Risk factors in the illness-death model: Simulation study and the partial differential equation about incidence and prevalence.

Recently, we developed a partial differential equation (PDE) that relates the age-specific prevalence of a chronic disease with the age-specific incidence and mortality rates in the illness-death model (IDM). With a view to planning population-wide interventions, the question arises how prevalence can be calculated if the distribution of a risk-factor in the population shifts. To study the impact of such possible interventions, it is important to deal with the resulting changes of risk-factors that affect the rates in the IDM.

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

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.