Competitive exclusion and coexistence for pathogens in an epidemic model with variable population size

We study an SIR epidemic model with a variable host population size. We prove that if the model parameters satisfy certain inequalities then competition between n pathogens for a single host leads to exclusion of all pathogens except the one with the largest basic reproduction number. It is shown that a knowledge of the basic reproduction numbers is necessary but not sufficient for determining competitive exclusion. Numerical results illustrate that these inequalities are sufficient but not necessary for competitive exclusion to occur. In addition, an example is given which shows that if such inequalities are not satisfied then coexistence may occur.