Page 1 Next

Displaying 1 – 20 of 84

Showing per page

A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2006)

Applications of Mathematics

In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability...

Analysis of immunotherapy models in the context of cancer dynamics

Zuzanna Szymańska (2003)

International Journal of Applied Mathematics and Computer Science

A basic mathematical model of the immune response when cancer cells are recognized is proposed. The model consists of six ordinary differential equations. It is extended by taking into account two types of immunotherapy: active immunotherapy and adoptive immunotherapy. An analysis of the corresponding models is made to answer the question which of the presented methods of immunotherapy is better. The analysis is completed by numerical simulations which show that the method of adoptive immunotherapy...

Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch

F. Crauste (2009)

Mathematical Modelling of Natural Phenomena

A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the...

Delays induced in population dynamics

Eva Sánchez (2003)

Banach Center Publications

This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to examine how the delays emerge from inner mechanisms in the model, how they induce oscillations and stability switches in the system and how the qualitative behaviour of a biological model depends on the form of the delay.

Currently displaying 1 – 20 of 84

Page 1 Next