Self-adapting infectious dynamics on random networks

TL;DR

This paper introduces a self-adaptive modeling framework for epidemic dynamics on random networks, capturing oscillations and criticality through co-evolution of node states and network topology.

Contribution

It formalizes a novel self-adaptive approach for epidemic models, deriving analytical expressions and exploring network structure effects.

Findings

Oscillatory behavior in epidemic dynamics under lockdown scenarios

Analytic expressions for oscillation periods in SIS models

Link between epidemic fluctuations and self-organized criticality

Abstract

Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the state of the system. This leads to piecewise deterministic Markovian dynamics coupled to a non-Markovian adaptive mechanism. We apply this framework to basic epidemic models (SIS, SIR) on random networks. We consider a co-evolutionary dynamical network where node-states change through the epidemics and network topology changes through creation and deletion of edges. For a simple threshold base application of lockdown measures we observe large regions in parameter space with oscillatory behavior. For the SIS epidemic model, we derive analytic expressions for the oscillation period from a pairwise closed model. Furthermore, we show that there is a link to self-organized criticality as the basic reproduction number fluctuates around one. We also study the dependence of our results on the underlying network structure.