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 - http://www.scopus.com/inward/record.url?scp=0037764863&partnerID=8YFLogxK
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 -