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In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view...
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is R₀< 1. Then the disease is controllable and dies out. In the absence...
The immune system is able to protect the host from tumor onset, and immune deficiencies
are accompanied by an increased risk of cancer. Immunology is one of the fields in biology
where the role of computational and mathematical modeling and analysis were recognized the
earliest, beginning from 60s of the last century. We introduce the two most common methods
in simulating the competition among the immune system, cancers and tumor immunology
strategies:...
We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...
We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...
We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations...
This article is devoted to the construction of a mathematical model describing the early
formation of atherosclerotic lesions. The early stage of atherosclerosis is an
inflammatory process that starts with the penetration of low density lipoproteins in the
intima and with their oxidation. This phenomenon is closely linked to the local blood flow
dynamics. Extending a previous work [5] that was mainly restricted to a
one-dimensional setting, we couple...
This special issue of Mathematical Modelling of Natural Phenomena on biomathematics education shares the work of fifteen groups at as many different institutions that have developed beautiful biological applications of mathematics that are different in three ways from much of what is currently available. First, many of these selections utilize current research in biomathematics rather than the well-known textbook examples that are at least a half-century old. Second, the selections focus on modules...
Electro-muscular disruption (EMD) devices such as TASER M26 and
X26 have been used as a less-than-lethal weapon. Such EMD devices
shoot a pair of darts toward an intended target to generate an
incapacitating electrical shock. In the use of the EMD device,
there have been controversial questions about its safety and
effectiveness. To address these questions, we need to investigate
the distribution of the current density J inside the target
produced by the EMD device. One approach is to develop a
computational...
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