Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling
This work addresses complex dynamics in epidemiological modeling, offering a data-driven approach applicable to other tipping point problems, though it appears incremental as it builds on existing methods like ResNet and Diffusion Maps.
The researchers tackled the problem of modeling tipping point dynamics in adaptive epidemiological networks by identifying a parameter-dependent effective stochastic differential equation using deep learning, revealing a subcritical Hopf bifurcation that causes rare, large-amplitude collective oscillations.
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We identify a parameter-dependent effective stochastic differential equation (eSDE) in terms of physically meaningful coarse mean-field variables through a deep-learning ResNet architecture inspired by numerical stochastic integrators. We construct an approximate effective bifurcation diagram based on the identified drift term of the eSDE and contrast it with the mean-field SIS model bifurcation diagram. We observe a subcritical Hopf bifurcation in the evolving network's effective SIS dynamics, that causes the tipping point behavior; this takes the form of large amplitude collective oscillations that spontaneously -- yet rarely -- arise from the neighborhood of a (noisy) stationary state. We study the statistics of these rare events both through repeated brute force simulations and by using established mathematical/computational tools exploiting the right-hand-side of the identified SDE. We demonstrate that such a collective SDE can also be identified (and the rare events computations also performed) in terms of data-driven coarse observables, obtained here via manifold learning techniques, in particular Diffusion Maps. The workflow of our study is straightforwardly applicable to other complex dynamics problems exhibiting tipping point dynamics.