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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
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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

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References

REFERENCES

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