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Application of Inverse Problems in Epidemiology and Biodemography

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Statistical Models and Methods for Biomedical and Technical Systems

Part of the book series: Statistics for Industry and Technology ((SIT))

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Abstract

Inverse problems play an important role in science and engineering. Estimation of boundary conditions on the temperature distribution inside a metallurgical furnace and reconstruction of tissue density inside a body on plane projections obtained with x-rays are some examples. Different problems in epidemiology, demography, and biodemography can be considered as solutions of inverse problems as well: when using observed data one estimates the process that generated the data. Examples are estimation of infection rate on dynamics of the disease, estimation of mortality rate on the sample of survival times, and estimation of survival in the wild on survival in the laboratory. A specific property of the inverse problem—the instability of a solution—is discussed and a procedure for the solution stabilization is presented. Examples of morbidity estimation on incomplete data, HIV infection rate estimation on dynamics of AIDS cases, and estimation of the survival function in a wild population on survival of captured animals are presented.

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Author information

Authors and Affiliations

  1. Institute of Control Sciences, Moscow, Russia

    A. Michalski

Authors
  1. A. Michalski
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, CY-1678, Nicosia, Cyprus

    Filia Vonta

  2. UFR Sciences et Modélisation, Université Victor Segalen Bordeaux 2, 33076, Bordeaux Cedex, France

    Mikhail Nikulin

  3. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, 60205, Compiègne Cedex, France

    Nikolaos Limnios

  4. Université Paris V, 45 rue des Saints-Pères, 75270, Paris Cedex 06, France

    Catherine Huber-Carol

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© 2008 Birkhäuser Boston

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Michalski, A. (2008). Application of Inverse Problems in Epidemiology and Biodemography. In: Vonta, F., Nikulin, M., Limnios, N., Huber-Carol, C. (eds) Statistical Models and Methods for Biomedical and Technical Systems. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4619-6_20

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