaceutical interventions focused on restricting movement can lead to regional disease elimination, not just reduction.
  • The random diffusion model results in a smaller final infection size compared to the symmetric model, decreasing with increased infection radius.

Conclusions:

  • The choice of diffusion law significantly impacts epidemic modeling outcomes.
  • Understanding cognitive dispersal is key to designing effective spatial interventions.
  • Nonpharmaceutical interventions can have complex, region-specific effects on disease dynamics.