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
Epidemiological models for invasion and persistence of pathogens.
TL;DR: An overarching modeling framework is presented that can be used to analyze disease invasion and persistence at a range of scales from the microscopic to the regional and for simple models of epidemics and for models with greater biological realism.
Journal ArticleDOI
Stability analysis of pathogen-immune interaction dynamics.
TL;DR: The paper considers models of dynamics of infectious disease in vivo from the standpoint of the mathematical analysis of stability, in which uninfected cells are involved in the immune response to pathogens, and are removed by the immune complexes.
Journal ArticleDOI
Homotopy Perturbation Method for Solving Partial Differential Equations
TL;DR: In this article, the homotopy perturbation method (HPM) is applied for solving linear and nonlinear partial differential equations. But the proposed algorithm is quite efficient and is practically well suited for use in these problems.
Journal ArticleDOI
Population size dependent incidence in models for diseases without immunity.
Jinshi Zhou,Herbert W. Hethcote +1 more
TL;DR: The persistence of the disease combined with disease-related deaths and reduced reproduction of infectives can greatly affect the population dynamics and cause the population size to decrease or to a new size below its carrying capacity.
Journal ArticleDOI
Quantitative modeling in cell biology: what is it good for?
TL;DR: The utility and methods of modeling are discussed and several current models of cell signaling, cytoskeletal self-organization, nuclear transport, and the cell cycle are reviewed and it is argued that the closer the complete systematic understanding of cell behavior is, the more important modeling becomes and the more experiment and theory merge.