MonographDOI
Mathematical Models in Biology
Reads0
Chats0
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
More filters
Journal ArticleDOI
Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment
TL;DR: In this article, the authors considered an SEIR model with constant population size and formulated an optimal control problem subject to vaccination and supportive treatment as controls, and found the optimal combination of vaccination and supporting treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios.
Journal ArticleDOI
Tier structure of strongly endotactic reaction networks
TL;DR: An analytical characterization of strongly endotactic networks in terms of tier structures is provided and an example which closes a conjecture in the negative by showing that stochastically modeled strongly endotacid networks can be transient (and even explosive).
Journal ArticleDOI
A preliminary mathematical model of the apple twig borer (Coleoptera: Bostrichidae) and grapes on the Texas high plains
TL;DR: A mathematical model of the interaction of the apple twig borer (ATB) and grape vines has been produced and reflects vineyard practices regarding the removal of pruned canes.
Journal ArticleDOI
Effects of asymmetric dispersal and environmental gradients on the stability of host–parasitoid systems
TL;DR: Host-parasitoid systems spatially distributed on a row of patches connected by dispersal are considered and it is found that stability is more likely when parasitoids move preferentially towards patches where they have high searching efficiency or when hosts go mainly to patchesWhere they have a low growth rate.
Journal ArticleDOI
An ultrasensitive sorting mechanism for EGF Receptor Endocytosis
TL;DR: A mathematical model of receptor sorting into alternative pathways that explains the EGF-concentration dependent response of CIE and describes extensibility of the model to more than two pathways which might play a role in contexts other than receptor internalization.