Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-06T05:19:48.943Z Has data issue: false hasContentIssue false
  • English
  • Français

Epidemic models featuring behaviour change

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Philip O'neill
Philip O'neill*
Affiliation:
University of Bradford
*
* Postal address: Department of Mathematics, University of Bradford, Bradford, BD7 1DP, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a model for the spread of an epidemic in a closed population whose members are in either a high-risk or a low-risk activity group. Further, members of the high-risk group may change their behaviour by entering the low-risk group. Both stochastic and deterministic models are examined. A limiting model, appropriate when there is a large number of initially susceptible individuals, is used to provide a threshold analysis. The epidemic is compared to a single group epidemic, and to suitably parametrised two-group epidemics, using a coupling method. The total size distribution and effects of changing the behaviour change rate are considered.

Keywords

SIZE OF EPIDEMICDETERMINISTIC AND STOCHASTIC MODELSCOUPLING METHODSINTERCONNECTED BIRTH-AND-DEATH PROCESSES

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 4 , December 1995 , pp. 960 - 979
Copyright
Copyright © Applied Probability Trust 1995 

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

Anderson, R. M., Blythe, S. P., Gupta, S. and Konings, E. (1989) The transmission dynamics of the human immunodeficiency virus type 1 in the male homosexual community in the United Kingdom: the influence of changes of sexual behaviour. Phil. Trans. R. Soc. London B 325, 45–98.Google Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases, 2nd edn. Griffin, London.Google Scholar
Ball, F. G. (1991) Dynamic population epidemic models. Math. Biosci. 107, 299–324.Google Scholar
Ball, F. G. (1995) Coupling methods in epidemic theory. In Epidemic Models: Their Structure and Relation to Data. Cambridge University Press.Google Scholar
Ball, F. G. and Donnelly, P. J. (1992) Branching process approximation of epidemic models. Proc. 2nd World Congress of the Bernoulli Soc., Uppsala, 1990, pp. 144–147.Google Scholar
Ball, F. G. and Donnelly, P. J. (1995) Strong approximations for epidemic models. Stoch. Proc. Appl. 55, 1–21.CrossRefGoogle Scholar
Ball, F. G. and O'Neill, P. D. (1993) A modification of the general stochastic epidemic motivated by AIDS modelling. Adv. Appl. Prob. 23, 39–62.Google Scholar
Ball, F. G. and O'Neill, P. D. (1994) Strong convergence of epidemic models. Adv. Appl. Prob. 26, 629–655.Google Scholar
Blythe, S. P., Brauer, F., Castillo-Chavez, C. and Velasco-Hernandez, J. X. (1992) Models for sexually transmitted diseases with recruitment. Proc. 2nd Int. Conf. Popn Dynamics, 1992, University of Pau, France.Google Scholar
Bmrb, (1987) AIDS advertising campaign, report on four surveys during the first year of advertising, 1986-87. British Market Research Bureau Limited.Google Scholar
Brauer, F., Blythe, S. P. and Castillo-Chavez, C. (1992). Demographic recruitment in sexually transmitted disease models. Biometrics Unit Technical Report BU-1154-M, Cornell University.Google Scholar
Gleibner, W. (1988) The spread of epidemics. Appl. Math. Comput. 27, 167–171.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
Kendall, D. G. (1956) Deterministic and stochastic epidemics in closed populations. Proc. 3rd Berkeley Symp. Math. Statist. Prob. 4, 149–165.Google Scholar
Kendall, W. S. and Saunders, I. W. (1983) Epidemics in competition II: The general epidemic. J. R. Statist. Soc. B 45, 238–244.Google Scholar
Kurtz, T. G. (1970) Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Prob. 7, 49–58.CrossRefGoogle Scholar
Kurtz, T. G. (1980) Relationships between stochastic and deterministic population models. In Lecture Notes in Biomathematics 38, pp. 449–467. Springer-Verlag, Berlin.Google Scholar
Lindvall, T. (1992) Lectures on the Coupling Method. Wiley, New York.Google Scholar
Puri, P. S. (1968) Interconnected birth and death processes. J. Appl. Prob. 5, 334–349.Google Scholar
Scalia-Tomba, G. (1991) The effect of structural behaviour change on the spread of HIV in a one-sex population. Math. Biosci. 107, 457–555.Google Scholar
Sellke, T. (1983) On the asymptotic distribution of the size of a stochastic epidemic. J. Appl. Prob. 20, 390–394.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar