MonographDOI
Mathematical Models in Biology
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TLDR
The theory of linear difference equations applied to population growth and the applications of nonlinear difference equations to population biology are explained.Abstract:
Part I. Discrete Process in Biology: 1. The theory of linear difference equations applied to population growth 2. Nonlinear difference equations 3. Applications of nonlinear difference equations to population biology Part II. Continuous Processes and Ordinary Differential Equations: 4. An introduction to continuous models 5. Phase-plane methods and qualitative solutions 6. Applications of continuous models to population dynamics 7. Models for molecular events 8. Limit cycles, oscillations, and excitable systems Part III. Spatially Distributed Systems and Partial Differential Equation Models: 9. An introduction to partial differential equations and diffusion in biological settings 10. Partial differential equation models in biology 11. Models for development and pattern formation in biological systems Selected answers Author index Subject index.read more
Citations
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Journal ArticleDOI
Toxicité et efficacité antitumorale de l'oxaliplatine sur l'ostéosarcome de Glasgow induit chez la souris : un modèle mathématique☆
TL;DR: A mathematical model of the action of a chemotherapy on the population of tumoral cells on the one hand, on a population of fast renewing healthy cells in mice for model parameter identification the treatment by oxaliplatin of Glasgow Osteosarcoma in mice is proposed.
Journal ArticleDOI
Teaching of Mathematical Modeling Elements in the Mathematics Course of the Secondary School
Marina V. Krutikhina,Vera K. Vlasova,Alexander A. Galushkin,Alexander A. Galushkin,Andrey A. Pavlushin +4 more
TL;DR: In this paper, the authors identify elements of mathematical modeling that can and should be appropriately formed at the secondary school and develop a system of tasks aimed to form training activities that are adequate to the identified elements.
Journal ArticleDOI
On the Dynamics of a Two-Strain Influenza Model with Isolation
TL;DR: It is shown that when there is a delay in isolation, it may lead to more serious outbreaks as compared to no delay, and proposed criteria that may be useful for controlling influenza are proposed.
Journal ArticleDOI
Bridging intracellular scales by mechanistic computational models
Lukas A. Widmer,Jörg Stelling +1 more
TL;DR: This work highlights recent progress in bridging these model classes and outlines current challenges in multi-scale models such as active transport and dynamic geometries.
Journal ArticleDOI
A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions
TL;DR: In this article, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied in a reaction-diffusion system which exhibits Turing's diffusion-driven instability, and it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) can be computed for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary in the classical case without unilateral obstacles.