  The paper studies multi-competitive continuous-time epidemic processes in the
presence of a shared resource. We consider the setting where multiple viruses
are simultaneously prevalent in the population, and the spread occurs due to
not only individual-to-individual interaction but also due to
individual-to-resource interaction. In such a setting, an individual is either
not affected by any of the viruses, or infected by one and exactly one of the
multiple viruses. We classify the equilibria into three classes: a) the healthy
state (all viruses are eradicated), b) single-virus endemic equilibria (all but
one viruses are eradicated), and c) coexisting equilibria (multiple viruses
simultaneously infect separate fractions of the population). We provide i) a
sufficient condition for exponential (resp. asymptotic) eradication of a virus;
ii) a sufficient condition for the existence, uniqueness and asymptotic
stability of a single-virus endemic equilibrium; iii) a necessary and
sufficient condition for the healthy state to be the unique equilibrium; and
iv) for the bi-virus setting (i.e., two competing viruses), a sufficient
condition and a necessary condition for the existence of a coexisting
equilibrium. Building on these analytical results, we provide two mitigation
strategies: a technique that guarantees convergence to the healthy state; and,
in a bi-virus setup, a scheme that employs one virus to ensure that the other
virus is eradicated. The results are illustrated in a numerical study of a
spread scenario in Stockholm city.
