Self-adaptive dynamics occurs in many fields of research, such as socio-economics, neuroscience, or biophysics. We consider 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 the creation and deletion of edges.

For a simple threshold base application of lockdown measures, we observe large regions in parameter space with oscillatory behavior, thereby exhibiting one of the most reduced mechanisms leading to oscillations. For the SIS epidemic model, we derive analytic expressions for the oscillation period from a pairwise closed model, which is validated with numerical simulations for random uniform networks.

Furthermore, the basic reproduction number fluctuates around one indicating a connection to self-organized criticality.

K. Clauß, C. Kuehn, Self-adapting infectious dynamics on random networks, Chaos 33(9) (2023) 093110.