Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Understanding epidemic dynamics in adaptive networks is crucial.
• Traditional models often simplify network structures and dynamics.
• Adaptive networks, where links change over time, present unique challenges for epidemic modeling.

Purpose of the Study:

• To investigate epidemic propagation in an adaptive network model.
• To analyze the occurrence of oscillations in disease dynamics.
• To compare stochastic simulations with mean-field approximations and identify limitations.

Main Methods:

• Developed an adaptive network model with SIS (Susceptible-Infected-Susceptible) epidemic propagation.
• Incorporated link-type-dependent link activation and deletion.
• Performed bifurcation analysis of pairwise ODE approximations.
• Conducted network-based stochastic simulations and analyzed results using Fourier analysis and master equations.

Main Results:

• Identified three typical behaviors: disease-free steady state, endemic steady state, and oscillatory behavior.
• Oscillatory dynamics were observed in stochastic simulations.
• Fourier analysis and master equation analysis provided insights into the oscillatory phenomena.

Conclusions:

• Adaptive network models can exhibit complex dynamics, including oscillations, not always captured by mean-field approximations.
• The study provides a deeper understanding of epidemic phenomena in dynamic networks.
• Limitations of mean-field models in capturing complex network dynamics were elucidated.