Deterministic epidemic waves
- 1 September 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 80 (2) , 315-330
- https://doi.org/10.1017/s0305004100052944
Abstract
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).Keywords
This publication has 3 references indexed in Scilit:
- The Rate of Spatial Propagation of Simple EpidemicPublished by University of California Press ,1972
- Possible velocities for a simple epidemicAdvances in Applied Probability, 1972
- The Laplace Transform. By D. V. Widder. Pp. x, 406. 36s. 1941. Princeton Mathematical series, 6. (Princeton University Press; Humphrey Milford)The Mathematical Gazette, 1943