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Epidemics: Models and Data

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  • Denis Mollison
  • Valerie Isham
  • Bryan Grenfell

Abstract

The problems of understanding and controlling disease raise a range of challenging mathematical and statistical research topics, from broad theoretical issues to specific practical ones. In particular, recent interest in acquired immune deficiency syndrome has stimulated much progress in diverse areas of epidemic modelling, particularly with regard to the treatment of heterogeneity, both between individuals and in mixing of subgroups of the population. At the same time better data and data analysis techniques have become available, and there have been exciting developments in relevant theory, ranging from random graphs and spatial stochastic processes to the structural stability of difference and differential equations. This progress in specific areas is now being matched by interdisciplinary cooperation aimed at elucidating relationships between the widely varying types of model that have been found useful, to determine their strengths and limitations in relation to basic aims such as understanding, prediction, and evaluation and implementation of control strategies. Such interdisciplinary work can be expected to make major contributions to the modelling of a wide range of human, animal and plant diseases, as well as to general statistical and biomathematical theory.

Suggested Citation

  • Denis Mollison & Valerie Isham & Bryan Grenfell, 1994. "Epidemics: Models and Data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(1), pages 115-129, January.
  • Handle: RePEc:bla:jorssa:v:157:y:1994:i:1:p:115-129
    DOI: 10.2307/2983509
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    Cited by:

    1. Ross, J.V., 2012. "On parameter estimation in population models III: Time-inhomogeneous processes and observation error," Theoretical Population Biology, Elsevier, vol. 82(1), pages 1-17.
    2. Jukka Ranta & Riitta Maijala, 2002. "A Probabilistic Transmission Model of Salmonella in the Primary Broiler Production Chain," Risk Analysis, John Wiley & Sons, vol. 22(1), pages 47-58, February.
    3. Meggan E Craft & Hawthorne L Beyer & Daniel T Haydon, 2013. "Estimating the Probability of a Major Outbreak from the Timing of Early Cases: An Indeterminate Problem?," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-7, March.
    4. Zhang, Tonglin & Lin, Ge, 2016. "On Moran’s I coefficient under heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 83-94.
    5. Benjamin Armbruster & Ekkehard Beck & Mustafa Waheed, 2014. "The importance of extended high viremics in models of HIV spread in South Africa," Health Care Management Science, Springer, vol. 17(2), pages 182-193, June.

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