Displaying 1681 – 1700 of 1854

Showing per page

The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response

Radouane Yafia (2009)

Applicationes Mathematicae

We consider a system of delay differential equations modelling the tumor-immune system competition with negative immune response and three positive stationary points. The dynamics of the first two positive solutions are studied in terms of the local stability. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence and stability of a limit cycle bifurcating from the second positive stationary point, when the delay (taken as a parameter) crosses some...

The Effects of HIV-1 Infection on Latent Tuberculosis

Amy L. Bauer, Ian B. Hogue, Simeone Marino, Denise E. Kirschner (2008)

Mathematical Modelling of Natural Phenomena

Tuberculosis is the leading cause of death due to infectious diseases in the world today, and it is increasing due to co-infection with HIV-1, the causative agent of AIDS. Here, we examine the impact that HIV-1 infection has on persons with latent tuberculosis. Based on previous work, we develop a mathematical model of an adaptive immune response in the lung which considers relevant immune effectors such as macrophages, various sub-populations of T-cells, and key cytokines to predict which mechanisms...

The EM algorithm and its implementation for the estimation of frequencies of SNP-haplotypes

Joanna Polańska (2003)

International Journal of Applied Mathematics and Computer Science

A haplotype analysis is becoming increasingly important in studying complex genetic diseases. Various algorithms and specialized computer software have been developed to statistically estimate haplotype frequencies from marker phenotypes in unrelated individuals. However, currently there are very few empirical reports on the performance of the methods for the recovery of haplotype frequencies. One of the most widely used methods of haplotype reconstruction is the Maximum Likelihood method, employing...

The formation of a tree leaf

Qinglan Xia (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...

The Geometric and Dynamic Essence of Phyllotaxis

P. Atela (2011)

Mathematical Modelling of Natural Phenomena

We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.

The Importance of Spatial Distribution of Stemness and Proliferation State in Determining Tumor Radioresponse

H. Enderling, D. Park, L. Hlatky, P. Hahnfeldt (2009)

Mathematical Modelling of Natural Phenomena

Tumor growth and progression is a complex phenomenon dependent on the interaction of multiple intrinsic and extrinsic factors. Necessary for tumor development is a small subpopulation of potent cells, so-called cancer stem cells, that can undergo an unlimited number of cell divisions and which are proposed to divide symmetrically with a small probability to produce more cancer stem cells. We show that the majority of cells in a tumor must indeed be non-stem cancer cells with limited life span and...

The Influence of Look-Ahead on the Error Rate of Transcription

Y. R. Yamada, C. S. Peskin (2010)

Mathematical Modelling of Natural Phenomena

In this paper we study the error rate of RNA synthesis in the look-ahead model for the random walk of RNA polymerase along DNA during transcription. The model’s central assumption is the existence of a window of activity in which ribonucleoside triphosphates (rNTPs) bind reversibly to the template DNA strand before being hydrolyzed and linked covalently to the nascent RNA chain. An unknown, but important, integer parameter of this model is the window...

The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology

H. G. Othmer, K. Painter, D. Umulis, C. Xue (2009)

Mathematical Modelling of Natural Phenomena

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding...

Currently displaying 1681 – 1700 of 1854