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Diagnostics of the AML with immunophenotypical data

A. Plesa, G. Ciuperca, V. Louvet, L. Pujo-Menjouet, S. Génieys, C. Dumontet, X. Thomas, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

Patients with acute myeloblastic leukemia (AML) are divided according to the French American British (FAB) classification into eight subgroups (M0 to M7) on the basis of their degree of maturation/differentiation. However, even if immunophenotypical characterization by flow cytometry is routinely used to distinguish between AML and acute lymphoblastic leukemia (ALL), it is not yet well established for the identification within the AML subgroups. Here we show that certain subgroups of AML can be...

Different models of chemotherapy taking into account drug resistance stemming from gene amplification

Jarosław Śmieja, Andrzej Świerniak (2003)

International Journal of Applied Mathematics and Computer Science

This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension,...

Differential growth models for microbial populations

Jaroslav Milota (1982)

Aplikace matematiky

Two models of microbial growth are derived as a resuslt of a discussion of the models of Monod and Hinshelwood types. The approach takes account of the lyse of dead cells in inhibitory products as well as in those which stimulate the growth. The asymptotic behaviour of the models is proved and the models applied to a chemostat.

Differential stability of solutions to air quality control problems in urban area

Piotr Holnicki, Jan Sokołowski, Antoni Żochowski (1987)

Aplikace matematiky

The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.

Diffusion limit for the phenomenon of random genetic drift

Anna Marciniak (2000)

Applicationes Mathematicae

The paper deals with mathematical modelling of population genetics processes. The formulated model describes the random genetic drift. The fluctuations of gene frequency in consecutive generations are described in terms of a random walk. The position of a moving particle is interpreted as the state of the population expressed as the frequency of appearance of a specific gene. This leads to a continuous model on the microscopic level in the form of two first order differential equations (known as...

Diffusion models of multicomponent mixtures in the lung*

L. Boudin, D. Götz, B. Grec (2010)

ESAIM: Proceedings

In this work, we are interested in two different diffusion models for multicomponent mixtures. We numerically recover experimental results underlining the inadequacy of the usual Fick diffusion model, and the importance of using the Maxwell-Stefan model in various situations. This model nonlinearly couples the mole fractions and the fluxes of each component of the mixture. We then consider a subregion of the lower part of the lung, in which we compare...

Digital search trees and chaos game representation*

Peggy Cénac, Brigitte Chauvin, Stéphane Ginouillac, Nicolas Pouyanne (2009)

ESAIM: Probability and Statistics

In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which one can visualize repetitions of subwords (seen as suffixes of subsequences). The CGR-tree turns a sequence of letters into a Digital Search Tree (DST), obtained from the suffixes of the reversed sequence. Several results are known concerning the height, the insertion depth for DST built from independent successive random sequences having the same distribution. Here the successive inserted words...

Discrete Groups and Internal Symmetries of Icosahedral Viral Capsids

Richard Kerner (2014)

Molecular Based Mathematical Biology

A classification of all possible icosahedral viral capsids is proposed. It takes into account the diversity of hexamers’ compositions, leading to definite capsid size.We showhowthe self-organization of observed capsids during their production results from definite symmetries of constituting hexamers. The division of all icosahedral capsids into four symmetry classes is given. New subclasses implementing the action of symmetry groups Z2, Z3 and S3 are found and described. They concern special cases...

Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations

Jens Christian Claussen (2008)

Banach Center Publications

Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit N → ∞ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in 1/√N. Consequences and relations to some previous approaches...

Discrete time markovian agents interacting through a potential

Amarjit Budhiraja, Pierre Del Moral, Sylvain Rubenthaler (2013)

ESAIM: Probability and Statistics

A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport...

Do Demographic and Disease Structures Affect the Recurrence of Epidemics ?

A. Castellazzo, A. Mauro, C. Volpe, E. Venturino (2012)

Mathematical Modelling of Natural Phenomena

In this paper we present an epidemic model affecting an age-structured population. We show by numerical simulations that this demographic structure can induce persistent oscillations in the epidemic. The model is then extended to encompass a stage-structured disease within an age-dependent population. In this case as well, persistent oscillations are observed in the infected as well as in the whole population.

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