An earlier paper (May, 1977) developed a theoretical framework for exploring the consequences of dioecy for the population dynamics of schistosomes, assuming an unbiased sex ratio. This paper extends the analysis to biased sex ratios, as have been reported in practice. We consider the relationships of the mean number and distribution of worms among hosts, the sex ratio, and the mating system (monogamous or polygamous) to: (i) the female mating probability, Φ the prevalence of mated female worms. Ω: and (iii) the mean number of mated female worms per host, ξ. Among other results, we show how high values of Φ are associated with male-biased sex ratios and polygamous mating; that Ω is independent of the mating system and is relatively unaffected by the sex ratio; and that ξ is maximal for unbiased sex ratios given monogamous mating, and for female-biased sex ratios if mating is polygamous. These results, together with the confounding effects of the mean number and distribution of worms, are described in detail in the main body of the paper.

The influence of density-dependent processes on the transmission of parasitic helminths is determined by both the severity of the regulatory constraints and the degree of parasite overdispersion among the host population. We investigate how overdispersed parasite distributions among humans influence transmission levels in both directly- and indirectly-transmitted nematodes (Ascaris lumbricoides and Onchocerca volvulus). While past work has assumed, for simplicity, that density dependence acts on the average worm load, here we model density-dependence as acting on individual parasite burdens before averaging across hosts. A composite parameter, which we call the effective transmission contribution, is devised to measure the number of transmission stages contributed by a given worm burden after incorporating overdispersion in adult worm mating probabilities and other density-dependent mechanisms. Results indicate that the more overdispersed the parasite population, the greater the effect of density dependence upon its transmission dynamics. Strong regulation and parasite overdispersion make the relationship between mean worm burden and its effective contribution to transmission highly non-linear. Consequently, lowering the intensity of infection in a host population using chemotherapy may produce only a small decline in transmission (relative to its initial endemic level). Our analysis indicates that when parasite burden is low, intermediate levels of parasite clustering maximize transmission. Implications are discussed in relation to existing control programmes and the spread of anthelmintic resistance.