Abstract

Most epidemiological models are rooted in the pioneering work proposed by Kermack and McKendrick and are based on systems of deterministic ODEs, which describe the temporal evolution of the spread of an infectious disease assuming population and territorial homogeneity. Generally, the concept of the average behavior of a population is sufficient to have a first reliable description of an epidemic development, but the inclusion of the spatial component becomes crucial when it is necessary to consider spatially heterogeneous interventions, as in the case of the COVID-19 pandemic. Moreover, 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 work, drawing inspiration from kinetic theory, recent advances on the development of stochastic multiscale kinetic transport models for the spread of epidemics under uncertain data are presented. The propagation of the infectious disease is described by the spatial movement and interactions of individuals divided into commuters moving in the territory on a wide scale and non-commuters acting only on urban scales. The resulting models are solved numerically through a suitable stochastic Asymptotic-Preserving IMEX Runge-Kutta Finite Volume Collocation Method, which ensures a consistent treatment of the system of equations, without loss of accuracy when entering in the stiff, diffusive regime. Application studies concerning the spread of the COVID-19 pandemic in Italy assess the validity of the proposed methodology.