Volume 55, Number 2, March-April 2021
|Page(s)||381 - 407|
|Published online||15 March 2021|
Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods
Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, 44121 Ferrara, Italy
* Corresponding author: firstname.lastname@example.org
Accepted: 24 November 2020
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 such reaction-diffusion models are recovered in an appropriate diffusive limit. The kinetic transport model is therefore considered within a spatial network, characterizing different places such as villages, cities, countries, etc. The transmission conditions in the nodes are analyzed and defined. Finally, the model is solved numerically on the network through a finite-volume IMEX method able to maintain the consistency with the diffusive limit without restrictions due to the scaling parameters. Several numerical tests for simple epidemic network structures are reported and confirm the ability of the model to correctly describe the spread of an epidemic.
Mathematics Subject Classification: 65M08 / 35L50 / 65L04 / 35K57 / 82C40 / 92D30
Key words: Kinetic equations / hyperbolic systems / spatial epidemic models / SIR model / network models / IMEX Runge–Kutta schemes / diffusive limit
© EDP Sciences, SMAI 2021
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