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Seasonally Forced SIR Systems Applied to Respiratory Infectious Diseases, Bifurcations, and Chaos
(2022-03-03)
We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years the aquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models ...
Understanding COVID-19 Epidemics: A Multi-Scale Modeling Approach
(2022-02-18)
COVID-19 was declared a pandemic by the World Health Organization in March 2020 and, since then, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease ...
Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission
(2022-02-13)
Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...