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Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany

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  • Brinks, Ralph
  • Landwehr, Sandra

Abstract

We derive a partial differential equation (PDE) that models the age-specific prevalence of a disease as a function of the incidence, remission and mortality rates. The main focus is on non-communicable diseases (NCDs), although the PDE is not restricted to NCDs. As an application of the PDE, the number of persons with dementia in Germany until the year 2050 is estimated based on German incidence data and official population projections. Uncertainty is treated by different scenarios about life expectancy, number of migrants, prevalence of the disease in migrants, and scenarios about the future incidence, and mortality of demented persons. Life expectancy and incidence of dementia have the strongest impact on the future number of persons with dementia. In nearly all scenarios, our estimated case numbers exceed former estimates. Furthermore, we use an example to show that the PDE method yields more accurate results than a common alternative approach.

Suggested Citation

  • Brinks, Ralph & Landwehr, Sandra, 2014. "Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany," Theoretical Population Biology, Elsevier, vol. 92(C), pages 62-68.
    • Handle: RePEc:eee:thpobi:v:92:y:2014:i:c:p:62-68
    DOI: 10.1016/j.tpb.2013.11.006
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    References listed on IDEAS

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    1. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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    Cited by:

    1. Ralph Brinks & Annika Hoyer, 2018. "Illness-death model: statistical perspective and differential equations," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 743-754, October.
    2. Wanneveich, Mathilde & Jacqmin-Gadda, Hélène & Dartigues, Jean-François & Joly, Pierre, 2018. "Projections of health indicators for chronic disease under a semi-Markov assumption," Theoretical Population Biology, Elsevier, vol. 119(C), pages 83-90.

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