## 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

3 | |

Discrete Population Models | 51 |

Continuous SingleSpecies Population | 95 |

Introduction and Mathematical Preliminaries 127 | 126 |

Continuous Models for Two Interacting Populations | 171 |

Harvesting in twospecies models | 231 |

Basic Ideas of Mathematical Epidemiology 275 | 274 |

Models for Populations with Age Structure | 339 |

Epilogue | 371 |

A Answers to Selected Exercises 375 | 374 |

### Other editions - View all

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 Limited preview - 2011 |

Mathematical Models in Population Biology and Epidemiology Fred Brauer,Carlos Castillo-Chavez No preview available - 2010 |

### Common terms and phrases

a f(x Allee effect an+1 approach assume assumption asymptotically stable asymptotically stable equilibrium basic reproductive number behavior of solutions biological birth rate budworm capita growth rate carrying capacity Castillo-Chavez characteristic equation chemostat coexistence community matrix competition computer algebra system condition consider constant critical depensation curve death rate decreases delay denotes depends describe determine difference equation differential equation differential-difference equation disease disease-free equilibrium dynamics eigenvalues endemic equilibrium epidemic epidemiological equilibrium aloe equilibrium is asymptotically eutrophic example Exercise exponential extinction FIGURE function gives immunity increases infective period initial value isocline limit cycle linear logistic equation logistic model mathematical maximum maximum sustainable yield nonlinear obtain oligotrophic orbit tends oscillations periodic orbit phase plane population model population sizes positive possible predator predator-prey prey isocline qualitative recruitment saddle point Section separatrices Show SIS model species survival susceptible tend to zero Theorem tion total population unstable variables yg(x