A modified version of the three-compartment susceptible-infectious-removed (SIR) epidemic model can be expressed exactly using a specific generalization of the logistic distribution, and its parameters can be estimated from epidemic surveillance data. The population proportion remaining Susceptible may be approximated using the inverse of a standard cumulative logistic distribution, while the population proportion actively Infectious may be approximated using the density of a logistic or log-logistic distribution. This knowledge may enable rapid local disease modeling without specialized skills. Highlights A modification of the three-compartment SIR model can be solved exactly in terms of a specific generalization of the logistic distribution The generalized logistic solution can be approximated using standard logistic and/or log-logistic distributions Surveillance data from an emerging epidemic, often initially modeled with standard logistic or log-logistic curves, can be used to derive parameters for an underlying modified SIR model