About this Journal Submit a Manuscript Table of Contents
Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 742086, 8 pages
http://dx.doi.org/10.1155/2012/742086
Research Article

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

1Department of Statistics and Operational Research, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
2Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA

Received 8 May 2012; Revised 25 June 2012; Accepted 3 July 2012

Academic Editor: Thierry Busso

Copyright © 2012 F. Santonja and B. Chen-Charpentier. 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.

Linked References

  1. H. W. Hethcote, “Mathematics of infectious diseases,” SIAM Review, vol. 42, no. 4, pp. 599–653, 2000. View at Scopus
  2. D. Burg, L. Rong, A. U. Neumann, and H. Dahari, “Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection,” Journal of Theoretical Biology, vol. 259, no. 4, pp. 751–759, 2009. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Suh, J. Lee, H. J. Chi et al., “Mathematical modeling of the novel influenza a (H1N1) virus and evaluation of the epidemic response strategies in the Republic of Korea,” Journal of Preventive Medicine and Public Health, vol. 43, no. 2, pp. 109–116, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. T. Soong, Probabilistic Modeling and Analysis in Science and Engineering, Wiley, New York, NY, USA, 1992.
  5. B. Oksendal, Stochastic Differential Equations, Springer, Heidelberg, The Netherlands, 6th edition, 2003.
  6. N. Metropolis and S. Ulam, “The Monte Carlo method,” Journal of the American Statistical Association, vol. 44, no. 247, pp. 335–341, 1949. View at Scopus
  7. G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, Springer, New York, NY, USA, 1995.
  8. M. Grigoriu and T. Soong, Random Vibration of Mechanical and Structural Systems, Prentice Hall, 1993.
  9. T. Soong, Random Differential Equations in Science and Engineering, Academic Press, New York, NY, USA, 1973.
  10. D. Xiu and G. Em Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM Journal on Scientific Computing, vol. 24, no. 2, pp. 619–644, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Stanescu and B. M. Chen-Charpentier, “Random coefficient differential equation models for bacterial growth,” Mathematical and Computer Modelling, vol. 50, no. 5-6, pp. 885–895, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. R. W. Walters, L. Huyse, et al., “Uncertainty quantification for fluid mechanics with applications,” ICASE Report 2002-1, NASA Langley Research Center, Hampton, Va, USA, 2002.
  13. D. Xiu and G. E. Karniadakis, “Modeling uncertainty in flow simulations via generalized polynomial chaos,” Journal of Computational Physics, vol. 187, no. 1, pp. 137–167, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. E. Tornatore, S. M. Buccellato, and P. Vetro, “Stability of a stochastic SIR system,” Physica A, vol. 354, no. 1–4, pp. 111–126, 2005. View at Publisher · View at Google Scholar · View at Scopus
  15. C. E. Dangerfield, J. V. Ross, and M. J. Keeling, “Integrating stochasticity and network structure into an epidemic model,” Journal of the Royal Society Interface, vol. 6, no. 38, pp. 761–774, 2009. View at Publisher · View at Google Scholar
  16. S. B. Caldwell, “Microsimulation: theory and practice,” IHS-Journal, vol. 6, pp. 135–147, 1982.
  17. L. Brown and A. Harding, “The new frontier of health and aged care: using microsimulation to assess policy options,” in Proceedings of the Quantitative Tools for Microeconomic Policy Analysis Conference, pp. 217–246, Productivity Commission, Canberra, Australia, November 2004.
  18. F. J. Santonja, R. J. Villanueva, L. Jódar, and G. Gonzalez-Parra, “Mathematical modelling of social obesity epidemic in the region of Valencia, Spain,” Mathematical and Computer Modelling of Dynamical Systems, vol. 16, no. 1, pp. 23–34, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. Valencian Department of Health, “Health Survey,” 2000, http://www.san.gva.es/val/prof/homeprof.html.
  20. World Health Organization, “Global strategy on diet, physical activity and health,” Tech. Rep., http://www.who.int/dietphysicalactivity/publications/obesity/en/.
  21. J. J. Arrizabalaga, L. Masmiquel, J. Vidal et al., “Recommendations and treatment algorithm of overweight and obesity in adults,” Medicina Clinica, vol. 122, no. 3, pp. 104–110, 2004. View at Publisher · View at Google Scholar · View at Scopus
  22. F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, 2001.
  23. A. Hoare, D. G. Regan, and D. P. Wilson, “Sampling and sensitivity analyses tools (SaSAT) for computational modelling,” Theoretical Biology and Medical Modelling, vol. 5, article 4, pp. 1–18, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology, vol. 254, no. 1, pp. 178–196, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Ross, A First Course in Probability, Prentice Hall, 2002.
  26. D. Xiu and G. Em Karniadakis, “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM Journal on Scientific Computing, vol. 24, no. 2, pp. 619–644, 2003. View at Publisher · View at Google Scholar · View at Scopus
  27. B. M. Chen-Charpentier and D. Stanescu, “Epidemic models with random coefficients,” Mathematical and Computer Modelling, vol. 52, no. 7-8, pp. 1004–1010, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. B. Sudret, “Global sensitivity analysis using polynomial chaos expansions,” Reliability Engineering and System Safety, vol. 93, no. 7, pp. 964–979, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. T. Crestaux, O. Le Maître, and J. M. Martinez, “Polynomial chaos expansion for sensitivity analysis,” Reliability Engineering and System Safety, vol. 94, no. 7, pp. 1161–1172, 2009. View at Publisher · View at Google Scholar · View at Scopus