Michael T. Meehana, Daniel G. Cocksb, Emma S. McBrydea. Global stability of the multi-strain Kermack-McKendrick epidemic model. 19 October 2018. https://arxiv.org/pdf/1710.06984.pdf
We extend a recent investigation by Meehan et al. (2017)  regarding the global stability properties of the general Kermack-McKendrick model to the multi-strain case. We demonstrate that the basic reproduction number of each strain R0j represents a sharp threshold parameter such that when R0j ≤ 1 for all j each strain dies out and the infection-free equilibrium is globally asymptotically stable; whereas for R01 ≡ maxj R0j > 1 the endemic equilibrium point P¯1 , at which only the fittest strain (i.e. strain 1) remains in circulation, becomes globally asymptotically stable.
a Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia
b College of Science and Engineering, James Cook University, Townsville, Australia