## Case studies in mathematical modeling−−ecology, physiology, and cell biologyThis volume is a collection of case studies designed to instruct advanced undergraduates and beginning graduate students in the art and science of modeling applied to biological problems. Students with quantitative science background (some knowledge of differential equations) are introduced to the diversity, excitement, and accessibility of problems in the life sciences, and exposed to the intellectual tools for successful mathematical modeling. Each chapter distills lectures given by a leading researcher during a Special Year in Mathematical Biology at the University of Utah in 1995-96. Authors were asked to provide an in-depth exposition of a crucial problem in their area of expertise. The resulting case studies lead students through the formulation, solution, and interpretation of cutting-edge research, catapulting them directly into the research process. To emphasize the unifying power of mathematical methods in biology, authors, have drawn from three highly active areas of research in the life sciences: ecology, physiology, and cell biology. |

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### Contents

A Population Dynamic Perspective | 25 |

Reflections on Models of Epidemics Triggered by the Case of Phocine | 51 |

Ancestral Inference from DNA Sequence Data | 81 |

Cell Biology | 97 |

Molecules Mechanisms and Mathematical | 127 |

Mathematical Models of Hematopoietic Cell Replication and Control | 149 |

Oscillations and Multistability in Delayed Feedback Control | 179 |

Calcium and Membrane Potential Oscillations in Pancreatic 6Cells | 199 |

Mathematical Modeling of Muscle Crossbridge Mechanics | 221 |

The Topology of Phase Resetting and the Entrainment of Limit Cycles | 255 |

Modeling the Interaction of Cardiac Muscle with Strong Electric Fields | 277 |

Fluid Dynamics of the Heart and its Valves | 309 |

Bioconvection | 339 |

A Agestructured Models | 353 |

An Introduction to Partial Differential Equations | 381 |

Subject Index | 399 |

Physiology | 219 |