Epidemics in Competition: Partial Cross-Immunity

The competition between two pathogen strains during the course of an epidemic represents a fundamental step in the early evolution of emerging diseases as well as in the antigenic drift process of influenza. The outcome of the competition, however, depends not only on the epidemic properties of the two strains but also on the timing and size of the introduction, characteristics that are poorly captured by deterministic mean-field epidemic models. We describe those aspects of the competition that can be determined from the mean-field models giving the range of possible final sizes of susceptible hosts and cumulated attack rates that could be observed after an epidemic with two cross-reacting strains. In the limit where the size of the initial infection goes to zero, the possible outcomes lie on a (one dimensional) curve in the outcome space.