Contact tracing in stochastic and deterministic epidemic models

Johannes Müller; Mirjam Kretzschmar; Klaus Dietz

doi:10.1016/S0025-5564(99)00061-9

Contact tracing in stochastic and deterministic epidemic models

Johannes Müller^*, Mirjam Kretzschmar, Klaus Dietz

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

49 Citations (Scopus)

Abstract

We consider a simple unstructured individual based stochastic epidemic model with contact tracing. Even in the onset of the epidemic, contact tracing implies that infected individuals do not act independent of each other. Nevertheless, it is possible to analyze the embedded non-stationary Galton-Watson process. Based upon this analysis, threshold theorems and also the probability for major outbreaks can be derived. Furthermore, it is possible to obtain a deterministic model that approximates the stochastic process, and in this way, to determine the prevalence of disease in the quasi-stationary state and to investigate the dynamics of the epidemic. (C) 2000 Elsevier Science Inc.

Original language	English
Pages (from-to)	39-64
Number of pages	26
Journal	Mathematical Biosciences
Volume	164
Issue number	1
DOIs	https://doi.org/10.1016/S0025-5564(99)00061-9
Publication status	Published - 1 Mar 2000

Keywords

Contact tracing
Epidemic models
Galton-Watson process
Quasi-stationary state
Threshold theorem

Access to Document

10.1016/S0025-5564(99)00061-9

Cite this

@article{57fa469d7b4c4bb09068c49c4bb33154,

title = "Contact tracing in stochastic and deterministic epidemic models",

abstract = "We consider a simple unstructured individual based stochastic epidemic model with contact tracing. Even in the onset of the epidemic, contact tracing implies that infected individuals do not act independent of each other. Nevertheless, it is possible to analyze the embedded non-stationary Galton-Watson process. Based upon this analysis, threshold theorems and also the probability for major outbreaks can be derived. Furthermore, it is possible to obtain a deterministic model that approximates the stochastic process, and in this way, to determine the prevalence of disease in the quasi-stationary state and to investigate the dynamics of the epidemic. (C) 2000 Elsevier Science Inc.",

keywords = "Contact tracing, Epidemic models, Galton-Watson process, Quasi-stationary state, Threshold theorem",

author = "Johannes M{\"u}ller and Mirjam Kretzschmar and Klaus Dietz",

year = "2000",

month = mar,

day = "1",

doi = "10.1016/S0025-5564(99)00061-9",

language = "English",

volume = "164",

pages = "39--64",

journal = "Mathematical Biosciences",

issn = "0025-5564",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Contact tracing in stochastic and deterministic epidemic models

AU - Müller, Johannes

AU - Kretzschmar, Mirjam

AU - Dietz, Klaus

PY - 2000/3/1

Y1 - 2000/3/1

N2 - We consider a simple unstructured individual based stochastic epidemic model with contact tracing. Even in the onset of the epidemic, contact tracing implies that infected individuals do not act independent of each other. Nevertheless, it is possible to analyze the embedded non-stationary Galton-Watson process. Based upon this analysis, threshold theorems and also the probability for major outbreaks can be derived. Furthermore, it is possible to obtain a deterministic model that approximates the stochastic process, and in this way, to determine the prevalence of disease in the quasi-stationary state and to investigate the dynamics of the epidemic. (C) 2000 Elsevier Science Inc.

AB - We consider a simple unstructured individual based stochastic epidemic model with contact tracing. Even in the onset of the epidemic, contact tracing implies that infected individuals do not act independent of each other. Nevertheless, it is possible to analyze the embedded non-stationary Galton-Watson process. Based upon this analysis, threshold theorems and also the probability for major outbreaks can be derived. Furthermore, it is possible to obtain a deterministic model that approximates the stochastic process, and in this way, to determine the prevalence of disease in the quasi-stationary state and to investigate the dynamics of the epidemic. (C) 2000 Elsevier Science Inc.

KW - Contact tracing

KW - Epidemic models

KW - Galton-Watson process

KW - Quasi-stationary state

KW - Threshold theorem

UR - https://www.scopus.com/pages/publications/0037764863

U2 - 10.1016/S0025-5564(99)00061-9

DO - 10.1016/S0025-5564(99)00061-9

M3 - Article

C2 - 10704637

AN - SCOPUS:0037764863

SN - 0025-5564

VL - 164

SP - 39

EP - 64

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 1

ER -

Contact tracing in stochastic and deterministic epidemic models

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this