Compartmental models, especially the Susceptible-Infected-Removed (SIR) model, have long been used to understand the behaviour of various diseases. Allowing parameters, such as the transmission rate, to be time-dependent functions makes it possible to adjust for and make inferences about changes in the process due to mitigation strategies or evolutionary changes of the infectious agent. In this article, we attempt to build a nonparametric inference framework for stochastic SIR models with time dependent infection rate. The framework includes three main steps: likelihood approximation, parameter estimation and confidence interval construction. The likelihood function of the stochastic SIR model, which is often intractable, can be approximated using methods such as diffusion approximation or tau leaping. The infection rate is modelled by a B-spline basis whose knot location and number of knots are determined by a fast knot placement method followed by a criterion-based model selection procedure. Finally, a point-wise confidence interval is built using a parametric bootstrap procedure. The performance of the framework is observed through various settings for different epidemic patterns. The model is then applied to the Ontario COVID-19 data across multiple waves.

翻译：长期以来，隔室模型（尤其是易感-感染-移除（SIR）模型）一直被用于理解各种疾病的行为。允许参数（例如传播率）成为时变函数，使得我们能够针对缓解策略或传染源进化变化所引起的过程变化进行调整和推断。本文试图为具有时变感染率的随机SIR模型构建一个非参数推断框架。该框架包含三个主要步骤：似然近似、参数估计和置信区间构建。随机SIR模型的似然函数通常难以处理，但可以通过扩散近似或tau-leaping等方法进行近似。感染率通过B样条基函数建模，其节点位置和数量由一种快速节点布置方法确定，随后进行基于准则的模型选择。最后，使用参数自助法构建逐点置信区间。通过针对不同流行模式的多种设置来观察该框架的性能。随后，将该模型应用于安大略省多波次的COVID-19数据。