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A forecasting model of disease prevalence based on the McKendrick-von Foerster equation.

ABSTRACT: 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.

SUBMITTER: Akushevich I

PROVIDER: S-EPMC6916255 | biostudies-literature | 2019 May

REPOSITORIES: biostudies-literature

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A forecasting model of disease prevalence based on the McKendrick-von Foerster equation.

Akushevich I I Yashkin A A Kravchenko J J Fang F F Arbeev K K Sloan F F Yashin A I AI

Mathematical biosciences 20181228

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 inc ...[more]

PMID: 30597156

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Project description:Prediction of the rate and extent of drug absorption upon oral dosing needs models that capture the complexities of both the drug molecule and intestinal physiology. We report here the development of a continuous intestinal absorption model based on the convection-diffusion equation. The model includes explicit enterocyte apical membrane and intracellular lipid radial compartments along the length of the intestine. Physiologic functions along length x are built into the model and include velocity, diffusion, surface areas, and pH of the intestine. Also included are expression levels of the intestinal active uptake transporter OATP2B1 and efflux transporter P-gp. Oral dosing of solution as well as solid (with a dissolution function) was modeled for several drugs. The fraction absorbed (FA) and concentration-time (C-t) profiles were predicted and compared with clinical data. Overall, FA was well predicted upon oral (n = 21) or colonic dosing (n = 11), with four outliers. The overall accuracy (prediction of the correct bin) was 81% with outliers and 90% without outliers. Of the nine solution dosing data sets, six drugs were very well predicted with an exposure overlap coefficient (EOC) > 0.9 and predicted Cmax and Tmax values similar to those observed. Of the six solid dose formulations evaluated, the EOC values were > 0.9 for all drugs except budesonide. The observed precipitation of nifedipine at high doses was predicted by the model. Most of the poor predictions were for drugs that are known to be transporter substrates. As proof of concept, incorporating OATP2B1 and P-gp markedly improved the EOC and predicted Cmax and Tmax for fexofenadine. Finally, the continuous intestinal model accurately recapitulated the known relationships between drug absorption and permeability, solubility, and particle size. Together, these results indicate that this preliminary intestinal absorption model offers a simple and straightforward framework to build in complexities such as drug permeability, lipid partitioning, solubility, metabolism, and transport for improved prediction of the rate and extent of drug absorption.

Dataset Information

A forecasting model of disease prevalence based on the McKendrick-von Foerster equation.

Publications

A forecasting model of disease prevalence based on the McKendrick-von Foerster equation.

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