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
Small-scale fungicide spray heterogeneity and the coexistence of resistant and sensitive pathogen strains.
TL;DR: It is shown that fungicide spray heterogeneity per se is not sufficient for coexistence but that the outcome depends crucially on the competitive relationship between resistant and sensitive strains, and that the maximum density of healthy host tissue is realized when resistant andsensitive pathogen strains coexist.
Journal ArticleDOI
Developmental causes of allometry: new models and implications for phenotypic plasticity and evolution.
TL;DR: Large evolutionary changes in allometry can be produced by small and simple changes in growth kinetics, and it is shown how understanding the development of traits can greatly simplify the interpretation of how they evolved.
Journal ArticleDOI
Mapping the architecture of the HIV-1 Tat circuit: A decision-making circuit that lacks bistability and exploits stochastic noise
TL;DR: This approach provided the first characterization of a 'decision-making' circuit that lacks bistability and instead exploits stochastic fluctuations in cellular molecules to generate a decision between an on or off transcriptional state.
Journal ArticleDOI
The role of membrane patch size and flow in regulating a proteolytic feedback threshold on a membrane: possible application in blood coagulation
Edward J. Beltrami,Jolyon Jesty +1 more
TL;DR: A partial differential equation model of an archetypal feedback loop is examined in which a proteolytic enzyme catalyzes its own formation from a zymogen on a membrane in contact with a flowing medium and an approximate mathematical statement of the dependence of the minimum activatable patch size on the kinetic and other parameters is formulated.
Journal ArticleDOI
Acid-induced unfolding kinetics in simulated gastric digestion of proteins.
TL;DR: Theoretical digestion patterns generated using consecutive and simultaneous exponential models, and the fit of a two stage consecutive exponential model (unfolding followed by pepsinolysis) to laboratory data, support unfolding kinetics as playing a critical role in determining the speed at which many proteins digest in SGF.