Extinction and quasi-stationarity in the stochastic logistic SIS model: A Maple module and Corrections.

A monograph dealing with extinction and quasi-stationarity in the logistic SIS model, and written by Ingemar Nåsell, was published as Volume 2022 in the Springer Lecture Notes in Mathematics Series in 2011. The monograph develops approximations of the quasi-stationary distribution of the SIS model in three separate parameter regions, and also gives approximations that are uniformly valid across all three parameter regions. In addition, the monograph gives approximations of the expected time to extinction from the quasi-stationary distribution and from the state one.

In the monograph, numerical evaluations are made with the aid of Maple procedures contained in a Maple module. As an aid for a reader who wishes to do numerical evaluations of his/her own particular cases, we make the Maple module available here. This Maple module is contained in a Maple worksheet that can be fed directly to Maple.

An unfortunate error is made in Chapter 6 of the monograph. A consequence of this error is that the conditions for validity of several of the approximations given in the monograph need to be changed. We emphasize, however, that the approximations themselves are in no cases affected by the error. A description of the changes in validity conditions is given here. This description suffices for the reader who is only concerned with the results of the analysis.

A detailed list of the changes in validity conditions is given here. This list also gives rederivations of two of the theorems in the monograph. The list is written for the reader who wants to follow the detailed mathematical derivations in the monograph.

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