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
Turing instability in an economic-demographic dynamical system may lead to pattern formation on a geographical scale.
Anna Zincenko,Anna Zincenko,Sergei Petrovskii,Vitaly Volpert,Vitaly Volpert,Vitaly Volpert,Malay Banerjee +6 more
TL;DR: In this paper, a mathematical model of the coupled demographic-economic dynamics is proposed to identify a few areas at different parts of the world where the environmental conditions (quantified by the temperature, precipitation and elevation) show a relatively small variation in space on the scale of thousands of kilometres.
Journal ArticleDOI
The evolutionary dynamics of a population model with a strong Allee effect.
TL;DR: The main results are that orbits equilibrate, that the extinction set (or Allee basin) shrinks when evolution occurs, and that the meant trait component of survival equilibria occur at maxima of the inherent growth rate.
Journal ArticleDOI
Compartmental Model Diagrams as Causal Representations in Relation to DAGs.
Sarah F Ackley,Elizabeth Rose Mayeda,Lee Worden,Wayne T. A. Enanoria,M. Maria Glymour,Travis C. Porco +5 more
TL;DR: It is shown how to use compartmental model diagrams to explicitly depict interaction and feedback cycles, as well as explicitly depict feedback cycles and interactions, as part of a long-term tradition of causal thinking in epidemiology.
Journal ArticleDOI
Transmission of Tuberculosis with Exogenous Re-infection and Endogenous Reactivation
TL;DR: The effects of vaccination and treatment of active TB cases suggest that even if these control strategies could have a significant effect on reducing TB incidence, the exogenous re-infection and the endogenous reactivation, mainly due to HIV infection, will still increase the incidence of TB.
Journal ArticleDOI
A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers’ Migration
TL;DR: Metaecoepidemic models generalize metapopulation systems, combining local population dynamics with inter-patch migration coupled with an epidemic proliferation with a focus on a grassland–herbivore environment.