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
Comparative effects of avoidance and vaccination in disease spread on a dynamic small-world network
TL;DR: The critical mobility required for an outbreak to occur as a function of the disease’s infectivity, recovery rate, avoidance rate, and vaccination rate is derived.
Journal ArticleDOI
A Caputo (discretization) fractional-order model of glucose-insulin interaction: numerical solution and comparisons with experimental data
TL;DR: In this paper, the authors investigated a (discretization) Caputo fractional glucose-insulin model qualitatively with incommensurate orders that appear in Bergman's minimal model.
Journal ArticleDOI
A two-barrier compartment model for volume flow across amphibian skin
TL;DR: This model shows that the predicted rehydration rates from apical bathing solutions are in good agreement with the experiment results in Hillyard and Larsen (J Comp Physiol 171: 283-292, 2001); and there is a substantial volume flux coupled to the active solute flux.
Journal ArticleDOI
The Role of Spatial Refuges in Coupled Map Lattice Model for Host-Parasitoid Systems
TL;DR: The results show that depending on many features such as position, size, and fragmentation of a refuge, as well as the dispersal parameters of hosts and parasitoids, together with the parasitoid attack rate, the inclusion of refuges may as well stabilize as destabilize the host-parasitoid dynamics.