This paper presents a critical analysis of the literature and perspective research ideas for
modeling the epidemics caused by the SARS-CoV-2 virus. It goes beyond deterministic …

A numerical approach to solve a new coupled stochastic kinetic–fluid model is proposed in
this paper. The approach yields a stable numerical scheme in the hydrodynamic limit as the …

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 …

Nonlinear Fokker–Planck equations play a major role in modeling large systems of
interacting particles with a proved effectiveness in describing real world phenomena ranging …

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 …

In this paper, we study the Vlasov-Poisson system with massless electrons (VPME) near
quasineutrality and with uncertainties. Based on the idea of reformulation on the Poisson …

There have been many challenges in studying multiscale kinetic models with uncertainties.
Quantifying uncertainties in the models such as arisen from collision kernels, initial or …

In financial mathematics, it is a typical approach to approximate financial markets operating
in discrete time by continuous-time models such as the Black Scholes model. Fitting this …

Data uncertainty is certainly one of the main problems in epidemiological modeling. The
need for efficient methods capable of quantifying the effects of random inputs on outputs is …