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
On a Generalized Model of Biological Evolution
TL;DR: A model for biological evolution with relative fitness between different species is proposed and contains both negative interactions, e.g., predation, competition, etc., and positive interactions, i.e., mutualism, sharing, etc.
Journal ArticleDOI
Immune response to a pathogen in corals.
TL;DR: This analysis suggests an alternative explanation for the spatial and temporal variability in disease incidence and mortality, which is based on the strength of the immune system of hosts rather than the virulence of the pathogen.
Book ChapterDOI
Methodological Steps and Issues When Deriving Individual Based-Models from Equation-Based Models: A Case Study in Population Dynamics
TL;DR: The methodological issues that arise when attempting to derive an IBM from an existing EBM model in population dynamics, dedicated to exploring the dynamics of two competing populations in a "two-patch" environment are explored.
Journal ArticleDOI
A complete Lie symmetry classification of a class of (1+2)-dimensional reaction-diffusion-convection equations
TL;DR: A group of equivalence transformations is constructed and it is proved that the algorithm leads to 32 reaction-diffusion-convection equations admitting nontrivial Lie symmetries, which are derived and applied for the reduction and finding exact solutions in the case of the porous-Fisher type equation with the Burgers term.