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. |
Contents
Spatial spread | 8 |
the art of averaging | 37 |
Dynamics at the demographic time scale | 41 |
The concept of state | 69 |
And everything else | 94 |
Age structure | 121 |
Elaborations for Part I | 177 |
Elaborations for Part II | 261 |
Appendix A Stochastic basis of the KermackMcKendrick | 291 |
| 297 | |
Common terms and phrases
assume assumption asymptotically basic reproduction become infected branching process calculate characterised characteristic equation compute condition consider constant contact process contacts per unit death rate defined demographic denote density depends derive describe determined deterministic Diekmann differential equation distribution dominant eigenvalue dynamics eigenvector endemic steady epidemic models equals example Exercise expected number exponential exponential growth exponentially distributed extinction Fa(a factor final-size equation force of infection formulation fraction function h-state Hence Hint host population i-state immune infected individual infection-age infectious period infective agent integral interpretation larvae linearised major outbreak Markov chain Math mathematical mean metapopulation microparasites N₁ number of contacts pair parameters parasites positive probability distribution probability of transmission probability per unit quantity recurrence relations right-hand side root Section sexual Show situation solution spectral radius stochastic submodels subpopulation susceptible t₁ threshold vaccinated 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 |