Browsing Mathematical Modelling in Biosciences by Title
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Numerical approximations for fractional elliptic equations via the method of semigroups
(ESAIM: Mathematical Modelling and Numerical Analysis, 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 ... 
Numerical simulation of a susceptibleexposedinfectious spacecontinuous model for the spread of rabies in raccoons across a realistic landscape
(Journal of Biological Dynamics, 20131231)We introduce a numerical model for the spread of a lethal infectious disease in wildlife. The reference model is a SusceptibleExposedInfectious system where the spatial component of the dynamics is modelled by a diffusion ... 
Optimized schwarz methods and model adaptivity in electrocardiology simulations
(Lecture Notes in Computational Science and Engineering, 20141231)[No abstract available] 
Optimized schwarz methods for the bidomain system in electrocardiology
(Mathematical Modelling and Numerical Analysis, 20131231)The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a ... 
Optimized Schwarz Methods in the StokesDarcy Coupling
(IMA J. Num. Analysis 38 (4), 20181016)This article studies optimized Schwarz methods for the Stokes–Darcy problem. Robin transmission conditions are introduced, and the coupled problem is reduced to a suitable interface system that can be solved using Krylov ... 
Parallelizing the KolmogorovFokkerPlanck Equation
(ESAIM M2AN: Mathematical Modelling and Numerical Analysis, 20151231)We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the FokkerPlanck equation describing the ... 
Patientspecific computational modeling of Cortical Spreading Depression via Diffusion Tensor Imaging
(International Journal for Numerical Methods in Biomedical Engineering, 20160629)Cortical Spreading Depression (CSD), a depolarization wave originat ing in the visual cortex and traveling towards the frontal lobe, is com monly accepted as a correlate of migraine visual aura. As of today, little is ... 
Patientspecific modelling of cortical spreading depression applied to migraine studies
(20190617)Migraine is a common neurological disorder and onethird of migraine patients suffer from migraine aura, a perceptual disturbance preceding the typically unilateral headache. Cortical spreading depression (CSD), a ... 
Qualitative analysis of kineticbased models for tumorimmune system interaction
(Discrete and Continuous Dynamical Systems  Series B, 201808)A mathematical model, based on a mesoscopic approach, describing the competition between tumor cells and immune system in terms of kinetic integrodifferential equations is presented. Four interacting populations are ... 
An RBFFD closest point method for solving PDEs on surfaces
(Journal of Computational Physics, 2018)Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):19431961, ... 
Reproduction ratio and growth rates: Measures for an unfolding pandemic
(PLoS ONE, 202005)The initial exponential growth rate of an epidemic is an important measure that follows directly from data at hand, commonly used to infer the basic reproduction number. As the growth rates λ(t) of tested positive COVID19 ... 
SDEdriven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness
(Discrete and Continuous Dynamical Systems  Series B, 2019)We deduce cell population models describing the evolution of a tumor (possibly interacting with its environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations of cancer cells ... 
Selfsimilar stochastic models with stationary increments for symmetric spacetime fractional diffusion
(20170428)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 heatsemigroup formalism. Specifically, we combine suitable ... 
SHAR and effective SIR models: from dengue fever toy models to a COVID19 fully parametrized SHARUCD framework
(Communication in Biomathematical Sciences, 2020)We review basic models of severe/hospitalized and mild/asymptomatic infection spreading (with classes of susceptibles S, hopsitalized H, asymptomatic A and recovered R, hence SHARmodels) and develop the notion of comparing ... 
A spacefractional Monodomain model for cardiac electrophysiology combining anisotropy and heterogeneity on realistic geometries
(20171004)Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatiotemporal description of excitation waves propagation. We consider a modification of the Monodomain ... 
Spectral analysis of a blocktriangular preconditioner for the bidomain system in electrocardiology
(Electronic Transactions on Numerical Analysis, 20121231)In this paper we analyze in detail the spectral properties of the blocktriangular preconditioner introduced by GerardoGiorda et al. [J. Comput. Phys., 228 (2009), pp. 36253639] for the Bidomain system in nonsymmetric ... 
Structuring targeted surveillance for monitoring disease emergence by mapping observational data onto ecological process
(Journal of the Royal Society Interface, 20131231)An efficient surveillance system is a crucial factor in identifying, monitoring and tackling outbreaks of infectious diseases. Scarcity of data and limited amounts of economic resources require a targeted effort from public ... 
Temporal excitation patterns on the cerebral cortex as a result of migraine modeling
(Springer Proceedings in Physics, 20160629)The complex, highly individual, geometry of the cerebral cortex in humans presents a major challenge in studying the spreading of spontaneous neuronal activity. Recent computational advances [1] allow to simulate the ... 
Tissue drives lesion: computational evidence of interspecies variability in cardiac radiofrequency ablation
(HE 10TH INTERNATIONAL CONFERENCE ON FUNCTIONAL IMAGING AND MODELING OF THE HEART, 2019)Radiofrequency catheter ablation (RFCA) is widely used for the treatment of various types of cardiac arrhythmias. Typically, the efficacy and the safety of the ablation protocols used in the clinics are derived from tests ... 
Transitions between bursting modes in the integrated oscillator model for pancreatic βcells
(Journal of Theoretical Biology, 20180620)Insulinsecreting $\beta$cells of pancreatic islets of Langerhans produce bursts of electrical impulses, resulting in intracellular Ca$^{2+}$ oscillations and pulsatile insulin secretion. The mechanism for this bursting ...