A paper with the title "A New Look at the Critical Community Size for Childhood Infections", written by Ingemar Nåsell, was published in Theoretical Popultaton Biology, Vol 67, (2005), pages 203-216. Section 14 of this paper gives differential equations for the cumulants of order 1 and 2 of the process, conditioned on non-extinction. The derivation of these differential equations has been done using Maple. The Maple worksheets that give these derivations are given here. Two situations are covered. In the first one, we derive cumulant equations for the 5 lowest-order cumulants of the unconditioned process. In the same worksheet, we also determine asymptotic expressions for the stationary solutions of these 5 cumulants. The second worksheet is used to derive cumulant equations for the 5 lowest-order cumulants of the conditioned process (conditioned on non-extinction). The worksheets have been prepared with the latest version of Maple available in May 2004, namely Maple 9.