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Learning Epidemic Trajectories Through Kernel Operator Learning: From Modelling to Optimal Control

Learning Epidemic Trajectories Through Kernel Operator Learning: From Modelling to Optimal Control

Year:    2025

Author:    Giovanni Ziarelli, Nicola Parolini, Marco Verani

Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 2 : pp. 285–324

Abstract

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-$∂,$ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2024-0097

Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 2 : pp. 285–324

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    40

Keywords:    Operator learning optimal control kernel regression kernel operator learning dynamical systems epidemiology.

Author Details

Giovanni Ziarelli

Nicola Parolini

Marco Verani