A model of insect—pathogen dynamics in which a pathogenic bacterium can also reproduce saprophytically

We developed a model of the population dynamic interaction between an insect and a pathogenic bacterium motivated by study of Serratia entomophila, a commercially exploited pathogen of the New Zealand grass grub (Costelytra zealandica). The bacterium is able to reproduce saprophytically, though it competes for saprophytic substrates with non–pathogenic strains, which appear to be superior competitors, probably because they lack a plasmid that carries genes required for pathogenicity. The effect of saprophytism and competition on the invasion criterion (R0), short–term dynamics and long–term dynamics are described. Saprophytism can reduce (possibly to zero) the host threshold at which the pathogen can invade, though this reduction is less when there is competition with non–pathogenic strains. In a model of short–term population dynamics designed to mimic the application of bacteria to a host epizootic, saprophytism enhances the reduction in host density, though again this is tempered by competition with non–pathogens. In the long term, a pathogen that can develop saprophytically can drive its host to extinction in the absence of competition with non–pathogens. When the latter are present, host extinction is prevented. The addition of saprophytic reproduction can stabilize an otherwise unstable host–pathogen model, but we were unable to find a stable equilibrium given the further addition of a wholly saprophytic bacterial strain. The model suggests that enhancing or selecting for saprophytic ability could be a way of improving biological control.