  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.
