Global stability for an epidemic model with applications to feline infectious peritonitis and tuberculosis

A general compartmental model of disease transmission is studied. The generality comes from the fact that new infections may enter any of the infectious classes and that there is an ordering of the infectious classes so that individuals can be permitted (or not) to pass from one class to the next. The model includes staged progression, differential infectivity, and combinations of the two as special cases. The exact etiology of feline infectious peritonitis and its connection to coronavirus is unclear, with two competing theories - mutation process vs multiple virus strains. We apply the model to each of these theories, showing that in either case, one should expect traditional threshold dynamics. A further application to tuberculosis with multiple progression routes through latency is also presented.