Approximations of the Quasi-Stationary Distribution of a Logistic SIS Model for Endemic Infections

TL;DR

This paper evaluates the accuracy of different approximations of the quasi-stationary distribution in a logistic SIS model for endemic infections, revealing new insights into their error bounds and introducing a novel approximation with exponentially small errors.

Contribution

The paper provides a numerical evaluation of approximation errors for the QSD in the logistic SIS model and introduces a new approximation with exponentially small errors above the threshold.

Findings

Two approximations have exponentially small errors above threshold.

The older approximation's error is proven to be exponentially small, a new result.

A new approximation method with improved accuracy is proposed.

Abstract

Errors of approximations of the quasi-stationary distribution (the QSD) of the logistic SIS model are evaluated numerically. The results are used to derive asymptotic approximations of the approximation errors for large populations. We show in particular that there are two approximations above threshold for which the approximation errors are exponentially small. One of these approximations has been known for some time, while the other one is new. The result that the older one of these two approximations has an exponentially small approximation error is new.