Self-adapting infectious dynamics on random networks.

Area of Science:

• Complex Systems
• Epidemiology
• Network Science

Background:

• Self-adaptive dynamics are prevalent across diverse scientific fields, including socio-economics, neuroscience, and biophysics.
• Adaptation mechanisms often depend on the historical states of a system, leading to complex dynamics.

Purpose of the Study:

• To develop and apply a self-adaptive modeling framework for epidemic dynamics on co-evolutionary networks.
• To investigate the emergence of oscillatory behaviors and self-organized criticality in epidemic models.

Main Methods:

• The study employs a self-adaptive modeling approach, integrating piecewise deterministic Markovian dynamics with non-Markovian adaptation.
• The framework is applied to Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) epidemic models on random networks.
• Co-evolutionary network dynamics, including node-state changes and edge modifications, are considered.

Main Results:

• Oscillatory behaviors are observed in large parameter regions for simple threshold-based lockdown measures.
• Analytic expressions for oscillation periods in the SIS model were derived from a pairwise model and validated via simulations.
• The basic reproduction number fluctuates around one, suggesting a link to self-organized criticality.

Conclusions:

• The self-adaptive modeling framework effectively captures complex epidemic dynamics on evolving networks.
• Reduced mechanisms can lead to significant oscillatory behaviors, offering insights into epidemic control strategies.
• The findings highlight potential connections between epidemic dynamics and self-organized criticality.