Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-24T12:47:58.234Z Has data issue: false hasContentIssue false
  • English
  • Français

Deterministic epidemic waves

Published online by Cambridge University Press:  24 October 2008

C. Atkinson  and
G. E. H. Reuter
C. Atkinson
Affiliation:
Department of Mathematics, Imperial College, London, S.W. 7
G. E. H. Reuter
Affiliation:
Department of Mathematics, Imperial College, London, S.W. 7
Get access Rights & Permissions [Opens in a new window]

Extract

In the well-known deterministic model for the spread of an epidemic, one considers a population of uniform density along a line and divides the population into three classes: susceptible but uninfected, infected and infectious, infected but removed. If we denote space and time variables by s, t and let x(s, t), y(s, t), z(s, t) be the proportions of the population at (s, t) in these three classes, then x + y + z = 1 and we suppose that

Here Ῡ(s, t) denotes a space average ∫ y(s + σ) p(σ) dσ, where p is a probability density function; b is the removal rate; the scale of t has been adjusted to remove a constant that would otherwise occur in (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 315 - 330
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Daniels, H. E. The deterministic spread of a simple epidemic, to appear in Perspectives in Probability and Statistics: Papers in honour of M. S. Bartlett on the occasion of his sixty-fifth birthday (London, Academic Press).Google Scholar
(2)Kendall, D. G. Mathematical models of the spread of infection, Mathematics and computer science in biology and medicine, pp. 213–224 (Medical Research Council, 1965).Google Scholar
(3)Mollison, D.Possible velocities for a simple epidemic. Adv. in Appl. Prob. 4 (1972), 233–257.CrossRefGoogle Scholar
(4)Mollison, D.The rate of spatial propagation of simple epidemics. Proc. Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. III, pp. 579–614 (1970).Google Scholar
(5)Tricomi, F. G.Differential equations (Blackie and Son, 1961).Google Scholar
(6)Widder, D. V.The Laplace transform (Princeton University Press, 1941).Google Scholar