## Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and InterpretationMathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation O. Diekmann University of Utrecht, The Netherlands J. A. P. Heesterbeek Centre for Biometry Wageningen, The Netherlands The mathematical modelling of epidemics in populations is a vast and important area of study. It is about translating biological assumptions into mathematics, about mathematical analysis aided by interpretation and about obtaining insight into epidemic phenomena when translating mathematical results back into population biology. Model assumptions are formulated in terms of, usually stochastic, behaviour of individuals and then the resulting phenomena, at the population level, are unravelled. Conceptual clarity is attained, assumptions are stated clearly, hidden working hypotheses are attained and mechanistic links between different observables are exposed. Features: * Model construction, analysis and interpretation receive detailed attention * Uniquely covers both deterministic and stochastic viewpoints * Examples of applications given throughout * Extensive coverage of the latest research into the mathematical modelling of epidemics of infectious diseases * Provides a solid foundation of modelling skills The reader will learn to translate, model, analyse and interpret, with the help of the numerous exercises. In literally working through this text, the reader acquires modelling skills that are also valuable outside of epidemiology, certainly within population dynamics, but even beyond that. In addition, the reader receives training in mathematical argumentation. The text is aimed at applied mathematicians with an interest in population biology and epidemiology, at theoretical biologists and epidemiologists. Previous exposure to epidemic concepts is not required, as all background information is given. The book is primarily aimed at self-study and ideally suited for small discussion groups, or for use as a course text. |

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### Contents

the art of averaging | 31 |

Dynamics at the demographic time scale | 41 |

The concept of state | 65 |

The basic reproduction ratio | 73 |

And everything else | 99 |

Age structure | 113 |

Spatial spread | 125 |

Macroparasites | 137 |

What is contact? | 153 |

Elaborations for Part I | 177 |

Appendix A Stochastic basis of the KermackMcKendrick | 291 |

297 | |

### Other editions - View all

Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis ... O. Diekmann,J. A. P. Heesterbeek No preview available - 2000 |

### Common terms and phrases

Ansatz argument assume assumption asymptotic basic reproduction become infected biological branching process calculate characterise characteristic equation compute condition consider constant contact process contact structure contacts per unit defined demographic denote density depend derive describe deterministic Diekmann differential equation distribution dominant eigenvalue dynamics eigenvector endemic steady epidemic models equals Exercise expected number exponential growth exponentially exponentially distributed expression Fa(a factor force of infection formulation fraction function graph h-state Hence Hint host population immune infected individual infection-age infectious period infective agent integral interpretation larvae linearised major outbreak Math mathematical mean metapopulation microparasites next-generation matrix nonlinear number of contacts obtain pair parameter parasites population density positive probability distribution probability of transmission probability per unit quantity recurrence relations rewrite right-hand side root Rož s(co s(oo Section sexual Show situation solution spectral radius stochastic submodels subpopulation susceptible threshold vaccination vector zero

### References to this book

Scale-Free Networks: Complex Webs in Nature and Technology Guido Caldarelli No preview available - 2007 |

Mathematics for Life Science and Medicine Yasuhiro Takeuchi,Yoh Iwasa,Kazunori Sato Limited preview - 2007 |