Monday, January 10, 2022

Effects of vaccination efficacy on wealth distribution in kinetic epidemic models

Emanuele Bernardi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella (preprint arXiv:2201.02553)

The spreading of Covid-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modelling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges.

Friday, December 3, 2021

Multi-fidelity methods for uncertainty propagation in kinetic equations

Giacomo Dimarco, Liu Liu, Lorenzo Pareschi, Xueyu Zhu (to appear in Panoramas & Synthèses, Société Mathématique de France, preprint arXiv:2112.00932)

The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand, precisely because of the curse of dimensionality, the construction of simplified models capable of providing approximate solutions at a computationally reduced cost has always represented one of the main research strands in the field of kinetic equations.

Tuesday, November 23, 2021

Constrained consensus-based optimization

Giacomo Borghi, Michael Herty, Lorenzo Pareschi (preprint arXiv:2111.10571)

In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with suitable penalization techniques is introduced for this purpose. The method relies on a reformulation of the constrained minimization problem in an unconstrained problem for a penalty function and extends to the constrained settings the class of CBO methods.

Thursday, October 28, 2021

Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties

Giulia Bertaglia, Liu Liu, Lorenzo Pareschi, Xueyu Zhu (to appear in Network and Heterogeneous Media, preprint arXiv:2110.14579)

Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertainty in the mathematical model is essential in order to produce realistic scenarios of the spread of infection. In this paper, we introduce a bi-fidelity approach to quantify uncertainty in spatially dependent epidemic models.

Monday, October 4, 2021

Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics

Giacomo Albi, Giulia Bertaglia, Walter Boscheri, Giacomo Dimarco, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella (to appear in Predicting Pandemics in a Globally Connected World, Vol. 1, N. Bellomo and M. Chaplain Editors, Springer-Nature (2021). Preprint arXiv:2110.00293)

In this survey we report some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role in the spread of an epidemic, such as the age of individuals, the number of social contacts, and their economic wealth.

Tuesday, September 28, 2021

Spreading of fake news, competence, and learning: kinetic modeling and numerical approximation

 Jonathan Franceschi, Lorenzo Pareschi (to appear in Philosophical Transactions of the Royal Society A. Preprint arXiv:2109.14087)

The rise of social networks as the primary means of communication in almost every country in the world has simultaneously triggered an increase in the amount of fake news circulating online. This fact became particularly evident during the 2016 U.S. political elections and even more so with the advent of the COVID-19 pandemic. Several research studies have shown how the effects of fake news dissemination can be mitigated by promoting greater competence through lifelong learning and discussion communities, and generally rigorous training in the scientific method and broad interdisciplinary education.