# Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods

@article{Bertaglia2020HyperbolicMF, title={Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods}, author={Giulia Bertaglia and Lorenzo Pareschi}, journal={ArXiv}, year={2020}, volume={abs/2007.04019} }

We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the spatial movement and interactions of a population of susceptible, infected and recovered individuals. Thanks to this, the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models, is removed. In particular, we formally show how…

## 25 Citations

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The ability of the model to correctly describe the spatial heterogeneity underlying the spread of an epidemic in a realistic city network is confirmed with a study of the outbreak of COVID-19 in Italy and its spread in the Lombardy Region.

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- Computer ScienceArXiv
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This Chapter addresses issues in light of recent results obtained in the development of Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic models with diﬀusive scaling, and shows how APNNs provide considerably better results with respect to the di-erent scales of the problem when compared with standard DNNs and PINNs.

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A new class of AP Neural Networks (APNNs) for multiscale hyperbolic transport models of epidemic spread that, thanks to an appropriate AP formulation of the loss function, is capable to work uniformly at the diﬀerent scales of the system.

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