Consider a data collection setup during a spread of an infectious disease. Examples include severe acute respiratory syndrome (SARS) or influenza A virus H3N2. The health management in such scenarios quickly removes the infected cases before the data collection is completed. The estimate of the incidence rate or the chance for anyone to be immune requires using a correct probability distribution. The usual Poisson distribution is inappropriate because of the impact of removing infected cases on the incidence rate as well as observing a new case. An appropriate new probability distribution is derived and is named as spinned Poisson distribution. The statistical properties of the spinned Poisson distribution are developed and illustrated using infectious smallpox incidence in Abakaliki, Nigeria.