Why the study?
Widespread application of a newly introduced system of partial differential equations to model chronic diseases with prolonged asymptomatic periods depended upon mathematical treatment of the system.
A system of partial differential equations can accurately model the age-specific prevalence of undiagnosed and diagnosed chronic diseases, such as hypertension, using cross-sectional survey data.
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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Brinks et al. (2019) studied Hypertension. System of partial differential equations (PDEs) modeling vs. Surveyed prevalence (NHANES data) was evaluated on Agreement between modeled and surveyed age-specific prevalences of hypertension.
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