Stochastic Epidemic Models and Their Statistical Analysis

ISBN-13: 9780387950501 / Angielski / Miękka / 2000 / 156 str.

Hakan Andersson; H. Andersson; T. Britton

Opis

This book describes stochastic epidemic models and methods for statistically analyzing them. It is aimed at statisticians, biostatisticians, and biomathematicians.

Spis treści

I: Stochastic Modelling.- 1. Introduction.- 1.1. Stochastic versus deterministic models.- 1.2. A simple epidemic model: The Reed-Frost model.- 1.3. Stochastic epidemics in large communities.- 1.4. History of epidemic modelling.- Exercises.- 2. The standard SIR epidemic model.- 2.1. Definition of the model.- 2.2. The Sellke construction.- 2.3. The Markovian case.- 2.4. Exact results.- Exercises.- 3. Coupling methods.- 3.1. First examples.- 3.2. Definition of coupling.- 3.3. Applications to epidemics.- Exercises.- 4. The threshold limit theorem.- 4.1. The imbedded process.- 4.2. Preliminary convergence results.- 4.3. The casemn/n??> 0 asn? ?.- 4.4. The casemn=mfor alln.- 4.5. Duration of the Markovian SIR epidemic.- Exercises.- 5. Density dependent jump Markov processes.- 5.1. An example: A simple birth and death process.- 5.2. The general model.- 5.3. The Law of Large Numbers.- 5.4. The Central Limit Theorem.- 5.5. Applications to epidemic models.- Exercises.- 6. Multitype epidemics.- 6.1. The standard SIR multitype epidemic model.- 6.2. Large population limits.- 6.3. Household model.- 6.4. Comparing equal and varying susceptibility.- Exercises.- 7. Epidemics and graphs.- 7.1. Random graph interpretation.- 7.2. Constant infectious period.- 7.3. Epidemics and social networks.- 7.4. The two-dimensional lattice.- Exercises.- 8. Models for endemic diseases.- 8.1. The SIR model with demography.- 8.2. The SIS model.- Exercises.- II: Estimation.- 9. Complete observation of the epidemic process.- 9.1. Martingales and log-likelihoods of counting processes.- 9.2. ML-estimation for the standard SIR epidemic.- Exercises.- 10. Estimation in partially observed epidemics.- 10.1. Estimation based on martingale methods.- 10.2. Estimation based on the EM-algorithm.- Exercises.- 11. Markov Chain Monte Carlo methods.- 11.1. Description of the techniques.- 11.2. Important examples.- 11.3. Practical implementation issues.- 11.4. Bayesian inference for epidemics.- Exercises.- 12. Vaccination.- 12.1. Estimating vaccination policies based on one epidemic.- 12.2. Estimating vaccination policies for endemic diseases.- 12.3. Estimation of vaccine efficacy.- Exercises.- References.