Stochastic host-parasite interaction models

 We contribute to the discussion of causes and effects of aggregation (overdispersion) of macroparasite counts, focussing particularly upon the effects of clumped infections and parasite-induced host mortality. The simple nonlinear stochastic model for the evolution of the parasite load of a single host, investigated in Isham (1995), is extended to allow three parasite stages (larval, mature and offspring), and to allow durations of these stages to be non-exponentially distributed. As in the earlier work, exact algebraic results are possible, providing insight into the aggregation mechanisms, as long as the only source of interaction between host and parasites is an excess host mortality linearly related to the parasite load. Results are obtained on the distribution of parasite lad and on host survival. In particular, although parasite-induced host mortality is usually thought of as a process that reduces parasite aggregation (Anderson and Gordon 1982), it is shown that, for this model, parasite-induced host mortality cannot cause the index of dispersion to fall below unity. Host heterogeneity and disease control are also discussed. An approximation based on moment assumptions appropriate to a specially-constructed multivariate negative binomial distribution is proposed. This approximation, which is applicable to other processes, and an alternative based on the multivariate normal distribution are compared with exact results.