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