A01=Horst R. Thieme
Applied mathematics
Arithmetic mean
Author_Horst R. Thieme
Bifurcation theory
Biomass (ecology)
Birth rate
Calculation
Category=JHBD
Category=PBWH
Category=PSAF
Characteristic equation (calculus)
Convex optimization
Degeneracy (mathematics)
Differential equation
Dirac measure
Eigenvalues and eigenvectors
Epidemiology
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
eq_society-politics
Equation
Ergodic theory
Estimation
Existential quantification
Exponential distribution
Fubini's theorem
Function (mathematics)
Growth curve (biology)
Growth curve (statistics)
Homoclinic orbit
Hopf bifurcation
Interval (mathematics)
Jacobian matrix and determinant
Lebesgue measure
Life expectancy
Linear algebra
Logarithm
Logistic function
Logistic map
Mathematical and theoretical biology
Mathematical model
Mathematical sciences
Mathematical theory
Mathematician
Mathematics
Measure (mathematics)
Mortality rate
National Science Foundation
Natural logarithm
Next-generation matrix
Optimization problem
Order of integration (calculus)
Ordinary differential equation
Parity (mathematics)
Periodic function
Population dynamics
Population model
Probability
Probability distribution
Probability measure
Probability space
Probability theory
Proportionality (mathematics)
Pure mathematics
Restriction (mathematics)
Riemann sum
Scientific notation
Separatrix (mathematics)
Statistical hypothesis testing
Stochastic calculus
Support (mathematics)
Theorem
Three-dimensional space (mathematics)
Trichotomy (mathematics)
Vaccination
Variable (mathematics)
Zorn's lemma
Product details
- ISBN 9780691092911
- Weight: 765g
- Dimensions: 152 x 235mm
- Publication Date: 22 Jul 2003
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies.
Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a "toolbox" provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.
Horst R. Thieme is Professor of Mathematics at Arizona State University. He has published more than seventy research papers and is an associate editor of the "Journal of Mathematical Analysis and Applications". .
