Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling

• URL: http://arxiv.org/abs/2311.00797v2
• Date: Fri, 10 Nov 2023 22:49:40 GMT
• Title: Tipping Points of Evolving Epidemiological Networks: Machine Learning-Assisted, Data-Driven Effective Modeling
• Authors: Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Alexei Makeev, Ioannis G. Kevrekidis
• Abstract summary: We study the tipping point collective dynamics of an adaptive susceptible-infected (SIS) epidemiological network in a data-driven, machine learning-assisted manner. We identify a complex effective differential equation (eSDE) in terms physically meaningful coarse mean-field variables. We study the statistics of rare events both through repeated brute force simulations and by using established mathematical/computational tools.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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