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
Discrete Competitive and Cooperative Models of Lotka–Volterra Type
Pingzhou Liu,Saber Elaydi +1 more
TL;DR: In this article, the dynamics of discrete Lotka-Volterra system of two species is investigated and it is shown that the proposed discrete models for competitive and cooperative systems possess "dynamical consistency" with their continuous counterparts.
Book ChapterDOI
Knowledge Epidemics and Population Dynamics Models for Describing Idea Diffusion
TL;DR: In this paper, three approaches are discussed for modeling the diffusion of ideas in the areas of science and technology, through deterministic, stochastic, and statistical approaches, illustrated through their corresponding population dynamics and epidemic models relative to the spreading of ideas, knowledge and innovations.
Journal ArticleDOI
Proximity networks and epidemics
TL;DR: The notion of dynamic proximity networks which takes into account the relevant time-scales for disease spread: contact duration, infectivity period, and rate of contact creation are introduced.
Journal ArticleDOI
Predicting and preventing measles epidemics in New Zealand: application of a mathematical model.
Mick G. Roberts,M. I. Tobias +1 more
TL;DR: A mathematical model of the dynamics of measles in New Zealand successfully predicted an epidemic in 1997 and was instrumental in the decision to carry out an intensive MMR immunization campaign in that year.
Journal ArticleDOI
Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology
TL;DR: The prefactors alpha N and beta N, computed exactly for all N, increase very slowly (logarithmically) with increasing N, which has interesting implications in an ecological context in estimating the home range of a herd of animals with a population size N.