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A Computational Framework to Assess the Efficacy of Cytotoxic Molecules and Vascular Disrupting Agents against Solid Tumours

M. Pons-Salort, B. van der Sanden, A. Juhem, A. Popov, A. Stéphanou (2012)

Mathematical Modelling of Natural Phenomena

A computational framework for testing the effects of cytotoxic molecules, specific to a given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The model is based on a cellular automaton to describe tumour cell states transitions from proliferation to death. It is coupled with a model describing the tumour vasculature and its adaptation to the blood rheological constraints when alterations are induced by VDAs treatment....

A free boundary problem for a predator-prey model with nonlinear prey-taxis

Mohsen Yousefnezhad, Seyyed Abbas Mohammadi, Farid Bozorgnia (2018)

Applications of Mathematics

This paper deals with a reaction-diffusion system modeling a free boundary problem of the predator-prey type with prey-taxis over a one-dimensional habitat. The free boundary represents the spreading front of the predator species. The global existence and uniqueness of classical solutions to this system are established by the contraction mapping principle. With an eye on the biological interpretations, numerical simulations are provided which give a real insight into the behavior of the free boundary...

A free boundary problem for some modified predator-prey model in a higher dimensional environment

Hongmei Cheng, Qinhe Fang, Yang Xia (2022)

Applications of Mathematics

We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as t goes to infinity and survives in the new environment, or it fails to establish...

A hyperbolic model of chemotaxis on a network: a numerical study

G. Bretti, R. Natalini, M. Ribot (2014)

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

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the...

A Modeling Framework For Immune-related Diseases

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

Mathematical Modelling of Natural Phenomena

About twenty five years ago the first discrete mathematical model of the immune system was proposed. It was very simple and stylized. Later, many other computational models have been proposed each one adding a certain level of sophistication and detail to the description of the system. One of these, the Celada-Seiden model published back in 1992, was already mature at its birth, setting apart from the topic-specific nature of the other models. This...

A topological model of site-specific recombination that predicts the knot and link type of DNA products

Karin Valencia (2014)

Banach Center Publications

This is a short summary of a topological model of site-specific recombination, a cellular reaction that creates knots and links out of circular double stranded DNA molecules. The model is used to predict and characterise the topology of the products of a reaction on double stranded DNA twist knots. It is shown that all such products fall into a small family of Montesinos knots and links, meaning that the knot and link type of possible products is significantly reduced, thus aiding their experimental...

A viscoelastic model with non-local damping application to the human lungs

Céline Grandmont, Bertrand Maury, Nicolas Meunier (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The...

Algebraic Methods for Studying Interactions Between Epidemiological Variables

F. Ricceri, C. Fassino, G. Matullo, M. Roggero, M.-L. Torrente, P. Vineis, L. Terracini (2012)

Mathematical Modelling of Natural Phenomena

BackgroundIndependence models among variables is one of the most relevant topics in epidemiology, particularly in molecular epidemiology for the study of gene-gene and gene-environment interactions. They have been studied using three main kinds of analysis: regression analysis, data mining approaches and Bayesian model selection. Recently, methods of algebraic statistics have been extensively used for applications to biology. In this paper we present...

An epidemic model with a time delay in transmission

Q. J. A. Khan, E. V. Krishnan (2003)

Applications of Mathematics

We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.

An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control

T. Dumrongpokaphan, Y. Lenbury, R. Ouncharoen, Y. Xu (2010)

Mathematical Modelling of Natural Phenomena

Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data.
We analyze a non-linear model of the human immunodeficiency virus (HIV)...

Analysis of a Mathematical Model for the Molecular Mechanism of Fate Decision in Mammary Stem Cells

O. U. Kirnasovsky, Y. Kogan, Z. Agur (2008)

Mathematical Modelling of Natural Phenomena

Recently, adult stem cells have become a focus of intensive biomedical research, but the complex regulation that allows a small population of stem cells to replenish depleted tissues is still unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that a feedback control of stem cells on their own proliferation and differentiation (denoted Quorum Sensing) suffices...

Analysis of Space-Temporal Symmetry in the Early Embryogenesis of Calla palustris L., Araceae

I.V. Rudskiy, G.E. Titova, T.B. Batygina (2010)

Mathematical Modelling of Natural Phenomena

Plants and animals have highly ordered structure both in time and in space, and one of the main questions of modern developmental biology is the transformation of genetic information into the regular structure of organism. Any multicellular plant begins its development from the universal unicellular state and acquire own species-specific structure in the course of cell divisions, cell growth and death, according to own developmental program. However the cellular mechanisms of plant development are...

Analysis of the Growth Control Network Specific for Human Lung Adenocarcinoma Cells

G. Pinna, A. Zinovyev, N. Araujo, N. Morozova, A. Harel-Bellan (2012)

Mathematical Modelling of Natural Phenomena

Many cancer-associated genes and pathways remain to be identified in order to clarify the molecular mechanisms underlying cancer progression. In this area, genome-wide loss-of-function screens appear to be powerful biological tools, allowing the accumulation of large amounts of data. However, this approach currently lacks analytical tools to exploit the data with maximum efficiency, for which systems biology methods analyzing complex cellular networks...

Approximating the Stability Region for a Differential Equation with a Distributed Delay

S. A. Campbell, R. Jessop (2009)

Mathematical Modelling of Natural Phenomena

We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular we show that a distribution independent stability region may be obtained in a similar way that delay independent...

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