Global stability of a multistrain SIS model with superinfection and patch structure

TL;DR

This paper analyzes the global stability of a complex multistrain SIS epidemiological model with superinfection and multiple patches, establishing threshold parameters that determine strain coexistence and correcting previous proofs for a special case.

Contribution

It introduces an iterative method to compute threshold parameters that fully determine the system's global dynamics, extending previous models to multiple patches and strains.

Findings

Threshold parameters determine strain coexistence.

Global stability depends on specific parameter values.

Corrects previous proof for a special case.

Abstract

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006 7:235-247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters. Finally, we return to the special case of one patch examined in [Math Biosci Eng. 2017 14:421-35] and give a correction to the proof of Theorem 2.2 of that paper.