Analysing detection of chronic diseases with prolonged sub-clinical periods: modelling and application to hypertension in the U.S.
Brinks R, Kaufmann S, Hoyer A, Gregg EW, Saal J (2019)
BMC Medical Research Methodology 19(1): 213.
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Gregg, Edward W;
Saal, Jürgen
**Background**
We recently introduced a system of partial differential equations (PDEs) to model the prevalence of chronic diseases with a possibly prolonged state of asymptomatic, undiagnosed disease preceding a diagnosis. Common examples for such diseases include coronary heart disease, type 2 diabetes or cancer. Widespread application of the new method depends upon mathematical treatment of the system of PDEs.
**Methods**
In this article, we study the existence and the uniqueness of the solution of the system of PDEs. To demonstrate the usefulness and importance of the system, we model the age-specific prevalence of hypertension in the US 1999–2010.
**Results**
The examinations of mathematical properties provide a way to solve the systems of PDEs by the method of characteristics. In the application to hypertension, we obtain a good agreement between modeled and surveyed age-specific prevalences.
**Conclusions**
The described system of PDEs provides a practical way to examine the epidemiology of chronic diseases with a state of undiagnosed disease preceding a diagnosis.
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