Now showing items 1-8 of 8

• #### Critical fluctuations in epidemic models explain COVID‑19 post‑lockdown dynamics ﻿

(2021-07-06)
As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an ...
• #### Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions ﻿

(2017-04-28)
In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable ...
• #### Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: A quantitative study ﻿

(2020-05)
Microscopic structural features of cardiac tissue play a fundamental role in determining complex spatio-temporal excitation dynamics at the macroscopic level. Recent efforts have been devoted to the development of mathematical ...
• #### Modeling cardiac structural heterogeneity via space-fractional differential equations ﻿

(2017)
We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ...
• #### Numerical approximations for fractional elliptic equations via the method of semigroups ﻿

(2020)
We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations $(-\Delta)^su=f$ in $\Omega$, subject to some homogeneous boundary conditions $\mathcal{B}(u)=0$ on $\partial \Omega$, where ...
• #### A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics ﻿

(2021)
Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as ...
• #### A space-fractional Monodomain model for cardiac electrophysiology combining anisotropy and heterogeneity on realistic geometries ﻿

(2017-10-04)
Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain ...
• #### Unlocking datasets by calibrating populations of models to data density: a study in atrial electrophysiology ﻿

(2018-01-10)
The understanding of complex physical or biological systems nearly always requires a characterization of the variability that underpins these processes. In addition, the data used to calibrate these models may also often ...