Abstract
In this paper, the behaviour of an epidemic of the SIR type in a large closed population is studied. By generalizing the imbedding representation of epidemics of Scalia-Tomba (1985), many of the available results on asymptotic final size distributions of various epidemic models can be obtained and generalized to include heterogeneity of susceptibility to infection.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
von Bahr B. and Martin-Lof A., Threshold limit theorems for some epidemic processes, Adv. Appl. Prob. 12 (1980), 319-349..
Ball F., The threshold behaviour of epidemic models, J. Appl. Prob. 20 (1983), 227-241.
Ball F., Deterministic and stochastic epidemics with several kinds of susceptibles, Adv. Appl. Prob 17 (1985), 1-22..
Billingsley P., "Convergence of Probability Measures," John Wiley, New York, 1968.
Cramer H. and Leadbetter M.R., "Stationary and Related Stochastic Processes," John Wiley, New York, 1967.
Lindvall T., Weak convergence of probability measures and random functions in the function space D(O,oo), J. Appl. Prob. 10 (1973), 109-121.
Sellke T., On the asymptotic distribution of the size of a stochastic epidemic, J. Appl. Pro b. 20 (1983), 390-394.
Serfozo R.F., Functional limit theorems for stochastic processes based on embedded processes, Adv. Appl. Prob. 7 (1975), 123-139.
Scalia-Tomba G., Asymptotic final size distribution for some chain-binomial processes, Adv. Appl. Prob. 17 (1985), 477-495.
Wang F.J.S., Gaussian approximation of some closed stochastic epidemic models, J. Appl. Prob. 14 (1977), 221-231.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Scalia-Tomba, G. (1990). On the asymptotic final size distribution of epidemics in heterogeneous populations. In: Gabriel, JP., Lefèvre, C., Picard, P. (eds) Stochastic Processes in Epidemic Theory. Lecture Notes in Biomathematics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10067-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-662-10067-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52571-4
Online ISBN: 978-3-662-10067-7
eBook Packages: Springer Book Archive