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The size of a major epidemic of a vector-borne disease

Part of: Applications

Published online by Cambridge University Press:  14 July 2016

Daryl J. Daley  and
Randall J. Swift
Daryl J. Daley
Affiliation:
The Australian National University and The University of Melbourne, Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia. Email address: [email protected]
Randall J. Swift
Affiliation:
California State Polytechnic University, Pomona, Department of Mathematics, California State Polytechnic University, Pomona, CA 91768, USA. Email address: [email protected]
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Abstract

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Based on a simple model due to Dietz, it is shown that the size of a major epidemic of a vector-borne disease with basic reproduction ratio R0>1 is dominated by the size of a standard SIR (susceptible–infected–removed) epidemic with direct host-to-host transmission of disease and the same R0. Further bounds and numerical illustrations are provided, broadly spanning situations where the size of the epidemic is short of infecting almost all those susceptible. The total size is moderately sensitive to changes in the population parameters that contribute to R0, so that the fluctuating behaviour in ‘annual’ epidemics is not surprising.

Keywords

Epidemicdenguebasic reproduction ratioepidemic total sizebranching processdeterministic epidemic modelseasonal infection

MSC classification

Primary: 92D30: Epidemiology
Secondary: 62P10: Applications to biology and medical sciences
Type
Part 5. Stochastic Growth and Branching
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 235 - 247
Copyright
Copyright © Applied Probability Trust 2011 

References

Daley, D. J., (2010). Comment on the paper by Gani. Austral. N. Z. J. Statist. 52, 330–334.Google Scholar
Daley, D. J. and Gani, J., (1999). Epidemic Modelling: An Introduction (Camb. Stud. Math. Biol. 15. Cambridge University Press.Google Scholar
Dietz, K., (1974). Transmission and control of arbovirus diseases. In Epidemiology, eds Ludwig, D. and Cooke, K. L., Society for Industrial and Applied Mathematics, Philadelphia, PA, pp. 104–121.Google Scholar
Esteva, L. and Vargas, C., (1998). Analysis of a dengue disease transmission model. Math. Biosci. 150, 131–151.CrossRefGoogle ScholarPubMed
Gani, J., (2010). Modelling epidemic diseases. Austral. N. Z. J. Statist. 52, 321–329.CrossRefGoogle Scholar
Gubler, D. J. and Kuno, G., (eds) (1997). Dengue and Dengue Hemorrhagic Fever. CAB International, Wallingford, Oxon.Google Scholar
Ooi, E.-E., Goh, K.-T. and Gubler, D. J., (2006). Dengue prevention and 35 years of vector control in Singapore. Emerging Infectious Diseases 12, 887–893.CrossRefGoogle ScholarPubMed