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Analysis of a Nonautonomous HIV/AIDS Model

G. P. Samanta (2010)

Mathematical Modelling of Natural Phenomena

In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDS epidemic model with an imperfect HIV vaccine, varying total population size and distributed time delay to become infectious due to intracellular delay between initial infection of a cell by HIV and the release of new virions. Here, we have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique....

Analysis of a Population Model Structured by the Cells Molecular Content

M. Doumic (2010)

Mathematical Modelling of Natural Phenomena

We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this...

Analysis of Synchronization in a Neural Population by a Population Density Approach

A. Garenne, J. Henry, C. O. Tarniceriu (2010)

Mathematical Modelling of Natural Phenomena

In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate...

Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis

D.P. Moualeu, S. Bowong, J.J. Tewa, Y. Emvudu (2012)

Mathematical Modelling of Natural Phenomena

Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease....

Analysis of the predator-prey model with climax prey population

Jitka Kühnová (2009)

Acta Mathematica Universitatis Ostraviensis

The aim of the contribution is to study ODE predator-prey system with a prey population embodying the Allee effect. Particular stationary points are analyzed and the results are illustrated by graphs of numerical solutions for various values of model parameters.

Analyzing sets of phylogenetic trees using metrics

Damian Bogdanowicz (2011)

Applicationes Mathematicae

The reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetic trees and give some basic properties of the Matching Split metric, which...

Ancestral processes with selection: Branching and Moran models

Ellen Baake, Robert Bialowons (2008)

Banach Center Publications

We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyse the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced...

Application of the adaptive center-weighted vector median framework for the enhancement of cDNA microarray images

Rastislav Lukac, Bogdan Smołka (2003)

International Journal of Applied Mathematics and Computer Science

In this paper a novel method of noise reduction in color images is presented. The new technique is capable of attenuating both impulsive and Gaussian noise, while preserving and even enhancing the sharpness of the image edges. Extensive simulations reveal that the new method outperforms significantly the standard techniques widely used in multivariate signal processing. In this work we apply the new noise reduction method for the enhancement of the images of the so called gene chips. We demonstrate...

Application of the Rasch model in categorical pedigree analysis using MCEM: I binary data

G. Qian, R. M. Huggins, D. Z. Loesch (2004)

Discussiones Mathematicae Probability and Statistics

An extension of the Rasch model with correlated latent variables is proposed to model correlated binary data within families. The latent variables have the classical correlation structure of Fisher (1918) and the model parameters thus have genetic interpretations. The proposed model is fitted to data using a hybrid of the Metropolis-Hastings algorithm and the MCEM modification of the EM-algorithm and is illustrated using genotype-phenotype data on a psychological subtest in families where some members...

Applications of topology to DNA

Isabel Darcy, De Sumners (1998)

Banach Center Publications

The following is an expository article meant to give a simplified introduction to applications of topology to DNA.

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