Stochastic epidemic models can estimate infection and removal rates, and derived quantities such as the basic reproductive number ($R_0$), when both infection and removal times are observed. In practice, however, removal times are often available while infection times are not, and existing methods that rely only on removal times can become unstable or biased. We study inference for stochastic SIR/SEIR models in a partial--observation setting. We develop imputation--based estimators that use a small calibration sample of fully observed infectious periods, derive closed--form expressions for the pairwise exposure terms they require, and use a studentized parametric bootstrap for bias correction and uncertainty quantification. In simulations, removal time--only methods performed poorly in moderate to large $R_0$ scenarios, while observing even tens of complete infectious periods substantially improved the estimation of the infection rate. A reanalysis of the 1861 Hagelloch measles outbreak under simulated missingness recovered stable qualitative differences in transmission between school classes. Based on our results, we advocate for the targeted collection of a modest number of complete infectious periods as a means of improving surveillance in the early stages of an epidemic.

翻译：随机流行病模型能够在同时观测到感染时间和移除时间的情况下，估计感染率、移除率以及基本再生数（$R_0$）等衍生量。然而在实践中，移除时间通常可获得而感染时间缺失，仅依赖移除时间的现有方法可能导致估计不稳定或存在偏差。本文针对部分观测场景下的随机SIR/SEIR模型展开推断研究。我们开发了基于插补的估计方法，该方法利用少量完全观测的传染病期校准样本，推导出所需成对暴露项的闭合表达式，并采用学生化参数自助法进行偏差校正与不确定性量化。模拟结果显示：在中等至较大$R_0$场景中，仅使用移除时间的方法表现欠佳，而即使仅观测数十个完整传染病期也能显著改善感染率的估计。对1861年哈格洛赫麻疹疫情在模拟缺失数据下的重新分析，成功恢复了学校班级间传播模式的定性差异。基于研究结果，我们建议在疫情早期阶段有针对性地收集适量完整传染病期数据，以提升监测能力。