Hostname: page-component-594f858ff7-hf9kg Total loading time: 0 Render date: 2023-06-07T10:37:52.268Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "corePageComponentUseShareaholicInsteadOfAddThis": true, "coreDisableSocialShare": false, "useRatesEcommerce": true } hasContentIssue false

Stochastic approximation for the general epidemic

Published online by Cambridge University Press:  14 July 2016

Donald Ludwig*
Courant Institute of Mathematical Sciences, New York University


A system of equations is introduced whose solutions are remarkably close to corresponding solutions of the “general stochastic epidemic”. If N is the population size, then there are approximately equations to be solved for the general stochastic epidemic while the number of equations in the approximating system is proportional to N. An asymptotic approximation to the general stochastic epidemic is also introduced. Numerical comparisons of the stochastic and asymptotic approximations with the exact solution are presented.

Research Papers
Copyright © Applied Probability Trust 1973 

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.)


Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London.Google Scholar
Bharucha-Reid, A. T. (1960) Elements of the Theory of Markov Processes and their Applications. McGraw-Hill, New York.Google Scholar
Cole, J. D. (1968) Perturbation Methods in Applied Mathematics. Blaisdell, Waltham, Mass.Google Scholar
Daniels, H. E. (1967) Distribution of the total size of an epidemic. Proc. 5th Berkeley Symp. Math. Stat. IV, 281293.Google Scholar
Kendall, D. G. (1956) Deterministic and stochastic epidemics in closed populations. Proc. 3rd Berkeley Symp. Math. Stat. IV, 149165.Google Scholar
Whittle, P. (1955) The outcome of a stochastic epidemic — a note on Bailey's paper. Biometrika 42, 116122.Google Scholar