## 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. |

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### 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