Persistence of Host-parasite Interactions in a Disturbed Environment

Seasonal disturbances are an inherent property of many plant, microbial and invertebrate populations yet most ecological and epidemiological models describe systems with continuous, uninterrupted interactions between populations. In this paper, we investigate the dynamics of a host-parasite system with disturbances, where the host is either not continuously present or does not continuously reproduce. Parasite persistence in a disturbed environment is analysed by considering three interrelated components: the ability of the parasite to invade the host population at the start of each season; the number of hosts a parasite can infect during a season; and the ability of the parasite to persist between seasons. We show that the population dynamics and, in particular, threshold for parasite invasion depend on the form of disease transmission. If the transmission rate increases linearly with parasite density, we obtain the classical invasion threshold,R0>1, whereR0is the parasite basic reproductive number. If there are nonlinearities in disease transmission, there are multiple threshold criteria. Furthermore, there are multiple stable equilibria that imply a threshold invasion population of the parasite. Criteria for parasite persistence between seasons are obtained, which show there is a critical inter-season period if the parasite is to persist. Numerical studies show there are also threshold for the duration of a season and the size of the returning host population at the beginning of a season. The results are illustrated using two simple examples.