The early stage behaviour of a stochastic sir epidemic with term-time forcing

Journal of Applied Probability

Volumn 46, Issue 4, 2009, Pages 975-992

  Britton, Tom ^a   Lindholm, Mathias ^a,b  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

Branching process in a seasonal environment; Seasonal forcing; Stochastic epidemic; Term time forcing; Threshold conditions

Indexed keywords

EID: 76449120748     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1261670683     Document Type: Article

References (23)

1. ALLEN, L. J. S. AND CORMIER, P. J. (1996). Environmentally driven epizootics. Math. Biosci. 131, 51-80.
2. ANDERSSON, H. AND BRITTON, T. (2000). Stochastic Epidemic Models and Their Statistical Analysis (Lecture Notes Statist. 151). Springer, New York.
3. ANDERSSON, H. AND BRITTON, T. (2000). Stochastic epidemics in dynamic populations: quasi-stationarity and extinction. J. Math. Biol. 41, 559-580.
4. ANDERSON, R. M. AND MAY, R. M. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
5. ATHREYA, K. B. AND NEY, P. E. (1972). Branching Processes. Springer, New York.
6. BALL, F. (1983). The threshold behaviour of epidemic models. J. Appl. Prob. 20, 227-241.
7. BALL, F. AND CLANCY, D. (1993). The final size and severity of a generalised stochastic multitype epidemic model. Adv. Appl. Prob. 25, 721-736.
8. BALL, F. AND DONNELY, P. (1995). Strong approximations for epidemic models. Stoch. Process. Appl. 55, 1-21.
9. BRITTON, T., DEIJFEN, M., LAGERÅS, A. N. AND LINDHOLM, M. (2008). Epidemics on random graphs with tunable clustering. J. Appl. Prob. 45, 743-756.
10. DURRETT, R. (2004). Probability: Theory and Examples, 3rd edn. Duxbury Press, Belmont, CA.
11. EARN, D. J. D., ROHANI, P., BOLKER, B. M. AND GRENFELL, B. T. (2000). A simple model for complex dynamical transitions in epidemics. Science 287, 667-670.
12. FELLER, W. (1957). An Introduction to Probability Theory and Its Applications, Vol. I, 2nd edn. John Wiley, New York.
13. FRANKE, J. E. AND YAKUBU, A.-Z. (2006). Discrete-time SIS epidemic model in a seasonal environment. SIAM J. Appl. Math. 66, 1563-1587.
14. HACCOU, P., JAGERS, P. AND VATUTIN, V. A. (2005). Branching Processes: Variation, Growth, and Extinction of Populations. Cambridge University Press.
15. HARRIS, T. E. (1963). The Theory of Branching Processes. Springer, Berlin.
16. JAGERS, P. (1975). Branching Processes with Biological Applications. John Wiley, London.
17. KARLIN, S. AND MCGREGOR, J. (1958). Linear growth, birth and death processes. J. Math. Mech. 7, 643-662.
18. KEELING, M. J., ROHANI, P. AND GRENFELL, B. T. (2001). Seasonally forced dynamics explored as switching between attractors. Physica D 148, 317-335.
19. KUSKE, R., GORDILLO, L. F. AND GREENWOOD, P. (2007). Sustained oscillations via coherence resonance in SIR. J. Theoret. Biol. 245, 459-469.
20. MOLLISON, D. (1977). Spatial contact models for ecological and epidemic spread. J. R. Statist. Soc. B 39, 283-326.
21. PIYAWONG, W., TWIZELL, E. H. AND GUMEL, A. B. (2003). An unconditionally convergent finite-difference scheme for the SIR model. Appl. Math. Comput. 146, 611-625.
22. PRAJNESHU, GUPTA, C. K. AND SHARMA, U. (1986). A stochastic epidemic model with seasonal variations in infection rate. Biometrical J. 28, 889-895.
23. STONE, L., OLINKY, R. AND HUPPERT, A. (2007). Seasonal dynamics of recurrent epidemics. Nature 446, 533-536.