Predicting the Herd Immunity Threshold during an Outbreak: A Recursive Approach

Background: The objective was to develop a novel algorithm that can predict, based on field survey data, the minimum vaccination coverage required to reduce the mean number of infections per infectious individual to less than one (the Outbreak Response Immunization Threshold or ORIT) from up to six days in the advance. Methodology/Principal Findings: First, the relationship between the rate of immunization and the ORIT was analyzed to establish a link. This relationship served as the basis for the development of a recursive algorithm that predicts the ORIT using survey data from two consecutive days. The algorithm was tested using data from two actual measles outbreaks. The prediction day difference (PDD) was defined as the number of days between the second day of data input and the day of the prediction. The effects of different PDDs on the prediction error were analyzed, and it was found that a PDD of 5 minimized the error in the prediction. In addition, I developed a model demonstrating the relationship between changes in the vaccination coverage and changes in the individual reproduction number. Conclusions/Significance: The predictive algorithm for the ORIT generates a viable prediction of the minimum number of vaccines required to stop an outbreak in real time. With this knowledge, the outbreak control agency may plan to expend the lowest amount of funds required stop an outbreak, allowing the diversion of the funds saved to other areas of medical need.