Towards global control of cystic and alveolar hydatid diseases

A mathematical model of the life-cycle of Echinococcus granulosus in dogs and sheep in New Zealand is constructed and used to discuss previously published experimental and survey data. The model is then used to describe the dynamics of transmission of the parasite, and the means by which it may be destabilized. It is found that under the conditions that prevailed in New Zealand during the late 1950s, at the time of surveys of this parasite, the dog-sheep life-cycle was not regulated by any effective density-dependent constraint. In contrast there was evidence for an effective acquisition of immunity to reinfection by cattle. The long time to maturity of the cyst in sheep, together with the practice of feeding aged sheep to dogs, provides a time delay in the intermediate host. By comparison, the time to maturity of the adult stage in dogs is short, but it is of sufficient magnitude to be a key factor in the destabilization of the system by a regular dog-dosing programme. The model used to describe the life-cycle is a linear integrodifferential equation of the Volterra type. Such equations are intrinsically unstable in that a small perturbation in parameters can drive a previous equilibrium solution to zero. At the time of the surveys, the value of the basic reproductive rate, R0, was close to 1, and it has since been reduced below 1 by control measures.

The numerical distributions of Echinococcus granulosus in an experimental dog population are described. At all dose rates of protoscoleces from 10 to 175000 the distribution of worms was over-dispersed. Host age had no effect. There was a direct proportionality between the infective-stage density and rate of infection, and between the latter and the index of clumping. The worm burdens were significantly higher in the proximal than distal portions of the small intestine. Lengths of the 3- and 4-segmented worms increased from 4 to 10 and 4 to 8 weeks of age, respectively. Thereafter apolysis was asynchronous and could not be determined. Eggs were first detected in the faeces at 6 weeks and the mean age at oogenesis was 7.26 weeks. Retarded growth of the whole population of worms was observed in some dogs. For the first few infections, worm burdens varied widely in the same dog, but by the 6th infection 50% of the dog population had developed a relative insusceptibility to infection. Growth or oogenesis of the worms were not affected. A short-acting immune response was artificially induced in some dogs following the parenteral injection of activated embryos of E. granulosus, Taenia hydatigena, T. ovis, T. multiceps, T. pisiformis and T. serialis. The response affected either the number of worms established, growth or oogenesis or all three parameters. There was a strong positive correlation between numbers and lengths of worms in dogs with acquired and induced immunity, indicating that no 'crowding' effects were involved. In sheep populations the mean number of cysts which established was directly proportional to the number of eggs given, implying that there was no negative feedback mechanism operating at this stage of the life-cycle. The distribution of the larval population in sheep was over-dispersed and the index of clumping increased with the size of the egg dose from 25 to 2500 eggs. Protoscoleces were first observed in cysts at 2 years and the proportion producing them increased with age, with an estimate of 50% of cysts containing protoscoleces at 6.29 years. No deaths were observed in dogs or sheep even when high parasite burdens were present, implying that E. granulosus does not regulate the population of its hosts.