arXiv subjects

Yassine Ouzrour

Publications and source records attributed to Yassine Ouzrour.

3 recordsLinked to original sources

arXiv2025

Waterborne epidemics via a new coupled SIR--Pathogen--Navier-Stokes system: Mathematical modeling, nonlinear analysis and numerical simulation

Water-borne diseases are still a major public health concern, as there are circumstances under which water could act as a carrier of the pathogen, extending their modeling beyond direct contact between hosts. In the present work, we introduce a new mathematical framework, coupling epidemiological dynamics with fluid motion, in order to understand the spatial spread of such an infection. Our model couples the classical Susceptible-Infected-Recovered (SIR) model with the Navier-Stokes equations describing the motion of fluids, which enhances the existing literature by simultaneously taking into account two aspects: the pathogen being transported by the water currents and the dependence of the effective viscosity of the fluid on the pathogen concentration. We apply the Faedo-Galerkin method and compactness arguments to prove the existence of a global, biologically feasible solution to the coupled SIR--Pathogen--Navier-Stokes (SIRPNS) system. Additionally, we investigate the uniqueness of such solutions in the two-dimensional case. Finally, by constructing a numerical scheme based on the semi-implicit scheme in time and the finite element method in space, we run several numerical simulations to show how infection dispersal, environmental contamination, and hydrodynamic feedback together govern the spatial dynamics, persistence, and eventual decline of waterborne epidemics.

math.AP↗

arXiv2024

Effect of energy dissipation on radiofrequency ablation model in cardiac tissue: modelling, analysis and numerical simulation

This paper deals with the mathematical analysis and numerical simulation of a new nonlinear ablation system modeling radiofrequency ablation phenomena in cardiac tissue, {which incorporates the effects of blood flow on the heat generated when ablation by radiofrequency. The model also considers the effects of viscous energy dissipation. It consists of a coupled thermistor problem and the incompressible Navier--Stokes equations that describe the evolution of temperature, velocity and potential in cardiac tissue.} In addition to Faedo--Galerkin method, we use Schauder's fixed-point theory to prove the existence of the weak solutions in two- and three-dimensional space. Moreover, we prove the uniqueness of the solution under some additional conditions on the data and the solution. Finally, we discuss some numerical results for the validation of the proposed model using the finite element method.

math.AP↗

arXiv2024

Mathematical study of a new coupled electro-thermo radiofrequency model of cardiac tissue

This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo-Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.

math.NA↗