Mathematical models in epidemiology /
Saved in:
| Author / Creator: | Brauer, Fred, author. |
|---|---|
| Imprint: | New York, NY : Springer, 2019. |
| Description: | 1 online resource (xvii, 619 pages) : illustrations (some color) |
| Language: | English |
| Series: | Texts in applied mathematics, 0939-2475 ; volume 69 Texts in applied mathematics ; 69. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11981472 |
Table of Contents:
- Intro; Foreword; Preface; Acknowledgments; Contents; Part I Basic Concepts of Mathematical Epidemiology; 1 Introduction: A Prelude to Mathematical Epidemiology; 1.1 Introduction; 1.2 Some History; 1.2.1 The Beginnings of Compartmental Models; 1.2.2 Stochastic Models; 1.2.3 Developments in Compartmental Models; 1.2.4 Endemic Disease Models; 1.2.5 Diseases Transmitted by Vectors; 1.2.6 Heterogeneity of Mixing; 1.3 Strategic Models and This Volume; References; 2 Simple Compartmental Models for Disease Transmission; 2.1 Introduction to Compartmental Models; 2.2 The SIS Model
- 2.3 The SIR Model with Births and Deaths2.4 The Simple Kermack-McKendrick Epidemic Model; 2.5 Epidemic Models with Deaths due to Disease; 2.6 *Project: Discrete Epidemic Models; 2.7 *Project: Pulse Vaccination; 2.8 *Project: A Model with Competing Disease Strains; 2.9 Project: An Epidemic Model in Two Patches; 2.10 Project: Fitting Data for an Influenza Model; 2.11 Project: Social Interactions; 2.12 Exercises; References; 3 Endemic Disease Models; 3.1 More Complicated Endemic Disease Models; 3.1.1 Exposed Periods; 3.1.2 A Treatment Model; 3.1.3 Vertical Transmission
- 3.2 Some Applications of the SIR Model3.2.1 Herd Immunity; 3.2.2 Age at Infection; 3.2.3 The Inter-Epidemic Period; 3.2.4 ``Epidemic'' Approach to Endemic Equilibrium; 3.3 Temporary Immunity; 3.3.1 *Delay in an SIRS Model; 3.4 A Simple Model with Multiple Endemic Equilibria; 3.5 A Vaccination Model: Backward Bifurcations; 3.5.1 The Bifurcation Curve; 3.6 *An SEIR Model with General Disease Stage Distributions; 3.6.1 *Incorporation of Quarantine and Isolation; 3.6.2 *The Reduced Model of (3.42) Under GDA; 3.6.3 *Comparison of EDM and GDM; 3.7 Diseases in Exponentially Growing Populations
- 3.8 Project: Population Growth and Epidemics3.9 *Project: An Environmentally Driven Infectious Disease; 3.10 *Project: A Two-Strain Model with Cross Immunity; 3.11 Exercises; References; 4 Epidemic Models; 4.1 A Branching Process Disease Outbreak Model; 4.1.1 Transmissibility; 4.2 Network and Compartmental Epidemic Models; 4.3 More Complicated Epidemic Models; 4.3.1 Exposed Periods; 4.3.2 A Treatment Model; 4.3.3 An Influenza Model; 4.3.4 A Quarantine-Isolation Model; 4.4 An SIR Model with a General Infectious Period Distribution; 4.5 The Age of Infection Epidemic Model
- 4.5.1 A General SEIR Model4.5.2 A General Treatment Model; 4.5.3 A General Quarantine/Isolation Epidemic Model; 4.6 The Gamma Distribution; 4.7 Interpretation of Data and Parametrization; 4.7.1 Models of SIR Type; 4.7.2 Models of SEIR Type; 4.7.3 Mean Generation Time; 4.8 *Effect of Timing of Control Programs on EpidemicFinal Size; 4.9 Directions for Generalization; 4.10 Some Warnings; 4.11 *Project: A Discrete Model with Quarantine and Isolation; 4.12 Project: Epidemic Models with Direct and IndirectTransmission; 4.13 Exercises; References; 5 Models with Heterogeneous Mixing