Estimating seasonal drivers in childhood infectious diseases with continuous time and discrete-time models

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 5137-5142

  Word, Daniel P ^c   Abbott III, George H ^c   Cummings, Derek ^a   Laird, Carl D ^b  

^a JOHNS HOPKINS BLOOMBERG SCHOOL OF PUBLIC HEALTH   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; DISEASES; NONLINEAR PROGRAMMING;

CONTINUOUS DIFFERENTIAL EQUATIONS; CONTINUOUS TIME MODELS; DIFFERENTIAL EQUATION SYSTEMS; DISCRETE-TIME METHODS; SIMULTANEOUS APPROACHES; TRANSMISSION COEFFICIENTS; TRANSMISSION PARAMETERS; TRANSMISSION PROFILES;

CONTINUOUS TIME SYSTEMS;

EID: 77957759694     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5530474     Document Type: Conference Paper

References (28)

1. R.M. Anderson and R.M. May. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press Inc., New York, 1991.
2. Richard C. Aster, Brian Borchers, and Clifford H. Thurber. Parameter Estimation and Inverse Problems. Elsevier Academic Press, 2005.
3. Norman T. Bailey and Larry Bailey. The Mathematical Theory of Infectious Diseases. A Charles Griffin Book, 1987.
4. Niels Becker. The uses of epidemic models. Biometrics, 35(1):295-305, 1979.
5. L. T. Biegler, A. M. Cervantes, and A. Wächter. Advances in simultaneous strategies for dynamic process optimization. Chem. Eng. Sci., 57:575-593, 2002.
6. Bjornstad, O.N. and Finkenstädt, B. and Grenfell, B.T. Dynamics of measles epidemics: Estimating Scaling of Transmission Rates Using a Time Series SIR Model. Ecological Monographs, 72:169-184, 2002.
7. S. Cauchemez and N.M. Ferguson. Likelihood-based estimation of continuous time epidemic models from time-series data: application to measles transmission in london. Journal of the Royal Society Interface, 2008. to appear: DOI: 10.1098/rsif.2007.1292. (Pubitemid 351882153)
8. K. Dietz. The first epidemic model: A historical note on p.d. en'ko. Australian & New Zealand Journal of Statistics, 1988.
9. K. Dietz and D. Schenzle. Mathematical models for infectious disease statistics. In Anthony C. Atkinson and Stephen E. Fienberg, editors, A Celebration of Statistics. Springer-Verlag, 1985.
10. Klaus Dietz. Epidemics and rumours: A survey. Journal of the Royal Statistical Society, 1967.
11. N.M. Ferguson, D.A.T. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn, and D.S. Burke. Strategies for containing an emerging influenza pandemic in southeast asia. Nature, 437(7056):209-214, 2005.
12. P.E. Fine and J.A. Clarkson. Measles in England and Wales I: An Analysis of Factors Underlying Seasonal Patterns. International journal of Epidemiology, 11(1):5-14, 1982.
13. B. Finkenstädt, O.N. Bjornstad, and B.T. Grenfell. A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks. Biostatistics, 3:493-510, 2002.
14. B.F. Finkenstädt and B.T. Grenfell. Time series modelling of childhood diseases: a dynamical systems approach. Journal of the Royal Statistical Society, Series C, 49:187-205, 2000.
15. R. Fourer, D. M. Gay, and B. W. Kernighan. AMPL: A Modeling Language for Mathematical Programming. The Scientific Press (now an imprint of Boyd & Fraser Publishing Co.), Danvers, MA, USA, 1993.
16. W.H. Hamer. Epidemic Disease in England. Bedford Press, 1906.
17. Herbert W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4):599-653, October 2000.
18. Valerie Isham and Graham Medley. Models for Infectious Human Diseases. Press Syndicate of the University of Cambridge, 1996.
19. M.J. Keeling. Modelling the Persistence of Measles. Trends in Microbiology, 5(12):513-518, 1997.
20. W.O. Kermack and A.G. McKendrick. Contributions to the mathematical theory of epidemics - i. Proceedings of the Royal Society of London Series A, 1927.
21. Wei-min Liu, H.W. Hethcote, and S.A. Levin. Dynamical behavior of epidemiological models with nonlinear incidence rates. Journal of Mathematical Biology, 25(4):359-380, 1987.
22. A.J. Lotka. The stability of the normal age distribution. Proceedings of the National Academy of Sciences of the USA, 1922.
23. A.G. McKendrick. Applications of mathematics to medical problems. Proceedings of the Edinburgh Mathematical Society, 1925.
24. Ronald Ross. The Prevention of Malaria. E.P. Dutton & Company, 1910.
25. H.E. Soper. The interpretation of periodicity in disease prevalence. Journal of the Royal Statistical Society, 92:34-73, 1929.
26. A. Wächter and L.T. Biegler. On the Implementation of an Interior- Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming. Mathematical Programming, 106(1):25-57, 2006.
27. Y. Xia, O.N. Bjornstad, and B.T. Grenfell. Measles metapopulation dynamics: A gravity model for epidemiological coupling and dynamics. The American Naturalist, 164(2):267-281, 2004.
28. J. A. Yorke and W. P. London. Recurrent outbreaks of measles, chickenpox, and mumps. American Journal of Epidemiology, 98(6):469-482, 1973.