There is often a need to estimate the characteristics of epidemics or seasonality from infectious disease data. For instance, accurately estimating the start and end date of respiratory syncytial virus (RSV) epidemics can be used to optimize the initiation of prophylactic medication. These characteristics can sometimes be estimated directly from disease incidence data; more often, widely-used methods for describing these characteristics begin with a regression model fit to a time series of disease incidence. The fitted model is then used to calculate the quantities of interest. Calculation of these quantities typically involves combining multiple estimated parameters from the fitted model, and consequently only point estimates (rather than measures of uncertainty) can be made in a straightforward way. Motivated by attempts to estimate the optimal timing of prophylaxis for RSV, we developed a general method for obtaining confidence intervals for characteristics of seasonal and sporadic infectious disease outbreaks. To do this, we use multivariate sampling of a generalized additive model with penalized basis splines. Our approach provides robust confidence intervals regardless of the complexity of the calculations of the outcome measures, and it generalizes to other systems (including outbreaks of other infectious diseases). Here we present our general approach, its application to RSV, and an R package that provides a convenient interface for conducting and validating this type of analysis in other areas.