Computing the extinction path for epidemic models

TL;DR

This paper introduces four computational algorithms with Matlab code to accurately compute the extinction path in epidemic models, addressing numerical challenges and improving upon existing methods.

Contribution

The paper presents new algorithms and implementation strategies to make WKB-based extinction path analysis more accessible and reliable in high-dimensional epidemic models.

Findings

Algorithms successfully compute extinction paths in standard models

Improved accuracy over previous methods

Enhanced convergence through algorithm tuning

Abstract

In infectious disease modelling, the expected time from endemicity to extinction (of infection) may be analysed via WKB approximation, a method with origins in mathematical physics. The method is very general, but its uptake to date may have been limited by the practical difficulties of implementation. It is necessary to compute a trajectory of a (high dimensional) dynamical system, the `extinction path', and this trajectory is maximally sensitive to small perturbations, making numerical computation challenging. Our objective here is to make this methodology more accessible by presenting four computational algorithms, with associated Matlab code, together with discussion of various ways in which the algorithms may be tuned to achieve satisfactory convergence. We illustrate our methods using three standard infectious disease models. For each such model, we demonstrate that our algorithms are able to improve upon previously available results.