The Leslie matrix provides a demographic technique for studying population growth. It is introduced into age‐prevalence studies, for describing the age‐specific growth of infection in a population which is subject to the fluctuations of birth and mortality. The application of the technique is illustrated with Onchocerciasis age‐prevalence data. The technique is also extended to study the stability of infection, introduced into three types of population.

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The solution of a hierarchical n-compartmental homogeneous process with multiple-valued migration rates is obtained using Laplace transform techniques. Such models are suggested for modelling the infection process of endemic diseases because of their property of gamma-distributed compartmental residence times in each of n compartments. Its relevance to the onchocerciasis infection process (with and without the imposition of controls) is discussed and application to age-prevalence data (having only two infective states into which an individual can be classified) is undertaken.

A simple compartmental process, which is time-homogeneous and has differing transition rates between compartments, is discussed. When such a process is hierarchical, with all individuals released into the first compartment, the resulting distribution of individuals over the various compartments is multinomial. This process is applied to the migration of Onchocerca volvulus in simuliids and appears to represent successfully the early migration from the stomach through the abdomen to the thorax, provided that allowances are made for the engorgement period and the encapsulation of the blood meal by a peritrophic membrane.

A stochastic model for a parasitic disease is proposed which describes the acquisition of infectious material from an external source and the subsequent deterioration of the host reacting to the internally produced parasite. The model considers the endemic situation, where the disease is uncontrolled and the structure is both hierarchical and irreversible. The resulting compartmental model can be modified to incorporate piecewise-constant migration rates to respond to possible geographical and sociological fluctuations, which could affect the epidemiological dynamics. The model is illustrated using onchocerciasis prevalence data collected from nine West African village communities in 1975 and 1981, before and after the implementation of widespread larvacide controls as part of the O.C.P. in the Upper Volta region. Significance of the sex effects within onchocerciasis transmission is investigated and the effectiveness of controls is discussed.