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Dynamics of an SIS network model with a periodic infection rate

Lei Zhang1,2, Maoxing Liu1,2, Qiang Hou2

  • 1School of Big Data, North University of China, Taiyuan Shanxi, 030051, China.

Applied Mathematical Modelling
|August 26, 2020
PubMed

Insights

This study models seasonal disease spread using a Susceptible-Infected-Susceptible (SIS) framework. Network heterogeneity significantly impacts disease dynamics and outbreak control strategies.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Periodic patterns in disease dynamics are influenced by seasonal forcing and contact patterns.
  • Previous research has not fully explored the interplay of these factors.

Purpose of the Study:

  • To develop and analyze a non-autonomous, degree-based mean-field network model for seasonal diseases.
  • To investigate the synergistic effects of periodic transmission rates and contact network heterogeneity on disease spread.

Main Methods:

  • Utilized a Susceptible-Infected-Susceptible (SIS) framework with a periodic transmission rate.
  • Employed a degree-based mean-field network model applied to scale-free networks.
  • Conducted both analytical and numerical analyses.

Main Results:

  • Established conditions for global asymptotic stability of the disease-free equilibrium (basic reproduction number < 1).
  • Demonstrated the existence of a unique global periodic solution with coexisting susceptible and infected individuals (basic reproduction number > 1).
  • Showed that contact network heterogeneity accelerates disease spread and increases the amplitude of periodic solutions.

Conclusions:

  • Contact network structure is crucial for understanding and predicting seasonal disease dynamics.
  • Effective disease control policies must consider both periodic transmission and contact network characteristics.
Keywords:
Amplitude of the infected populationBasic reproduction numberDegree-based mean field network modelPeriodicityScale-free networkSeasonal forcing

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