The time to extinction for a stochastic SIS-household-epidemic model

Journal of Mathematical Biology

Volumn 61, Issue 6, 2010, Pages 763-779

  Britton, Tom ^a   Neal, Peter ^b  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Contact process; Households model; Ornstein Uhlenbeck process; SIS epidemics; Time to extinction

Indexed keywords

ARTICLE; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; COMPUTER SIMULATION; EPIDEMIC; EPIDEMIOLOGY; FAMILY SIZE; HUMAN; PROBABILITY; STATISTICS;

BASIC REPRODUCTION NUMBER; COMPUTER SIMULATION; DISEASE OUTBREAKS; EPIDEMIOLOGIC METHODS; FAMILY CHARACTERISTICS; HUMANS; MARKOV CHAINS; MODELS, BIOLOGICAL; STOCHASTIC PROCESSES;

EID: 77957160711     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-009-0320-5     Document Type: Article

References (24)

1. Andersson H (1999) Epidemic models and social networks. Math Sci 24: 128-147.
2. Andersson H, Britton T (2000) Stochastic epidemics in dynamic populations: quasi-stationarity and extinction. J Math Biol 41: 559-580.
3. Andersson H, Djehiche B (1998) A threshold limit theorem for the stochastic logistic epidemic. J Appl Probab 35: 662-670.
4. Anderson R, May R (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford.
5. Arrigoni F, Pugliese A (2007) Global stability of equilibria for a metapopulation S-I-S model. In: Aletti G, Burger M, Micheletti A, Morale D (eds) Math everywhere. Springer, Berlin, pp 229-240.
6. Ball F (1999) Stochastic and deterministic models for SIS epidemics among a population partitioned into households. Math Biosci 156: 41-67.
7. Bezuidenhout C, Grimmett G (1990) The critical contact process dies out. Ann Probab 18: 1462-1482.
8. Cauchemez S, Valleron AJ, Boëlle PY, Flahault A, Ferguson NM (2008) Estimating the impact of school closure on influenza transmission from sentinel data. Nature 452: 750-754.
9. Doering C, Sargsyan K, Sander L (2005) Extinction times for birth-death processes: exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation. Multiscale Model Simul 3: 283-299.
10. Ethier S, Kurtz T (1986) Markov processes: characterization and convergence. Wiley, New York.
11. Ferguson NM, Cummings DA, Fraser C, Cajka JC, Cooley PC, Burke DS (2006) Strategies for mitigating an influenza pandemic. Nature 442: 448-452.
12. Ghoshal G, Sander L, Sokolov I (2004) SIS epidemics with household structure: the self-consistent field method. Math Biosci 190: 71-85.
13. Griffeath D (1981) The basic contact processes. Stoch Proc Appl 11: 151-185.
14. Hagenaars T, Donnelly C, Ferguson N (2004) Spatial heterogeneity and the persistence of infectious diseases. J Theor Biol 229: 349-359.
15. Harris T (1974) Contact interactions on a lattice. Ann Probab 2: 969-988.
16. House T, Keeling M (2008) Deterministic epidemic models with explicit household structure. Math Biosci 213: 29-39.
17. Kryscio R, Lefèrve C (1989) On the extinction of the SIS stochastic logistic epidemic. J Appl Probab 26: 685-694.
18. Liggett T (1999) Stochastic interacting systems: contact, voter and exclusion processes. Springer, Berlin.
19. Lindholm M (2008) On the time to extinction for a two-type version of Bartlett's epidemic model. Math Biosci 212: 99-108.
20. Nåsell I (1999) On the time to extinction in recurrent epidemics. J R Stat Soc Ser B Stat Methodol 61: 309-330.
21. Neal P (2006) Stochastic and deterministic analysis of SIS household epidemics. Adv Appl Probab 38: 943-968.
22. Neal P (2008) The SIS great circle epidemic model. J Appl Probab 45: 513-530.
23. Shwartz A, Weiss A (1995) Large deviations for performance analysis. Chapman and Hall, London.
24. Wallinga J, Teunis P (2004) Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J Epidemiol 160: 509-516.