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.

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