PERSISTENCE OF HOST-PARASITE INTERACTIONS IN A DISTURBED ENVIRONMENT

Seasonal disturbances are an inherent property of many plant, microbia l and invertebrate populations yet most ecological and epidemiological models describe systems with continuous, uninterrupted interactions b etween populations. In this paper, we investigate the dynamics of a ho st-parasite system with disturbances, where the host is either not con tinuously present or does not continuously reproduce. Parasite persist ence in a disturbed environment is analysed by considering three inter related components: the ability of the parasite to invade the host pop ulation at the start of each season; the number of hosts a parasite ca n infect during a season; and the ability of the parasite to persist b etween seasons. We show that the population dynamics and, in particula r, thresholds for parasite invasion depend on the form of disease tran smission. If the transmission rate increases linearly with parasite de nsity, we obtain the classical invasion threshold, R-0 > 1, where R-0 is the parasite basic reproductive number. If there are nonlinearities in disease transmission, there are multiple threshold criteria. Furth ermore, there are multiple stable equilibria that imply a threshold in vasion population for the parasite. Criteria for parasite persistence between seasons are obtained, which show there is a critical inter-sea son period if the parasite is to persist. Numerical studies show there are also thresholds for the duration of a season and the size of the returning host population at the beginning of a season. The results ar e illustrated using two simple examples. (C) 1997 Academic Press Limit ed.