Introduction

Acquired immunity is a particular type of density-dependent process that may affect the establishment, mortality or fecundity of parasitic helminths, as functions both of current infection and of past infection; that is, a densitydependent process with ‘memory’. This type of process is likely to have complicated impacts on parasite population dynamics because of this memory component (Woolhouse 1992a). The epidemiological impact of acquired immunity will also depend on which parasite life-cycle stage provides the antigen stimulating a protective response and on which stage is the target of the response. For human schistosomes (the main example used here), the relevant life cycle stages are larvae (cercariae and schistosomulae) (L), adult worms (A), and eggs (E). The evidence for different forms of immunity to schistosomes has been elegantly reviewed in Hagan and Wilkins (1993); possible combinations of target and response are: larval antigen/anti-larval response (an LL process); adult antigen/anti-larval response (an AL process); and adult antigen/antiadult response (an AA process).

Mathematical models

The models used here are described in detail elsewhere (Woolhouse 1992b, 1993, 1994) and are based on earlier elaborations of a simple immigrationdeath process (Anderson and May 1985, Roberts and Grenfell 1991). The models describe the dynamics of the worm burden, experience of infection, and level of resistance for a set of individuals in a population. Worm burden is self explanatory. Experience of infection corresponds to the (discounted) cumulative exposure to parasite antigens and can be interpreted as related to the numbers of specific memory cells.