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
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Journal ArticleDOI
Mathematical Model for Spatial Segregation of the Rho-Family GTPases Based on Inhibitory Crosstalk
TL;DR: It is shown that cooperativity is an essential ingredient in the interactions of the proteins, and the fast diffusion of the inactive forms is essential for stabilizing the transition fronts in the PDE formulation of the model, leading to robust spatial polarization, rather than traveling waves.
Journal ArticleDOI
Predator-Prey Dynamics in Models of Prey Dispersal in Two-Patch Environments*
Yang Kuang,Yasuhiro Takeuchi +1 more
TL;DR: This example indicates that a stable migrating predator-prey system can be made unstable by changing the amount of migration in both directions.
Journal ArticleDOI
A modelling framework for understanding social insect foraging
TL;DR: It is demonstrated how understanding of the proximate mechanisms involved in social insect foraging ultimately furthers understanding, not only of how insect societies function, but also of how these mechanisms are used to optimise colony fitness and survival.
Journal ArticleDOI
Phytoseiid life-histories, local predator-prey dynamics, and strategies for control of tetranychid mites
Arne Janssen,Maurice W. Sabelis +1 more
TL;DR: This paper shows how rms can be used to use a simple model for the local dynamics of predator and prey populations, and shows that the rm of phytoseiid and tetranychid mites are correlated with mean and peak oviposition rates.
Journal ArticleDOI
An SIS epidemic model with variable population size and a delay
TL;DR: The SIS epidemiological model has births, natural deaths, disease-related deaths and a delay corresponding to the infectious period, where the endemic infective-fraction equilibrium is asymptotically stable, but for other parameter values, it is unstable and a surrounding periodic solution appears by Hopf bifurcation.