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The Deterministic Spread of a Simple Epidemic

Published online by Cambridge University Press:  05 September 2017

Abstract

An approximation technique is developed for studying the deterministic spread of a simple epidemic which avoids a difficulty inherent in the diffusion approximation. Travelling wave solutions are found and calculated for various contact distributions. The solution developing from an isolated infective is also briefly discussed.

Type
Part IX — Biomathematics and Epidemiology
Copyright
Copyright © 1975 Applied Probability Trust 

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References

[1] Bartlett, M. S. (1960) Stochastic Population Models. Methuen, London.Google Scholar
[2] Daniels, H. E. (1960) Approximate solutions of Green's type for univariate stochastic processes. J. R. Statist. Soc. B 22, 376401.Google Scholar
[3] Fisher, R. A. (1937) The wave of advance of advantageous genes. Ann. Eugen. 7, 355369.CrossRefGoogle Scholar
[4] Kendall, D. G. (1965) Mathematical models of the spread of infection. Mathematics and Computer Science in Biology and Medicine. Medical Research Council. 213225.Google Scholar
[5] Kolmogoroff, A. N., Petrovsky, I. and Piscounoff, N. (1937) Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Bull. de l'Univ. d'État à Moscou. Al fasc. 6, 125.Google Scholar
[6] Mollison, D. (1972) Possible velocities for a simple epidemic. Adv. Appl. Prob. 4, 233257.Google Scholar
[7] Mollison, D. (1972) The rate of spatial propagation of simple epidemics. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 3, 579614.Google Scholar