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
A mathematical model for dispersal of an annual plant population with a seed bank
TL;DR: It is showed that the seed bank can significantly alter the dynamics of annual plants, since it can have both a stabilizing and a destabilizing effect on the total population and can also homogenize the spatial distribution of the plants.
Journal ArticleDOI
Dynamics analysis of epidemic and information spreading in overlay networks.
Guirong Liu,Zhimei Liu,Zhen Jin +2 more
TL;DR: An SIS-UAU model is established to present the dynamics of epidemic and information spreading in overlay networks and shows that the effect of awareness can reduce the basic reproduction number of disease.
Journal ArticleDOI
Quiescence as an explanation of Gompertzian tumor growth revisited
TL;DR: If an avascular tumor grows according to the three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero and the size of the tumor will increase.
Journal ArticleDOI
Modeling Microbial Communities: A Call for Collaboration between Experimentalists and Theorists
TL;DR: This work believes that the synergy emerging from a coherent collection facilitates a better understanding of important processes that determine microbial community functions and emphasizes the importance of close collaboration between theoreticians and experimentalists in formulating, classifying, and improving models of microbial communities.
Journal ArticleDOI
Evolutionary ecology in silico: Does mathematical modelling help in understanding 'generic' trends?
TL;DR: In this article, several unified mathematical models of evolutionary ecology have been developed over the last few years with the aim of describing the statistical properties of data related to the evolution of ecosystems.