Learning epidemic trajectories through Kernel Operator Learning: from
  modelling to optimal control
Giovanni Ziarelli Nicola Parolini Marco Verani
Since infectious pathogens start spreading into a susceptible population,
mathematical models can provide policy makers with reliable forecasts and
scenario analyses, which can be concretely implemented or solely consulted. In
these complex epidemiological scenarios, machine learning architectures can
play an important role, since they directly reconstruct data-driven models
circumventing the specific modelling choices and the parameter calibration,
typical of classical compartmental models. In this work, we discuss the
efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics
during epidemic outbreaks, where the transmission rate is ruled by an input
strategy. In particular, we introduce two surrogate models, named KOL-m and
KOL-$\partial$, which reconstruct in two different ways the evolution of the
epidemics. Moreover, we evaluate the generalization performances of the two
approaches with different kernels, including the Neural Tangent Kernels, and
compare them with a classical neural network model learning method. Employing
synthetic but semi-realistic data, we show how the two introduced approaches
are suitable for realizing fast and robust forecasts and scenario analyses, and
how these approaches are competitive for determining optimal intervention
strategies with respect to specific performance measures.