Lambert's W meets Kermack-McKendrick Epidemics

摘要

The central aim of this partly expository paper is pressing the point that a certain transcendental equation for the final size of an susceptible-infected-removed epidemic model has an explicit solution in terms of the Lambert W-function, an elementary function. Known branch point and continued fraction approximations yield simple and highly accurate numerical approximations which are considerably better than the traditional Kermack-McKendrick approximation. A Karamata expansion easily yields refined forms of the second threshold theorem.