.

0 (hodnocen0 x )

(2) Půjčeno:2x 

BK

Chichester : John Wiley & Sons, 2000

xvi,303 s.

ISBN 0-471-49241-8 (brož.)

Wiley series in mathematical and computational biology

Obsahuje bibliografii na s. 297-300 a rejstřík

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 outside02of 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..

Epidemiologie - modely matematické - studie

000058625

Preface, Creed and Apology // What it is all about and what not xi // The top down approach xi // A workbook xii // Portrait of the reader as a young person xiii // A brief outline of the book xiii // Acknowledgements xiv // And what about reality? xv // I The bare bones: basic issues explained in the simplest context i // 1 The epidemic in a closed population 3 // 1.1 The questions (and the underlying assumptions) 3 // 1.2 Initial growth 4 // 1.2.1 Initial growth on a generation basis 4 // 1.2.2 The influence of demographic stochasticity 5 // 1.2.3 Initial growth in real time 9 // 1.3 The final size 12 // 1.3.1 The standard final-size equation 12 // 1.3.2 Derivation of the standard final-size equation (and reflection upon the underlying assumptions) 15 // 1.3.3 The final size of epidemics within herds 18 // 1.3.4 The final size in a finite population 22 // 1.4 The epidemic in a closed population: summary 26 // 2 Heterogeneity: the art of averaging 31 // 2.1 Differences in infecti vity 31 // 2.2 Differences in infectivity and susceptibility 37 // 2.3 Heterogeneity: a preliminary conclusion 39 // 3 Dynamics at the demographic time scale 41 // 3.1 Repeated outbreaks versus persistence 41 // 3.2 Fluctuations around the endemic steady state 43 // 3.3 Regulation of host populations 55 // 3.4 Beyond a single outbreak: summary 59 // 3.5 Some evolutionary considerations about virulence 60 // II Structured populations 63 // 4 The concept of state 65 // 4.1 i-states 65 // 4.1.1 d-states 66 // 4.1.2 h-states 68 // 4.2 p-states 69 // 4.3 Recapitulation, problem formulation and outlook 70 // 5 The basic reproduction ratio 73 // 5.1 The definition of i?o 73 // 5.2 General h-state 77 // 5.3 On conditions that simplify the computation of ?? 79 // 5.3.1 One-dimensional range 80 // 5.3.2 Additional within-group contacts 81 // 5.3.3 Finite-dimensional range 82 //

5.4 Submodels for the kernel 83 // 5.5 Extended example: two diseases 85 // 5.6 Pair formation models 91 // 5.7 Summary’: a recipe for fío 95 // 6 And everything else 99 // 6.1 Partially vaccinated populations (a first example) 99 // 6.2 The intrinsic growth rate r 103 // 6.3 Some generalities 108 // 6.4 Separable mixing 110 // 7 Age structure 113 // 7.1 Demography 113 // 7.2 Contacts 115 // 7.3 The next-generation operator 115 // 7.4 Interval decomposition 117 // 7.5 Inferring parameters from endemic data 117 // 7.6 Vaccination 122 // 8 Spatial spread 125 // 8.1 Posing the problem 125 // 8.2 Warming up: the linear diffusion equation 125 // 8.3 Verbal reflections suggesting robustness 128 // 8.4 Linear structured population models 130 // 8.5 The nonlinear situation 132 // 8.6 How to make the theory operational? 134 // 8.7 Summary: The speed of propagation 134 // 9 Macroparasites 137 // 9.1 Introduction 137 // 9.2 Counting parasite load 139 // 9.3 The calculation of Rq for life cycles 146 // 9.4 Seasonality and Rq 148 // 9.5 A ‘pathological’ model 149 // 10 What is contact? 153 // 10.1 Introduction 153 // 10.2 Contact duration 154 // 10.3 Consistency conditions 159 // 10.4 Effects of subdivision 162 // 10.4.1 Aggregation 162 // 10.4.2 What is a core group? 165 // 10.5 Network models (an idiosyncratic survey) 166 // 10.5.1 Reflections: what do we want and why? 166 // 10.5.2 A network with hardly any structure 169 // III The hard part: elaborations to (almost) all exercises 175 // 11 Elaborations for Part I 177 // 11.1 Elaborations for Chapter 1 177 // 11.2 Elaborations for Chapter 2 197 // 11.3 Elaborations for Chapter 3 203 // 12 Elaborations for Part II 221 // 12.1 Elaborations for Chapter 5 221 // 12.2 Elaborations for Chapter 6 241 // 12.3 Elaborations for Chapter 7 252 // 12.4 Elaborations for Chapter 8 261 // 12.5 Elaborations for Chapter 9 265 //

12.6 Elaborations for Chapter 10 277 // Appendix A Stochastic basis of the Kermack-McKendrick // ODE model 291 // Appendix B Bibliographic skeleton 297 // Epidemic modelling 297 // Population dynamics 299 // Non-negative matrices and operators 299 // Dynamical systems and bifurcations 300 // Analysis 300 // Stochastic processes 300 // Index 301