Shigellosis, a diarrheal disease, is endemic worldwide and is responsible for approximately 15,000 laboratory-confirmed cases in the United States every year. However, patients with shigellosis often do not seek medical care. To estimate the burden of shigellosis, we extended time-series susceptible- infected-recovered models to infer epidemiologic parameters from underreported case data. We applied the time-series susceptible-infected-recovered-based inference schemes to analyze the largest surveillance data set of Shigella sonnei in the United States from 1967 to 2007 with county-level resolution. The dynamics of shigellosis transmission show strong annual and multiyear cycles, as well as seasonality. By using the schemes, we inferred individual-level parameters of shigellosis infection, including seasonal transmissibilities and basic reproductive number (R0). In addition, this study provides quantitative estimates of the reporting rate, suggesting that the shigellosis burden in the United States may be more than 10 times the number of laboratory-confirmed cases. Although the estimated reporting rate is generally under 20%, and R0 is generally under 1.5, there is a strong negative correlation between estimates of the reporting rate and R0. Such negative correlations are likely to pose identifiability problems in underreported diseases. We discuss complementary approaches that might further disentangle the true reporting rate and R0.
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