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We investigate how a population's natural and vaccine immunity affects thecompetitive balance between two strains of an infectious disease with differentepidemiological characteristics. Specifically, we consider the case where onestrain is more transmissible and the other strain is more immune-resistant. Thecompetition of these strains is modeled by two SIR-type models whichincorporate waning natural immunity and which have distinct mechanisms forvaccine immunity. Waning immunity is implemented as a gamma-distributed delay,which is analyzed using the linear chain trick to transform the delaydifferential equation systems into a system of ordinary differential equations.Our analysis shows that vaccination has a significant effect on the competitivebalance between two strains, potentially leading to dramatic flips from onestrain dominating in the population to the other. We also show that whichstrain gains an advantage as a population's immunity level increases dependsupon the integration between the mechanisms of natural and vaccine immunity.The results of this paper are consequently relevant for public policy.

The Effect of Vaccination on the Competitive Advantage of Two Strains of an Infectious Disease