On complementary levels of description in applied mathematics II. Mathematical models in cancer biology
- 1 July 1988
- journal article
- research article
- Published by Taylor & Francis in International Journal of Mathematical Education in Science and Technology
- Vol. 19 (4) , 519-535
- https://doi.org/10.1080/0020739880190404
Abstract
The main stages of mathematical modelling are illustrated by examining some complementary levels of description of tumour growth, and characteristics of cancerous tissue. Four basic types of model are considered, although there can be variations within each category: deterministic diffusion models, probabilistic models, models based on the qualitative theory of differential equations, and topological models. Each category addresses different, but related issues, and exemplifies the contrasting approaches that may be used in establishing coherent mathematical models in the biological and other sciences.Keywords
This publication has 11 references indexed in Scilit:
- Some mathematical aspects of wave motionInternational Journal of Mathematical Education in Science and Technology, 1984
- Mathematical methods in linear inviscid hydrodynamic stability theoryInternational Journal of Mathematical Education in Science and Technology, 1982
- Optimization of Human Cancer RadiotherapyPublished by Springer Nature ,1981
- Stochastic processes for solid tumor kinetics II. Diffusion-regulated growthMathematical Biosciences, 1974
- Stochastic processes for solid tumor kinetics I. surface-regulated growthMathematical Biosciences, 1974
- Instability and Mitotic Patterns in Tissue GrowthJournal of Dynamic Systems, Measurement, and Control, 1973
- A system of axioms for mathematical biologyMathematical Biosciences, 1973
- Models for the Growth of a Solid Tumor by DiffusionStudies in Applied Mathematics, 1972
- Qualitative study of unstable behavior of cancerous cellsCancer, 1969
- Dynamics of cancerous cellsCancer, 1969