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

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.