  The rise of antimicrobial drug resistance is an imminent threat to global
health that has warranted, and duly received, considerable attention within the
medical, microbiological and modelling communities. Outbreaks of drug-resistant
pathogens are ignited by the emergence and transmission of mutant variants
descended from wild-type strains circulating in the community. In this work we
investigate the stochastic dynamics of the emergence of a novel disease strain,
introduced into a population in which it must compete with an existing endemic
strain. In analogy with past work on single-strain epidemic outbreaks, we apply
a branching process approximation to calculate the probability that the new
strain becomes established. As expected, a critical determinant of the survival
prospects of any invading strain is the magnitude of its reproduction number
relative to that of the background endemic strain. Whilst in most circumstances
this ratio must exceed unity in order for invasion to be viable, we show that
differential control scenarios can lead to less-fit novel strains invading
populations hosting a fitter endemic one. This analysis and the accompanying
findings will inform our understanding of the mechanisms that have led to past
instances of successful strain invasion, and provide valuable lessons for
thwarting future drug-resistant strain incursions.
