Bayesian compartmental model for an infectious disease with dynamic states of infection

Population-level proportions of individuals that fall at different points in the spectrum [of disease severity], from asymptomatic infection to severe disease, are often difficult to observe, but estimating these quantities can provide information about the nature and severity of the disease in a particular population. Logistic and multinomial regression techniques are often applied to infectious disease modeling of large populations and are suited to identifying variables associated with a particular disease or disease state. However, they are less appropriate for estimating infection state prevalence over time because they do not naturally accommodate known disease dynamics like duration of time an individual is infectious, heterogeneity in the risk of acquiring infection, and patterns of seasonality. We propose a Bayesian compartmental model to estimate latent infection state prevalence over time that easily incorporates known disease dynamics. We demonstrate how and why a stochastic compartmental model is a better approach for determining infection state proportions than multinomial regression is by using a novel method for estimating Bayes factors for models with high-dimensional parameter spaces. We provide an example using visceral leishmaniasis in Brazil and present an empirically-adjusted reproductive number for the infection.

从无症状感染到重症的疾病严重程度谱系中，处于不同位点的个体在人群中的占比通常难以直接观测，但对该类占比进行估算，可为解析特定人群中疾病的本质与严重程度提供依据。逻辑回归与多项回归技术常被应用于大人群传染病建模，可有效识别与特定疾病或疾病状态相关的变量。然而，此类方法并不适于估算随时间动态变化的感染状态患病率，因其无法自然纳入已知的疾病动力学特征，例如个体的传染持续时长、感染风险异质性以及季节性流行规律。为此，我们提出一种贝叶斯分室模型（Bayesian compartmental model），用于估算随时间变化的潜在感染状态患病率，该模型可便捷整合已知的疾病动力学特征。我们通过一种针对高维参数空间模型估算贝叶斯因子（Bayes factors）的新型方法，论证了随机分室模型相较多项回归在确定感染状态占比方面的优势及内在逻辑。我们以巴西内脏利什曼病（visceral leishmaniasis）为例开展实证分析，并给出了该感染的经验校正再生数。