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
Recovery and maintenance of North Island kokako (Callaeas cinerea wilsoni) populations through pulsed pest control
Britta Basse,Ian Flux,John Innes +2 more
TL;DR: Mathematical modelling supports empirical evidence that pests need not be controlled every year in order to maintain or greatly increase kokako populations, and predicts that the total number of years during which there is pest control is the main factor determining population size.
Journal ArticleDOI
Local Explanations of Landscape Patterns: Can Analytical Approaches Approximate Simulation Models of Spatial Processes?
TL;DR: It may sometimes be possible to answer important questions about spatial processes using crude spatial information obtained when a comprehensive map is not available, and even in the absence of an explicitly spatial broad-scale map, to study spatial processes by understanding which local-scale characteristics of space are important.
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Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak
TL;DR: In this paper, the authors derived an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak (fade-out).
Journal ArticleDOI
Adaptive host preference and the dynamics of host-parasitoid interactions.
TL;DR: Models of two independent host populations and a common parasitoid are investigated, showing that adaptive behavior and evolution frequently destabilize population dynamics and frequently increase the average difference between host densities.
Journal ArticleDOI
Within-host disease ecology in the sea fan Gorgonia ventalina: modeling the spatial immunodynamics of a coral-pathogen interaction.
TL;DR: A spatially explicit model for the within‐host interactions between a fungal pathogen and the immune response by its coral host provides possible mechanistic explanations for effects of environmental stressors on aspergillosis prevalence and severity and for the observed high spatial and between‐host variability in disease impacts.