CONTENTS -- Foreword -- Preface -- The Basic Epidemiology Models: Models, Expressions for R0, Parameter Estimation, and Applications Herbert W. Hethcote -- Contents -- 1.1 Introduction -- 1.2 Why do epidemiology modeling? -- 1.3 Definitions, assumptions and model formulations -- 1.3.1 Formulating epidemiology models -- 1.3.2 Three threshold quantities: R0, σ, and R -- 1.4 The basic SIS endemic model -- 1.5 The basic SIR epidemic model -- 1.6 The basic SIR endemic model -- 1.7 Similar models with M and E epidemiological states -- 1.7.1 The SEIR epidemic model -- 1.7.2 The MSEIRS endemic model -- 1.8 Threshold estimates using the two SIR models -- 1.9 Comparisons of some directly transmitted diseases -- 1.10 The effectiveness of vaccination programs -- 1.10.1 Smallpox -- 1.10.2 Poliomyelitis -- 1.10.3 Measles -- 1.10.4 Rubella -- 1.10.5 Chickenpox (varicella) -- 1.10.6 Influenza -- 1.11 Other epidemiology models with thresholds -- References -- Epidemiology Models with Variable Population Size Herbert W. Hethcote -- Contents -- 2.1. Introduction -- 2.2. Epidemiological compartment structures -- 2.3. Horizontal incidences -- 2.4. Waiting times in the E, I and R compartments -- 2.5. Demographic structures -- 2.6. Epidemiological-demographic interactions -- 2.7. SIRS model with recruitment-death and standard incidence -- 2.8. SIRS model with logistic demographics and standard incidence -- 2.9. SIRS model with exponential demographics and standard incidence -- 2.10. Discussion of the 3 previous SIRS models -- 2.11. Periodicity in SEI endemic models -- 2.11.1. The SEI model for fox rabies with mass action incidence -- 2.11.2. An SEI model with standard incidence -- 2.11.2.1. The equilibria in T -- 2.11.2.2. Asymptotic behavior -- 2.11.3. Discussion of the cause of periodicity in SEI models -- References.

Age-Structured Epidemiology Models and Expressions for R0 Herbert W. Hethcote -- Contents -- 3.1. Introduction -- 3.2. Three threshold quantities: R0, σ, and R -- 3.3. Two demographic models -- 3.3.1. The demographic model with continuous age -- 3.3.2. The demographic model with age groups -- 3.4. The MSEIR model with continuous age structure -- 3.4.1. Formulation of the MSEIR model -- 3.4.2. The basic reproduction number R0 and stability -- 3.4.3. Expressions for the average age of infection A -- 3.4.4. Expressions for R0 and A with negative exponential survival -- 3.4.5. The MSEIR model with vaccination at age Av -- 3.4.6. Expressions for R0 and A for a step survival function -- 3.5. The SEIR model with age groups -- 3.5.1. Formulation of the SEIR model with age groups -- 3.5.2. The basic reproduction number R0 and stability -- 3.5.3. Expressions for the average age of infection A -- 3.6. Application to measles in Niger -- 3.7. Application to pertussis in the United States -- 3.8. Discussion -- References -- Clinical and Public Health Applications of Mathematical Models John W. Glasser -- 1. Introduction -- 1.1. Modeling -- 2. Measles -- 2.1. Outbreak in S˜ao Paulo, 1997 -- 3. Congenital Rubella Syndrome -- 3.1. Assessing the burden -- 3.1.1. Mitigating the burden - Costa Rica -- 3.1.2. Mitigating the burden - Romania -- 4. Pertussis -- 5. Varicella and Herpes Zoster -- 6. Smallpox -- 7. Emerging Infectious Diseases -- 8. Conclusions and Outlook -- Acknowledgments -- References -- Non-identifiables and Invariant Quantities in Infectious Disease Models Ping Yan -- 1. Introduction -- 1.1. Observed data versus stochastic mechanisms that manifest data -- 1.2. Stochastic mechanisms that lead to transmission of an infectious disease -- 1.3. Structure of this chapter -- 2. Some statistical models and methods for identifying the non-identifiables.

2.1. Retrospectively ascertained data -- 2.2. Partially identifiable information in retrospectively ascertained data -- 2.2.1. The identi.able part of F(x) -- 2.2.2. Discrete time model and non-parametric approach -- 2.2.3. Continuous time model and parametric approach -- 2.2.4. Caution against the naı̈ve approach -- 2.3. Data without retrospective ascertainment -- 2.3.1. The back-calculation philosophy -- 2.3.2. Back-calculation methods in a nutshell -- 2.3.3. Some modeling paradigms for i1(t -- θ) -- 3. Stochastic aspects of disease transmission mechanisms -- 3.1. Formulating the stochastic mechanisms in infectious disease transmission -- 3.1.1. The distributions for the latent and infectious periods -- 3.1.2. The infectious contact process {K(x), x ∈ [0,∞)} -- 4. The role of stationary increment infectious contact processes in modeling disease transmission -- 4.1. With respect to the intrinsic growth rate ρ -- 4.2. With respect to the basic reproduction number R0 and uncertainties -- 4.3. Relations between R0 and ρ when {K(x)} has stationary increment -- 4.3.1. A remark on serial intervals and a formula used in [12] -- 4.3.2. Generalized formula for R0 as a function of ρ with gamma distributed latent and infectious periods -- 4.4. Stationary increment infectious contact process {K(x)} and the final size of a large outbreak -- 5. Robustness, invariance and identifiability -- 5.1. Robustness and sensitivity -- 5.1.1. Robustness -- 5.1.2. Sensitivity -- 5.2. Identifiability -- 5.3. Usefulness of models -- 5.3.1. Based on .nal size equations -- 5.3.2. The case with limited supply -- 5.3.3. On the reduction of intrinsic growth rate ρ -- 6. Some conclusion remarks -- Acknowledgements -- References.