Related papers: Mathematical modeling of Buruli ulcer spread
We propose an discontinuous Galerkin local orthogonal decomposition multiscale method for convection-diffusion problems with rough, heterogeneous, and highly varying coefficients. The properties of the multiscale method and the…
In this article we propose to extend the model of simulation of dispersions in turning based on the geometrical specifications. Our study is articulated around two trends of development: the first trend relates to the geometrical model. The…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
The study of infectious disease propagation is essential for understanding and controlling epidemics. One of the most useful tools for gaining insights into the spread of infectious diseases is mathematical modelling. In terms of…
By far, the fractional derivative model is mainly related to the modelling of complicated solid viscoelastic material. In this study, we try to build the fractional derivative PDE model for broadband ultrasound propagation through human…
Fire blight is a bacterial plant disease that affects apple and pear trees. We present a mathematical model for its spread in an orchard during bloom. This is a PDE-ODE coupled system, consisting of two semilinear PDEs for the pathogen,…
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical…
We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…
Existing burn resuscitation protocols exhibit large variability in treatment efficacy. Hence, they must be further optimized based on comprehensive knowledge of burn pathophysiology. A physics-based mathematical model that can replicate…
This paper concerns a general class of PDE-ODE reaction-diffusion systems, which features a singular fast-reaction limit towards a reaction-diffusion equation coupled to a scalar hysteresis operator. As prototypical application, we present…
Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…
In this article we propose a generalization of the theory of diffusion approximation for random ODE to a nonlinear system of random Schr\"{o}dinger equations. This system arises in the study of pulse propagation in randomly birefringent…
In this paper, we investigate a mathematical model describing the interactions between effector cells (E), cancer cells (T), and the IL-2 compound (IL). The model considered here is a generalization, taking into account some cross-diffusion…
We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…