Advertisement

A Continuous Time-and-State Epidemic Model Fitted to Ordinal Categorical Data Observed on a Lattice at Discrete Times

  • Rémi Crété
  • Besnik Pumo
  • Samuel Soubeyrand
  • Frédérique Didelot
  • Valérie Caffier
Article

Abstract

We consider a spatio-temporal model to describe the spread of apple scab within an orchard composed of several plots. The model is defined on a regular lattice and evolves in continuous time. Based on ordinal categorical data observed only at some discrete instants, we adopt a continuous-time approach and apply a Bayesian framework for estimating unknown parameters.

Key Words

Spatial-temporal process Multivariate point process Markov Chain Monte Carlo Categorical data Bayesian inference Apple scab 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aylor, D. E. (1998), “The Aerobiology of Apple Scab,” Plant Disease, 82 (8), 838–849. CrossRefGoogle Scholar
  2. — (1999), “Biophysical Scaling and the Passive Dispersal of Fungus Spores: Relationship to Integrated Pest Management,” Agricultural and Forest Meteorology, 97, 275–292. CrossRefGoogle Scholar
  3. Bus, V. G. M., Rikkerink, E. H. A., Caffier, V., Durel, C. E., and Plummers, K. M. (2011), “Revision of the Nomenclature of the Differential Host–Pathogen Interactions of Venturia inaequalis and Malus,” Annual Review of Phytopathology, 49, 391–413. CrossRefGoogle Scholar
  4. Caffier, V., Didelot, F., Orain, G., Lemarquand, A., and Parisi, L. (2010), “Efficiency of Association of Scab Control Methods on Resistance Durability of Apple: The Case Study of Cultivar Ariane,” IOBC-WPRS Bulletin, 54, 327–330. Google Scholar
  5. Chadoeuf, J., Nandris, D., Geiger, J. P., Nicole, M., and Pierrat, J. C. (1992), “Modélisation Spatio-Temporelle d’Une Épidémie par un Processus de Gibbs: Estimation et Tests,” Biometrics, 48, 1165–1175. MathSciNetCrossRefGoogle Scholar
  6. Cressie, N., and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, New York: Wiley. zbMATHGoogle Scholar
  7. Daley, D. J., and Vere-Jones, D. (2003), An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods (2nd ed.), Berlin: Springer. Google Scholar
  8. Didelot, F., Caffier, V., Baudin, M., Orain, G., Lemarquand, A., and Parisi, L. (2010), “Integrating Scab Control Methods With Partial Effects in Apple Orchards: The Association of Cultivar Resistance, Sanitation and Reduced Fungicide Schedules,” IOBC-WPRS Bulletin, 54, 525–528. Google Scholar
  9. Gamerman, D., and Lopes, H. F. (2006), Markov Chain Monte Carlo, Stochastic Simulation for Bayesian Inference, Boca Raton: Chapman and Hall/CRC. zbMATHGoogle Scholar
  10. Gelman, A., and Rubin, D. B. (1992), “Inference From Iterative Simulation Using Multiple Sequences” (with discussion), Statistical Science, 7, 457–511. CrossRefGoogle Scholar
  11. Geyer, C. J. (1992), “Practical Markov Chain Monte Carlo,” Statistical Science, 7 (4), 473–483. MathSciNetCrossRefGoogle Scholar
  12. Gibson, G. J. (1997), “Markov Chain Monte Carlo Methods for Fitting Spatiotemporal Stochastic Models in Plant Epidemiology,” Applied Statistics, 46, 215–233. CrossRefzbMATHGoogle Scholar
  13. Guyon, X., and Pumo, B. (2007), “Space-Time Estimation of a Particle System Model,” Statistics, 41 (5), 395–407. MathSciNetCrossRefzbMATHGoogle Scholar
  14. Illian, J., Penttinen, A., Stoyan, H., and Stoyan, D. (2008), Statistical Analysis and Modelling of Spatial Point Patterns, Chichester: Wiley. zbMATHGoogle Scholar
  15. Johnson, N. L., Kotz, S., and Balakrishnan, N. (1995), Continuous Univariate Distributions, Vol. 2, New York: Wiley-Interscience. zbMATHGoogle Scholar
  16. Lateur, M., Wagemans, C., and Populer, C. (1998), “Evaluation of Tree Genetic Resources as Sources of Polygenic Scab Resistance in an Apple Breeding Programme,” Acta Horticulturae, 484, 35–42. Google Scholar
  17. Madden, L. V., Hughes, G., and Van Den Bosch, F. (2007), The Study of Plant Disease Epidemics, St. Paul: The American Phytopathological Society. APS Press. Google Scholar
  18. Mills, W. D., and Laplante, A. A. (1951), “Diseases and Insects in the Orchard.” Cornell Extension Bulletin, 711. Google Scholar
  19. Mollison, D. (1977), “Spatial Contact Models for Ecological and Epidemic Spread” (with discussion), Journal of the Royal Statistical Society. Series B, 39, 283–326. MathSciNetzbMATHGoogle Scholar
  20. Olivier, J. M. (1986), “La Tavelure du Pommier, Conduite D’une Protection Raisonnée,” Adalia, 1, 3–19. Google Scholar
  21. Rasmussen, J. G., Moller, J., Aukema, B. H., Raffa, K. F., and Zhu, J. (2007), “Continuous Time Modelling of Dynamical Spatial Lattice Data Observed at Sparsely Distributed Times,” Journal of the Royal Statistical Society. Series B, 69(4), 701–713. MathSciNetCrossRefGoogle Scholar
  22. Robert, C. P., and Casella, G. (2004), Monte Carlo Statistical Methods, Berlin: Springer. CrossRefzbMATHGoogle Scholar
  23. Roberts, G. O., Gelman, A., and Gilks, W. R. (1997), “Weak Convergence and Optimal Scaling of Random Walk Metropolis Algorithms,” The Annals of Applied Probability, 7, 110–120. MathSciNetCrossRefzbMATHGoogle Scholar
  24. Soubeyrand, S., Laine, A.-L., Hanski, I., and Penttinen, A. (2009), “Spatiotemporal Structure of Host–Pathogen Interactions in a Metapopulation,” The American Naturalist, 174, 308–320. CrossRefGoogle Scholar
  25. Van der Plank, J. E. (1963), Plant Diseases: Epidemics and Control, New York: Academic Press. Google Scholar
  26. Verhulst, P.-F. (1845), “Recherches Mathématiques sur la Loi D’accroissement de la Population,” Nouveaux Mémoires de l’Académie Royale des Sciences et Belles-Lettres de Bruxelles, 18, 1–41. Google Scholar
  27. Zhu, J., Rasmussen, J. G., Moller, J., Aukema, B., and Raffa, K. F. (2008), “Spatial-Temporal Modeling of Forest Gaps Generated by Colonization From Below- and Above-Ground Bark Beetle Species,” Journal of the American Statistical Association, 103(481), 162–177. MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© International Biometric Society 2013

Authors and Affiliations

  • Rémi Crété
    • 1
    • 2
  • Besnik Pumo
    • 3
  • Samuel Soubeyrand
    • 7
  • Frédérique Didelot
    • 4
    • 5
    • 6
  • Valérie Caffier
    • 4
    • 5
    • 6
  1. 1.UMR CNRS 6093 LAREMAUniversité d’AngersAngersFrance
  2. 2.Agrocampus Ouest—Centre d’AngersAngersFrance
  3. 3.Statistics, Statistical and Compter Science DepartmentAgrocampus Ouest—Centre d’AngersAngersFrance
  4. 4.INRA, UMR 1345IRHS (Institut de Recherche en Horticulture et Semences)BeaucouzéFrance
  5. 5.UMR 1345 IRHS, SFR 4207 QUASAVUniversité d’AngersAngersFrance
  6. 6.UMR 1345 IRHSAgroCampus OuestAngersFrance
  7. 7.UR546 Biostatistics and Spatial ProcessesINRAAvignonFrance

Personalised recommendations