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A forecasting model of disease prevalence based on the McKendrick-von Foerster Equation
Akushevich, I., Yashkin, A., Kravchenko, J., Fang, F., Arbeev, K., Sloan, F., & Yashin, A. I. (2019). A forecasting model of disease prevalence based on the McKendrick-von Foerster Equation. Mathematical Biosciences, 311, 31-38. https://doi.org/10.1016/j.mbs.2018.12.017
A new model for disease prevalence based on the analytical solutions of McKendric-von Foerster's partial differential equations is developed. Derivation of the model and methods to cross check obtained results are explicitly demonstrated. Obtained equations describe the time evolution of the healthy and unhealthy age-structured sub-populations and age patterns of disease prevalence. The projection of disease prevalence into the future requires estimates of time trends of age-specific disease incidence, relative survival functions, and prevalence at the initial age and year available in the data. The computational scheme for parameter estimations using Medicare data, analytical properties of the model, application for diabetes prevalence, and relationship with partitioning models are described and discussed. The model allows natural generalization for the case of several diseases as well as for modeling time trends in cause-specific mortality rates.
