Superspreading events (SSEs) produce extreme, rare bursts of disease transmission that standard compartment models, which assume population homogeneity, fail to capture. This inability to model heterogeneity in transmission rates can result in biased estimates of transmissivity. To address this limitation, we present a modular framework that treats SSEs as statistical outliers in case count time series and incorporates them into SIR-type models via pulse terms that transfer SSE cases directly from susceptible to infected compartments. This separation isolates anomalous SSE-driven transmission from background spread, which reduces bias when estimating mean transmission rates. We validate the approach on synthetic data generated by a stochastic model with embedded SSEs, demonstrating accurate recovery of the true non-SSE transmission parameter. We then apply the method to COVID-19 outbreaks in Hong Kong and the German district of Gutersloh, showing improved model fits and more robust estimates of background transmissivity both for a period with constant transmission and for a period with temporally structured NPI-driven heterogeneities. The framework's interchangeable outlier-detection, compartment, and SSE modules make it adaptable to diverse diseases and data contexts.