Mathematical Models in Population Biology and EpidemiologyThis book is an introduction to the principles and practice of mathematical modeling in the biological sciences, concentrating on applications in population biology, epidemiology, and resource management. The core of the book covers models in these areas and the mathematics useful in analyzing them, including case studies representing real-life situations. The emphasis throughout is on describing the mathematical results and showing students how to apply them to biological problems while highlighting some modeling strategies. A large number and variety of examples, exercises, and projects are included. Additional ideas and information may be found on a web site associated with the book. Senior undergraduates and graduate students as well as scientists in the biological and mathematical sciences will find this book useful. Carlos Castillo-Chavez is professor of biomathematics in the departments of biometrics, statistics, and theoretical and applied mechanics at Cornell University and a member of the graduate fields of applied mathematics, ecology and evolutionary biology, and epidemiology. H is the recepient of numerous awards including two White House Awards (1992 and 1997) and QEM Giant in Space Mentoring Award (2000). Fred Brauer is a Professor Emeritus of Mathematics at the University id Wisconsin, where he taught from 1960 to 1999, and has also been an Honorary Professor of Mathematics at the University of British Columbia since 1997. |
From inside the book
Results 1-5 of 96
Page vi
Fred Brauer, Carlos Castillo-Chavez. in a variety of ways. For example, many problems and projects have been motivated or have been adapted from the 144 technical reports generated over those 15 years, all collected in an accessible web ...
Fred Brauer, Carlos Castillo-Chavez. in a variety of ways. For example, many problems and projects have been motivated or have been adapted from the 144 technical reports generated over those 15 years, all collected in an accessible web ...
Page viii
... example, with populations structured by disease status. The core of the book, which should be included in any ... examples and exercises that may be too simplistic for more experienced students, who may progress through this material a ...
... example, with populations structured by disease status. The core of the book, which should be included in any ... examples and exercises that may be too simplistic for more experienced students, who may progress through this material a ...
Page xii
... Example: A Predator and Two Competing Prey . . . . . . . . . . . . . . . . . 214 5.11 Example: Two Predators Competing for Prey . . . . . . . . . . . . . . . . . . . 217 5.12 Project: A Simple Neuron Model ...
... Example: A Predator and Two Competing Prey . . . . . . . . . . . . . . . . . 214 5.11 Example: Two Predators Competing for Prey . . . . . . . . . . . . . . . . . . . 217 5.12 Project: A Simple Neuron Model ...
Page xvii
... example, Cohen notes that in the fourteenth century repeated waves of Black Death, a form of bubonic plague, together with wars, heavy taxes, insurrections, and poor and sometimes malicious governments, killed an estimated one third of ...
... example, Cohen notes that in the fourteenth century repeated waves of Black Death, a form of bubonic plague, together with wars, heavy taxes, insurrections, and poor and sometimes malicious governments, killed an estimated one third of ...
Page xix
... per capita growth rate G depends on the size of the population. In mathematical terms, we have the model dx dt = xG(x), x(0) = x0. The most common example is provided by the logistic equation On Population Dynamics xix.
... per capita growth rate G depends on the size of the population. In mathematical terms, we have the model dx dt = xG(x), x(0) = x0. The most common example is provided by the logistic equation On Population Dynamics xix.
Contents
Discrete Population Models 49 | 48 |
4 | 123 |
Continuous Models for Two Interacting Populations | 165 |
Harvesting in Twospecies Models 223 | 222 |
Models for Populations with Age Structure | 267 |
Models for Populations with Spatial Structure 293 | 292 |
Epidemic Models 345 | 343 |
Models for Endemic Diseases | 411 |
Index | 501 |
Other editions - View all
Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez Limited preview - 2013 |
Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez Limited preview - 2001 |
Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez No preview available - 2010 |
Common terms and phrases
assume assumption asymptotically stable equilibrium basic reproduction number behavior of solutions biological budworm capita growth rate characteristic equation coexistence community matrix competition computer algebra system consider constant critical depensation curve decreases denote depends describe determine difference equation differential equation differential–difference equation diffusion disease disease-free equilibrium dynamics eigenvalues endemic equilibrium epidemic models equilibrium is asymptotically eutrophic example Exercises exponential extinction fraction function gives harvesting individuals initial condition initial value integral isocline linear logistic equation Lotka–Volterra M-matrix mathematical maximum maximum sustainable yield node nonlinear nonnegative number of infectives obtain orbit tends ordinary differential equations outbreak patch periodic orbit phase plane population model population sizes positive possible predator predator–prey problem saddle point satisfy Section separation of variables separatrices Show species Springer Science+Business Media susceptible tend to zero Theorem tion total population unstable vaccination variables vector x-isocline