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A minimal model for adaptive SIS epidemics.

Massimo A Achterberg1, Mattia Sensi2

  • 1Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

Nonlinear Dynamics
|June 26, 2023
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Summary

This study models disease spread by incorporating adaptive personal networks. The model shows that while endemic equilibria exist, it cannot simulate epidemic waves due to a lack of complex dynamics.

Keywords:
Adaptive networksNetwork epidemiologyPlanar systemRisk perceptionSIS epidemics

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Biology

Background:

  • Understanding disease transmission dynamics is crucial for public health.
  • Personal risk perception significantly influences contact network structures during epidemics.
  • Existing epidemic models often overlook the adaptive nature of social networks.

Purpose of the Study:

  • To develop a mathematical model for the co-evolution of disease spread and personal contact networks.
  • To investigate how adaptive network structures, driven by risk perception, affect epidemic dynamics.
  • To analyze the theoretical properties of the proposed model, including equilibrium states and wave generation.

Main Methods:

  • Formulation of a planar system of ordinary differential equations (ODEs).
  • Incorporation of two functional responses for personal risk perception (link-breaking and link-creation).
  • Derivation of the basic reproduction number and analysis of endemic equilibria.

Main Results:

  • The model guarantees the existence of at least one endemic equilibrium for all functional responses.
  • The model demonstrates that limit cycles do not exist for any functional response.
  • The proposed minimal model is incapable of reproducing subsequent epidemic waves.

Conclusions:

  • Adaptive personal networks, influenced by risk perception, are essential components of epidemic modeling.
  • While the model captures basic endemic states, it requires further complexity to simulate epidemic waves.
  • Future research should explore more intricate disease or behavioral dynamics to capture epidemic wave phenomena.