TY - JOUR
T1 - Hyperbolic compartmental models for epidemic spread on networks with uncertain data
T2 - Application to the emergence of COVID-19 in Italy
AU - Bertaglia, Giulia
AU - Pareschi, Lorenzo
N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources such as the amount of infectious individuals. In this paper, we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interactions of a population partitioned, from an epidemiological point of view, on the basis of an extended compartmental structure and divided into commuters, moving on a suburban scale, and non-commuters, acting on an urban scale. Through a diffusive rescaling, the model allows us to recover classical diffusion equations related to commuting dynamics. The numerical solution of the resulting multiscale hyperbolic system with uncertainty is then tackled using a stochastic collocation approach in combination with a finite volume Implicit-Explicit (IMEX) method. 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.
AB - The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources such as the amount of infectious individuals. In this paper, we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interactions of a population partitioned, from an epidemiological point of view, on the basis of an extended compartmental structure and divided into commuters, moving on a suburban scale, and non-commuters, acting on an urban scale. Through a diffusive rescaling, the model allows us to recover classical diffusion equations related to commuting dynamics. The numerical solution of the resulting multiscale hyperbolic system with uncertainty is then tackled using a stochastic collocation approach in combination with a finite volume Implicit-Explicit (IMEX) method. 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.
KW - COVID-19
KW - IMEX finite volume methods
KW - Kinetic transport equations
KW - asymptotic-preserving scheme
KW - diffusion limit
KW - epidemic models
KW - hyperbolic systems
KW - network modeling
KW - uncertainty quantification
UR - http://www.scopus.com/inward/record.url?scp=85111449845&partnerID=8YFLogxK
U2 - 10.1142/S0218202521500548
DO - 10.1142/S0218202521500548
M3 - Article
AN - SCOPUS:85111449845
SN - 0218-2025
VL - 31
SP - 2495
EP - 2531
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 12
ER -