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Mathematical analysis of the optimizing acquisition and retention over time problem

Adi Ditkowski (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...

Mathematical and Computational Models in Tumor Immunology

F. Pappalardo, A. Palladini, M. Pennisi, F. Castiglione, S. Motta (2012)

Mathematical Modelling of Natural Phenomena

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:...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

Sébastien Benzekry (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Mathematical and numerical analysis of a stratigraphic model

Véronique Gervais, Roland Masson (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h , the L surface concentrations c i s in lithology i of the sediments at the top...

Mathematical and numerical analysis of a stratigraphic model

Véronique Gervais, Roland Masson (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we consider a multi-lithology diffusion model used in stratigraphic modelling to simulate large scale transport processes of sediments described as a mixture of L lithologies. This model is a simplified one for which the surficial fluxes are proportional to the slope of the topography and to a lithology fraction with unitary diffusion coefficients. The main unknowns of the system are the sediment thickness h, the L surface concentrations c i s in lithology i of the sediments at the...

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Yao-Chuang Han, Yu-Feng Nie, Zhan-Bin Yuan (2019)

Applications of Mathematics

This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm...

Mathematical and numerical modeling of early atherosclerotic lesions***

Vincent Calvez, Jean Gabriel Houot, Nicolas Meunier, Annie Raoult, Gabriela Rusnakova (2010)

ESAIM: Proceedings

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...

Mathematical and numerical studies of non linear ferromagnetic materials

Patrick Joly, Olivier Vacus (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we are interested in the numerical modeling of absorbing ferromagnetic materials obeying the non-linear Landau-Lifchitz-Gilbert law with respect to the propagation and scattering of electromagnetic waves. In this work we consider the 1D problem. We first show that the corresponding Cauchy problem has a unique global solution. We then derive a numerical scheme based on an appropriate modification of Yee's scheme, that we show to preserve some important properties of the continuous...

Mathematical modeling of antigenicity for HIV dynamics

François Dubois, Hervé V.J. Le Meur, Claude Reiss (2010)

MathematicS In Action

This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which...

Mathematical Modeling of Atmospheric Flow and Computation of Convex Envelopes

A. Caboussat (2011)

Mathematical Modelling of Natural Phenomena

Atmospheric flow equations govern the time evolution of chemical concentrations in the atmosphere. When considering gas and particle phases, the underlying partial differential equations involve advection and diffusion operators, coagulation effects, and evaporation and condensation phenomena between the aerosol particles and the gas phase. Operator splitting techniques are generally used in global air quality models. When considering organic aerosol...

Mathematical modeling of delamination and nonmonotone friction problems by hemivariational inequalities

Charalambos C. Baniotopoulos, Jaroslav Haslinger, Zuzana Morávková (2005)

Applications of Mathematics

The paper deals with approximations and the numerical realization of a class of hemivariational inequalities used for modeling of delamination and nonmonotone friction problems. Assumptions guaranteeing convergence of discrete models are verified and numerical results of several model examples computed by a nonsmooth variant of Newton method are presented.

Mathematical Modeling of Leukemogenesis and Cancer Stem Cell Dynamics

T. Stiehl, A. Marciniak-Czochra (2012)

Mathematical Modelling of Natural Phenomena

The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts....

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