Analysing detection of chronic diseases with prolonged sub-clinical periods: modelling and application to hypertension in the U.S.

Abstract

Abstract 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.