The competitive exclusion principle in epidemiology implies that more transmissible strains will tend to outcompete other strains, leading to the extinction of less competitive strains over time. This principle holds true when the recovery by one strain provides complete immunity to other strains' infections. Nevertheless, studies have shown that there is coexistence among competing strains in epidemic systems with various interactions between the strains, but these studies focus only on cases where there are slight differences in transmissibility, resulting in limited competition between the strains. One can expect that if one strain has a substantial competitive advantage over others, the competitive exclusion principle would come into play, overriding coexistence mechanisms.
In this work, we use asymptotic methods to test the validity of the exclusion principle at an ultimate limit in which one strain has a vast competitive advantage over the other strains. We show that in the case of partial cross-immunity, such systems have a stable multi-species endemic equilibrium. Thus, the competitive exclusion principle does not hold beyond the established case of complete immunity. Furthermore, we have provided examples of cases where the less transmissible strain is driven to extinction when the other strain is moderately more transmissible, but not when the other strain is significantly more transmissible.