Predictability in a highly stochastic system: Final size of measles epidemics in small populations

Journal of the Royal Society Interface

Volumn 12, Issue 102, 2015, Pages

  Caudron, Q ^a   Mahmud, A S ^a   Metcalf, C J E ^a,b   Gottfredsson, M ^b,c,d   Viboud, C ^b   Cliff, A D ^e   Grenfell, B T ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b NATIONAL INSTITUTES OF HEALTH   (United States)

^c LANDSPITALI UNIVERSITY HOSPITAL   (Iceland)

^d UNIVERSITY OF ICELAND   (Iceland)

^e UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Dynamics; Epidemiology; Measles; Small populations

Indexed keywords

DISEASES; DYNAMICS; POPULATION STATISTICS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CHILDHOOD INFECTIONS; COMPARTMENTAL MODEL; DATA HETEROGENEITY; DEMOGRAPHIC INFORMATION; DYNAMICS OF INFECTIONS; MEASLES; SMALL POPULATION; STANDARD ASSUMPTIONS;

EPIDEMIOLOGY;

ARTICLE; EPIDEMIC; HUMAN; MEASLES; METAPOPULATION; MORBIDITY; POPULATION SIZE; SEASONAL VARIATION; STOCHASTIC MODEL; DEMOGRAPHY; DENMARK; ICELAND; INCIDENCE; INFECTION CONTROL; POPULATION DYNAMICS; SEASON; STATISTICAL MODEL; STATISTICS; TIME;

MEASLES VACCINE;

COMMUNICABLE DISEASE CONTROL; DEMOGRAPHY; DENMARK; DISEASE OUTBREAKS; EPIDEMICS; HUMANS; ICELAND; INCIDENCE; MEASLES; MEASLES VACCINE; MODELS, STATISTICAL; POPULATION DYNAMICS; SEASONS; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 84964312911     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2014.1125     Document Type: Article

References (22)

1. Anderson RM, May RM. 1991 Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press.
2. London WP, Yorke JA. 1973 Recurrent outbreaks of measles, chicken-pox and mumps. I. Seasonal variation in contact rates. Am. J. Epidemiol. 98, 453-468.
3. Fine PE, Clarkson JA. 1982 Measles in England and Wales. I: an analysis of factors underlying seasonal patterns. Int. J. Epidemiol. 11, 5-14. (doi:10.1093/ije/11.1.5)
4. Schenzle D. 1984 An age-structured model of preand post-vaccination measles transmission. IMA J. Math. Appl. Med. Biol. 1, 169-191. (doi:10.1093/imammb/1.2.169)
5. Bartlett MS. 1957 Measles periodicity and community size. J. R. Stat. Soc. Series A (General) 120, 48-70. (doi:10.2307/2342553)
6. Black FL. 1966 Measles endemicity in insular populations: critical community size and its evolutionary implication. J. Theor. Biol. 11, 207-211. (doi:10.1016/0022-5193(66)90161-5)
7. Keeling MJ, Grenfell BT. 1997 Disease extinction and community size: modeling the persistence of measles. Science 275, 65-67. (doi:10.1126/science.275.5296.65)
8. Bolker BM, Grenfell BT. 1995 Space, persistence and the dynamics of measles epidemics. Phil. Trans. R. Soc. Lond. B 348, 309-320. (doi:10.1098/ rstb.1995.0070)
9. Grenfell BT, Harwood J. 1997 (Meta)population dynamics of infectious diseases. Trends Ecol. Evol. 12, 395-399. (doi:10.1016/S0169-5347(97)01174-9)
10. Bjornstad ON, Finkenstadt BF, Grenfell BT. 2002 Dynamics of measles epidemics: estimating scaling of transmission rates using a time series SIR model. Ecol. Monogr. 72, 169-184. (doi:10.1890/0012-9615(2002)072[0169:DOMEES]2.0.CO;2)
11. Rhodes CJ, Anderson RM. 1996 Power law governing epidemics in isolated populations. Nature 381, 600-602. (doi:10.1038/381600a0)
12. Keeling MJ, Grenfell BT. 1997 Disease extinction and community size: modeling the persistence of measles. Science 275, 65-67. (doi:10.1126/science.275.5296.65)
13. Finkenstädt BF, Grenfell BT. 2000 Time series modelling of childhood diseases: a dynamical systems approach. J. R. Stat. Soc. Series C 49, 187-205. (doi:10.1111/1467-9876.00187)
14. Glass K, Xia Y, Grenfell B. 2003 Interpreting timeseries analyses for continuous-time biological models-measles as a case study. J. Theor. Biol. 223, 19-25. (doi:10.1016/S0022-5193(03)00031-6)
15. Metcalf CJE, Munayco CV, Chowwell G, Grenfell BT, Bjornstad ON. 2010 Rubella metapopulation dynamics and importance of spatial coupling to the risk of congenital rubella syndrome in Peru. J. R. Soc. Interface 8, 369-376. (doi:10.1098/rsif.2010.0320)
16. Grenfell BT, Bjornstad ON, Finkenstädt BF. 2002 Dynamics of measles epidemics: scaling noise, determinism, and predictability with the TSIR model. Ecol. Monogr. 72, 185-202. (doi:10.1890/0012-9615(2002)072[0185:DOMESN]2.0.CO;2)
17. Cliff AD, Haggett P, Ord JK, Versey GR. 1981 Spatial diffusion: an historical geography of epidemics in an Island community. Cambridge, UK: Cambridge University Press.
18. Cliff AD, Haggett P, Smallman-Raynor MR. 2000 Island epidemics. Oxford, UK: Oxford University Press.
19. Lancaster HO. 1991 Expectations of life: a study in the demography, statistics, and history of world mortality. Berlin, Germany: Springer.
20. Denmark. Medical Report for the Kingdom of Denmark. 1927-1968 National Health Service of Denmark. Copenhagen.
21. Earn JD, Rohani P, Bolker BM, Grenfell BT. 2000 Measles in England and Wales. I. An analysis of factors underlying seasonal patterns. Science 287, 667-670. (doi:10.1126/science.287.5453.667)
22. Rhodes CJ, Anderson RM. 1996 A scaling analysis of measles epidemics in a small population. Phil. Trans. R. Soc. Lond. B 351, 1679-1688. (doi:10.1098/rstb.1996.0150)