The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

中文翻译：

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疾病死亡模型：统计角度和微分方程。

这项工作的目的是将随机过程的理论与与多状态（隔室）模型相关的微分方程联系起来。我们表明，Kolmogorov正向微分方程可用于推导疾病死亡模型中患病率与转移率之间的关系。然后，我们证明该疾病的流行率在数学上具有明确的定义和流行病学意义。作为一种应用，我们从一系列横截面中得出糖尿病的发病率。