Tipping points of evolving epidemiological networks: Machine learning-assisted, data-driven effective modeling.

Area of Science:

• Complex Systems
• Epidemiology
• Network Science

Background:

• Adaptive epidemiological networks exhibit complex dynamics, including tipping points.
• Understanding these tipping points is crucial for predicting disease spread and network behavior.

Purpose of the Study:

• To investigate tipping point collective dynamics in adaptive susceptible-infected-susceptible (SIS) networks using a data-driven approach.
• To identify an effective stochastic differential equation (eSDE) that captures the network's coarse-grained behavior.

Main Methods:

• Employed a deep-learning ResNet architecture inspired by numerical stochastic integrators to identify the eSDE.
• Constructed an approximate effective bifurcation diagram from the eSDE's drift term.
• Utilized manifold learning techniques, specifically Diffusion Maps, for data-driven observable identification.

Main Results:

• Identified a parameter-dependent eSDE capturing the network's dynamics.
• Observed a subcritical Hopf bifurcation leading to tipping point behavior characterized by rare, large-amplitude collective oscillations.
• Successfully identified the collective SDE and performed rare event computations using data-driven coarse observables.

Conclusions:

• The study reveals a subcritical Hopf bifurcation as the mechanism for tipping points in adaptive SIS networks.
• The developed machine learning framework effectively models complex dynamics and tipping phenomena.
• The methodology is broadly applicable to other complex dynamic systems exhibiting tipping point behavior.