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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...