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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 390694, 13 pages
Inference for Ecological Dynamical Systems: A Case Study of Two Endemic Diseases
Department of Biology, Duke University, Box 90338, Durham, NC 27708, USA
Received 2 September 2011; Revised 19 November 2011; Accepted 21 November 2011
Academic Editor: Vikas Rai
Copyright © 2012 Daniel A. Vasco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. S. Clark, Models for Ecological Data, Princeton University Press, Princeton, NJ, USA, 2007.
- D. J. Wilkinson, Stochastic Modelling for Systems Biology, Chapman and Hall, Boca Raton, Fla, USA, 2006.
- H. Andersson and T. Britton, Stochastic Epidemic Models and Their Analysis, Springer, Berlin, Germany, 2000.
- P. D. O'Neill and G. O. Roberts, “Bayesian inference for partially observed stochastic epidemics,” Journal of the Royal Statistical Society. Series A, vol. 162, no. 1, pp. 121–129, 1999.
- P. D. O'Neill, “A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods,” Mathematical Biosciences, vol. 180, pp. 103–114, 2002.
- N. G. Becker, Analysis of Infectious Disease Data, Chapman and Hall, London, UK, 1989.
- N. G. Becker and T. Britton, “Statistical studies of infectious disease incidence,” Journal of the Royal Statistical Society. Series B, vol. 61, no. 2, pp. 287–307, 1999.
- 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, vol. 5, no. 25, pp. 885–897, 2008.
- G. J. Gibson and E. Renshaw, “Estimating parameters in stochastic models using Markov chain methods,” IMA J. Math. Appl. Med. Biol., vol. 15, pp. 19–40, 1998.
- D. Alonso, A. J. McKane, and M. Pascual, “Stochastic amplification in epidemics,” Journal of the Royal Society Interface, vol. 4, no. 14, pp. 575–582, 2007.
- R. Kuske, L. F. Gordillo, and P. Greenwood, “Sustained oscillations via coherence resonance in SIR,” Journal of Theoretical Biology, vol. 245, no. 3, pp. 459–469, 2007.
- W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society of London Series A, vol. 115, pp. 700–721, 1927.
- R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, UK, 1991.
- A. G. McKendrick, “Applications of mathematics to medical problems,” Proceedings of the Edinburgh Mathematical Society, vol. 44, pp. 98–130, 1926.
- M. S. Barlett, “Some evolutionary stochastic processes,” Journal of the Royal Statistical Society: Series B, vol. 11, pp. 211–229, 1949.
- P. Billingsley, Statistical Inference for Markov Processes, University of Chicago, Chicago, Ill, USA, 1961.
- P. Guttorp, Stochastic Modeling of Scientifc Data, Chapman and Hall, Boca Rotan, Fla, USA, 1995.
- W. N. Rida, “Asymptotic properties of some estimators for the infection rate in the general stochastic epidemic model,” Journal of the Royal Statistical Society: Series B, vol. 53, pp. 269–283, 1991.
- R. J. Kryscio, “The transition probabilities of the general stochastic epidemic model,” Journal of Applied Probability, vol. 12, pp. 415–424, 1975.
- R. J. Boys, D. J. Wilkinson, and T. B. L. Kirkwood, “Bayesian inference for a discretely observed stochastic kinetic model,” Statistics and Computing, vol. 18, no. 2, pp. 125–135, 2008.
- D. T. Gillespie, “Approximate accelerated stochastic simulation of chemically reacting systems,” Journal of Chemical Physics, vol. 115, no. 4, pp. 1716–1733, 2001.
- G. V. Bobashev, S. P. Ellner, D. W. Nychka, and B. T. Grenfell, “Reconstructing susceptible and recruitment dynamics from measles epidemic data,” Mathematical Population Studies, vol. 8, no. 1, pp. 1–29, 2000.
- W. H. Hamer, “Epidemic disease in England—the evidence of variability and of persistence of type,” Lancet, vol. 1, pp. 733–739, 1906.
- H. E. Soper, “The interpretation of periodicity in disease prevalence,” Journal of the Royal Statistical Society: Series B, vol. 92, pp. 34–73, 1929.
- M. S. Bartlett, Stochastic Models in Ecology and Epidemiology, Methuen, London, UK, 1960.
- M. S. Bartlett, “Chance or chaos?” Journal of the Royal Statistical Society: Series A, vol. 153, pp. 321–349, 1990.
- N. T. J. Bailey, The Mathematical Theory of Infectious Disease and Its applications, Griffin, London, UK, 1975.
- I. Nåsell, “On the time to extinction in recurrent epidemics,” Journal of the Royal Statistical Society. Series B, vol. 61, no. 2, pp. 309–330, 1999.
- I. Nasell, “Measles outbreaks are not chaotic,” in Mathematical Approaches for Emerging and Reemerging Infectious Disease: Models, Methods and Theory, Springer, 2002.
- N. G. V. Kampen, Stochastic Processes in Physics and Chemistry, North-Holland, Amstserdam, The Netherlands, 1981.
- A. J. McKane and T. J. Newman, “Predator-prey cycles from resonant amplification of demographic stochasticity,” Physical Review Letters, vol. 94, no. 21, Article ID 218102, pp. 1–4, 2005.
- B. P. Carlin and T. A. Louis, Bayes and Empirical Bayes Methods for Data Analysis, CRC Press, Boca Raton, Fla, USA, 2000.
- A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, CRC Press, Boca Raton, Fla, USA, 2004.
- J. S. Clark, “Why environmental scientists are becoming Bayesians,” Ecology Letters, vol. 8, no. 1, pp. 2–14, 2005.
- C. Priami, “Algorithmic systems biology,” Communications of the ACM, vol. 52, no. 5, pp. 80–88, 2009.
- S. K. Poovathingal and R. Gunawan, “Global parameter estimation methods for stochastic biochemical systems,” BMC Bioinformatics, vol. 11, article 414, 2010.
- T. Tian, S. Xu, J. Gao, and K. Burrage, “Simulated maximum likelihood method for estimating kinetic rates in gene expression,” Bioinformatics, vol. 23, no. 1, pp. 84–91, 2007.
- Y. Wang, S. Christley, E. Mjolsness, and X. Xie, “Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent,” BMC Systems Biology, vol. 4, article 99, 2010.
- B. J. Daigle, M. K. Roh, D. T. Gillespie, and L. R. Petzold, “Automated estimation of rare event probabilities in biochemical systems,” Journal of Chemical Physics, vol. 134, no. 4, Article ID 044110, 2011.
- H. Kuwahara and I. Mura, “An efficient and exact stochastic simulation method to analyze rare events in biochemical systems,” Journal of Chemical Physics, vol. 129, no. 16, Article ID 165101, 2008.
- D. T. Gillespie, M. Roh, and L. R. Petzold, “Refining the weighted stochastic simulation algorithm,” Journal of Chemical Physics, vol. 130, no. 17, Article ID 174103, 2009.
- D. A. Vasco, H. J. Wearing, and P. Rohani, “Tracking the dynamics of pathogen interactions: modeling ecological and immune-mediated processes in a two-pathogen single-host system,” Journal of Theoretical Biology, vol. 245, no. 1, pp. 9–25, 2007.
- M. J. Keeling and P. Rohani, Modelling Infectious Diseases, Princeton University Press, Princeton, NJ, USA, 2007.
- P. Rohani, C. J. Green, N. B. Mantilla-Beniers, and B. T. Grenfell, “Ecological interference between fatal diseases,” Nature, vol. 422, no. 6934, pp. 885–888, 2003.