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.

The idea of the Leslie matrix, introduced into the analysis of age prevalence data, is extended to cover prevalence data for general epidemic processes. The use of the projection matrix in such situations is discussed, focusing on model construction and estimation of parameters of the projection matrices that arise. Applications of the technique to data covering varous epidemiological situations (vector-borne disease and virus infection) are illustrated. It is also shown how the technique can be of use in evolving an immunization strategy for arresting the spread of virus infection. dS dt = -(:3IS with initial conditions 1(0) = Q and S(o) = Nand 1(1) + S(I) = N + Q.This is the simplest basic epidemic model called an SI-model. There are others, discussed in Bailey (1975) and Hethcote (1989), named according to the model assumptions adopted, e.g.(a) the SIS-model, in which an individual is susceptible, becomes infective on being infected and returns to the susceptible class again after recovery and (b) the SIR-model, where the recovered infectives are permanently immune and so are classified as removed, R.The system of equations which arises for the continuous time treatment (stochastic or deterministic) is usually mathematically intractable because the equations involve non-linear systems of differential equations. tAddress

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Probability distributions are used in the evaluation of wind energy potentials to describe the wind speed characteristics of the chosen location for wind farm establishment. However, the Weibull distribution that is the most chosen by wind energy modelers may likely fail to properly describe the wind speed data of certain locations, or it may not be the best model to describe wind speed when compared to the fitness of other probability distributions. Thus, in this study, four probability distributions are fitted to wind speed data from Yola, Nigeria. They are the Weibull, the exponentiated Weibull, the generalized power Weibull and the exponentiated epsilon distributions; and, all provided good fit to the wind speed dataset. The exponentiated epsilon distribution is new and provided the best fit. These models are compared based on the relative likelihood gain per data point; it is found that there is about 5% gain by the other three probability distributions over the Weibull distribution. Hence all the three distributions can also be used as wind models. The estimated average wind speeds computed using the four models at various hub heights show that wind is sufficiently available to support a wind turbine with a cut-in speed of 3 m/s at hub heights 90 m above ground level. For the exponentiated-epsilon model, average wind speed of 3.68 m/s at hub height of 120 m above ground level can generate 6.11 W/m 2 of electricity; and for a wind turbine of rotor diameter of 128 m with 12,868 m 2 swept area, this amounts to 78.6 kW of electricity supply for a small-scale wind power project. Consequently, Yola holds a good potential for the establishment of a wind farm.