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Heterogeneity in epidemic models and its effect on the spread of infection

Published online by Cambridge University Press:  14 July 2016

Håkan Andersson  and
Tom Britton
Håkan Andersson*
Affiliation:
Stockholm University
Tom Britton*
Affiliation:
Uppsala University
*
∗Postal address: Mathematical Statistics, Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden. Email address: [email protected].
∗∗Postal address: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden.
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Abstract

We first study an epidemic amongst a population consisting of individuals with the same infectivity but with varying susceptibilities to the disease. The asymptotic final epidemic size is compared with the corresponding size for a homogeneous population. Then we group a heterogeneous population into households, assuming very high infectivity within households, and investigate how the global infection pressure is affected by rearranging individuals between the households. In both situations considered, it turns out that whether or not homogenizing the individuals or households will result in an increased spread of infection actually depends on the infectiousness of the disease.

Keywords

Epidemic modelheterogeneous populationtotal sizehousehold population

MSC classification

Primary: 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 651 - 661
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

T.B. supported by The Bank of Sweden Tercentenary Foundation.

References

Andersson, H. (1998). Limit theorems for a random graph epidemic model. To appear in Ann. Appl. Prob.Google Scholar
Ball, F. (1985). Deterministic and stochastic epidemics with several kinds of susceptibles. Adv. Appl. Prob. 17, 1–22.Google Scholar
Ball, F. (1990). A new look at Downton's carrier-borne epidemic model. In Stochastic Processes in Epidemic Theory, Eds Gabriel, J.-P., Lefèvre, C. and Picard, P. (Lecture Notes in Biomathematics 86.) Springer, Berlin, pp. 71–85.Google Scholar
Ball, F. (1991). Dynamic population epidemic models. Math. Biosci. 107, 299–324.CrossRefGoogle ScholarPubMed
Ball, F., and Clancy, D. (1993). The final size and severity of a generalised stochastic multitype epidemic model. Adv. Appl. Prob. 25, 721–736.CrossRefGoogle Scholar
Ball, F., and O'Neill, P. (1993). A modification of the general stochastic epidemic motivated by AIDS modelling. Adv. Appl. Prob. 25, 39–62.Google Scholar
Ball, F., Mollison, D., and Scalia-Tomba, G. (1997). Epidemics with two levels of mixing. Ann. Appl. Prob. 7, 46–89.Google Scholar
Becker, N. G. (1973). Carrier-borne epidemics in a community consisting of different groups. J. Appl. Prob. 10, 491–501.CrossRefGoogle Scholar
Becker, N. G., and Marschner, I. (1990). The effect of heterogeneity on the spread of disease. In Stochastic Processes in Epidemic Theory, Eds Gabriel, J.-P., Lefèvre, C. and Picard, P. (Lecture Notes in Biomathematics 86.) Springer, Berlin, pp. 90–103.CrossRefGoogle Scholar
Becker, N. G., and Dietz, K. (1995). The effect of household distribution on transmission and control of highly infectious diseases. Math. Biosci. 127, 207–219.Google Scholar
Britton, T. (1997). Tests to detect clustering of infected individuals within families. Biometrics 53, 98–109.CrossRefGoogle ScholarPubMed
Clancy, D. (1994). Some comparison results for multitype epidemic models. J. Appl. Prob. 31, 9–21.Google Scholar
Lefèvre, C., and Malice, M.-P. (1988). Comparisons for carrier-borne epidemics in heterogeneous and homogeneous populations. J. Appl. Prob. 25, 663–674.Google Scholar
Marschner, I. (1992). The effect of preferential mixing on the growth of an epidemic. Math. Biosci. 109, 39–67.Google Scholar
O'Neill, P. (1995). Epidemic models featuring behaviour change. Adv. Appl. Prob. 27, 960–979.CrossRefGoogle Scholar
Sellke, T. (1983). On the asymptotic distribution of the size of a stochastic epidemic. J. Appl. Prob. 20, 390–394.Google Scholar