Mathematical tools for understanding infectious diseases dynamics
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the...
Guardat en:
| Autor principal: | |
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| Altres autors: | , |
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Princeton :
Princeton University Press
2011.
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| Matèries: | |
| Accés en línia: | Accès Université Orléans et IFPM |
| Nota: |
La pagination de l'édition imprimée correspondante est de 517 p. Cyberlibris (ScholarVox) corpus Santé |
| Autres localisations: | Voir dans le Sudoc |
Taula de continguts:
- 12.2 Contact duration
- 3.1 The prototype stochastic epidemic model3.2 Two special cases; 3.3 Initial phase of the stochastic epidemic; 3.4 Approximation of the main part of the epidemic; 3.5 Approximation of the final size; 3.6 The duration of the epidemic; 3.7 Stochastic modeling: summary; 4 Dynamics a t the demographic time scale; 4.1 Repeated outbreaks versus persistence; 4.2 Fluctuations around the endemic steady state; 4.3 Vaccination; 4.4 Regulation of host populations; 4.5 Tools for evolutionary contemplation; 4.6 Markov chains: models of infection in the ICU
- 4.7 Time to extinction and critical community size4.8 Beyond a single outbreak: summary; 5 Inference, or how to deduce conclusions from data; 5.1 Introduction; 5.2 Maximum likelihood estimation; 5.3 An example of estimation: the ICU model; 5.4 The prototype stochastic epidemic model; 5.5 ML-estimation of and in the ICU model; 5.6 The challenge of reality: summary; II: Structured populations; 6 The concept of state; 6.1 i-states; 6.2 p-states; 6.3 Recapitulation, problem formulation and outlook; 7 The basic reproduction number; 7.1 The definition of R[sub(0)]
- 7.2 NGM for compartmental systems7.3 General h-state; 7.4 Conditions that simplify the computation of R[sub(0)]; 7.5 Sub-models for the kernel; 7.6 Sensitivity analysis of R[sub(0)]; 7.7 Extended example: two diseases; 7.8 Pair formation models; 7.9 Invasion under periodic environmental conditions; 7.10 Targeted control; 7.11 Summary; 8 Other indicators of severity; 8.1 The probability of a major outbreak; 8.2 The intrinsic growth rate; 8.3 A brief look at final size and endemic level; 8.4 Simplifications under separable mixing; 9 Age structure; 9.1 Demography; 9.2 Contacts
- 9.3 The next-generation operator9.4 Interval decomposition; 9.5 The endemic steady state; 9.6 Vaccination; 10 Spatial spread; 10.1 Posing the problem; 10.2 Warming up: the linear diffusion equation; 10.3 Verbal reffections suggesting robustness; 10.4 Linear structured population models; 10.5 The nonlinear situation; 10.6 Summary: the speed of propagation; 10.7 Addendum on local finiteness; 11 Macroparasites; 11.1 Introduction; 11.2 Counting parasite load; 11.3 The calculation of R[sub(0)] for life cycles; 11.4 A 'pathological' model; 12 What is contact?; 12.1 Introduction
- Cover; Title; Copyright; Contents; Preface; A brief outline of the book; I: The bare bones: Basic issues in the simplest context; 1 The epidemic in a closed population; 1.1 The questions (and the underlying assumptions); 1.2 Initial growth; 1.3 The final size; 1.4 The epidemic in a closed population: summary; 2 Heterogeneity: The art of averaging; 2.1 Differences in infectivity; 2.2 Differences in infectivity and susceptibility; 2.3 The pitfall of overlooking dependence; 2.4 Heterogeneity: a preliminary conclusion; 3 Stochastic modeling: The impact of chance