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

Giulia Bertaglia, Lorenzo Pareschi (8/7/2020, preprint arXiv: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 such reaction-diffusion models are recovered in an appropriate diffusive limit.

Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model

Giulia Bertaglia, Valerio Caleffi, Lorenzo Pareschi, Alessandro Valiani (3/7/2020 preprint arXiv:2007.01907)

This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeling of the human arterial hemodynamics. The chosen uncertain parameters are modeled as random Gaussian-distributed variables, making stochastic the system of governing equations. The proposed methodology is initially discussed for a model equation, presenting a thorough convergence study which confirms the spectral accuracy of the stochastic collocation method and the second-order of accuracy of the IMEX finite volume scheme chosen to solve the mathematical model.

Relaxing lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (13/5/2020 medRxiv preprint doi: 10.1101/2020.05.12.20099721)

After an initial phase characterized by the introduction of timely and drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments are preparing to relax such measures in the face of a severe economic crisis caused by lockdowns. Assessing the impact of such openings in relation to the risk of a resumption of the spread of the disease is an extremely difficult problem due to the many unknowns concerning the actual number of people infected, the actual reproduction number and infection fatality rate of the disease. In this work, starting from a compartmental model with a social structure, we derive models with multiple feedback controls depending on the social activities that allow to assess the impact of a selective relaxation of the containment measures in the presence of uncertain data.

Wealth distribution under the spread of infectious diseases

G. Dimarco, L. Pareschi, G. Toscani, M. Zanella (28/4/2020 preprint arXiv:2004.13620)

We develop a mathematical framework to study the economic impact of infectious diseases by integrating epidemiological dynamics with a kinetic model of wealth exchange. The multi-agent description leads to study the evolution over time of a system of kinetic equations for the wealth densities of susceptible, infectious and recovered individuals, whose proportions are driven by a classical compartmental model in epidemiology.