Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T14:18:44.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Threshold behaviour of emerging epidemics featuring contact tracing

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Frank G. Ball ,
Edward S. Knock  and
Philip D. O'Neill
Frank G. Ball*
Affiliation:
University of Nottingham
Edward S. Knock*
Affiliation:
University of Nottingham
Philip D. O'Neill*
Affiliation:
University of Nottingham
*
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is concerned with a stochastic model for the spread of an epidemic with a contact tracing scheme, in which diagnosed individuals may name some of their infectious contacts, who are then removed if they have not been already. Traced individuals may or may not also be asked to name their own contacts. The epidemic is studied by considering an approximating, modified birth-death process with intersibling dependencies, for which a threshold parameter and expressions from which extinction probabilities may be calculated are derived. When all individuals can name their contacts, it is shown that this threshold parameter depends on the infectious period distribution only through its mean. Numerical studies show that the infectious period distribution choice can have a material effect on the threshold behaviour of an epidemic, while the dependencies help reduce spread.

Keywords

Stochastic epidemiccontact tracingbranching processreproduction number

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 1048 - 1065
Copyright
Copyright © Applied Probability Trust 2011 

References

Athreya, K. B. and Karlin, S. (1971). On branching processes with random environments. I. Extinction probabilities. Ann. Math. Statist. 42, 1499–1520.Google Scholar
Ball, F. G. (1983). The threshold behaviour of epidemic models. J. Appl. Prob. 20, 227–241.Google Scholar
Ball, F. and Donnelly, P. (1995). Strong approximations for epidemic models. Stoch. Process. Appl. 55, 1–21.Google Scholar
Ball, F. G., Knock, E. S. and O'Neill, P. D. (2008). Control of emerging infectious diseases using responsive imperfect vaccination and isolation. Math. Biosci. 216, 100–113.CrossRefGoogle ScholarPubMed
Ball, F., O'Neill, P. D. and Pike, J. (2007). Stochastic epidemic models in structured populations featuring dynamic vaccination and isolation. J. Appl. Prob. 44, 571–585.Google Scholar
Becker, N. G., Glass, K., Li, Z. and Aldis, G. K. (2005). Controlling emerging infectious diseases like SARS. Math. Biosci. 193, 205–221.Google Scholar
Britton, T., Janson, S. and Martin-Löf, A. (2007). Graphs with specified degree distributions, simple epidemics, and local vaccination strategies. Adv. Appl. Prob. 39, 922–948.Google Scholar
Haccou, P., Jagers, P. and Vatutin, V. A. (2005). Branching processes: Variation, Growth, and Extinction of Populations. Cambridge University Press.Google Scholar
Heesterbeek, J. A. P. and Roberts, M. G. (2007). The type-reproduction number T in models for infectious disease control. Math. Biosci. 206, 3–10.Google Scholar
Kaplan, E. H., Craft, D. L. and Wein, L. M. (2002). Emergency response to a smallpox attack: the case for mass vaccination. Proc. Nat. Acad. Sci. USA 99, 10935–10940.Google Scholar
Klebaner, F. C. (1989). Linear growth in near-critical population-size-dependent multitype Galton–Watson processes. J. Appl. Prob. 26, 431–445.Google Scholar
Klinkenberg, D., Fraser, C. and Heesterbeek, H. (2006). The effectiveness of contact tracing in emerging epidemics. PLoS ONE 1, e13.Google Scholar
Knock, E. S. (2011). Stochastic epidemic models for emerging diseases incorporating household structure and contact tracing. , University of Nottingham. Available at http://etheses.nottingham.ac.uk/2046.Google Scholar
Lambert, A. (2010). The contour of splitting trees is a Lévy process. Ann. Prob. 38, 348–395.Google Scholar
Müller, J., Kretzschmar, M. and Dietz, K. (2000). Contact tracing in stochastic and deterministic epidemic models. Math. Biosci. 164, 39–64.Google Scholar
Olofsson, P. (1996). Branching processes with local dependencies. Ann. Appl. Prob. 6, 238–268.Google Scholar
Shaban, N., Andersson, M., Svensson, Å. and Britton, T. (2008). Networks, epidemics and vaccination through contact tracing. Math. Biosci. 216, 1–8.Google Scholar