Models to assess the potential ofCapillaria hepaticato control population outbreaks of house mice

SUMMARY Population outbreaks of house mice ( Mus domesticus ) occur periodically in the wheatlands of southeastern Australia. This paper uses mathematical models to assist in the evaluation of the potential of a nematode, Capillaria hepatica , as a biological control agent to reduce the severity of these ‘plagues’. C. hepatica is unique amongst helminths of mammals in that its eggs are released only upon the death of an infected host. The major goal of the modelling in this paper is to determine the impact of this feature on the population dynamics of the host-parasite interaction. Simple differential equation models are used to examine the general properties of the system and determine which population parameters are most crucial to the outcome of the interaction. These models are supplemented by age-structured models which investigate the initial behaviour of the system after introduction of the parasite. The necessity of host death for transmission is a strongly destabilizing factor, suggesting that C. hepatica cannot regulate most populations stably in the absence of strong resource limitation, although it has the potential to depress mouse populations below infection-free levels. Although C. hepatica influences mouse fecundity at lower burdens than it affects mortality, the age-structured models show that parasite-induced host death cannot be neglected. Because transmission requires host death, the parasite life-cycle operates on a time-scale similar to that of the hosts, and introduction of the parasite as early as possible in the development period of an outbreak will therefore be necessary to achieve substantial reductions in plague intensity.