Department of Logistics

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Browsing Department of Logistics by browse.metadata.advisor "Conlong, D. E."

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    A mathematical model for the control of Eldana saccharina Walker using the sterile insect technique
    (Stellenbosch : Stellenbosch University, 2013-12) Potgieter, Linke; Van Vuuren, J. H.; Conlong, D. E.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Logistics.
    ENGLISH ABSTRACT: Two mathematical models are formulated in this dissertation for the population growth of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The first model describes the population growth of and interaction between normal and sterile E. saccharina moths in a temporally variable, but spatially homogeneous environment. The model consists of a deterministic system of difference equations subject to strictly positive initial data. The primary objective of this model is to determine suitable parameters in terms of which the above population growth and interaction may be quantified and according to which E. saccharina infestation levels and the associated sugarcane damage may be measured. The second model describes this growth and interaction under the influence of partially sterile insects which are released in a temporally variable and spatially heterogeneous environment. The model consists of a discretized reaction-diffusion system with variable diffusion coefficients, subject to strictly positive initial data and zero-flux Neumann boundary conditions on a bounded spatial domain. The primary objectives in this case are to establish a model which may be used within an area-wide integrated pest management programme for E. saccharina in order to investigate the efficiency of different sterile moth release strategies in various scenarios without having to conduct formal field experiments, and to present guidelines by which release ratios, frequencies and distributions may be estimated that are expected to lead to suppression of the pest. In addition to the mathematical models formulated, two practical applications of the models are described. The first application is the development of a user-friendly simulation tool for simulating E. saccharina infestation under the influence of sterile insect releases over differently shaped spatial domains. This tool provides the reader with a deeper understanding as to what is involved in applying mathematical models, such as the two described in this dissertation, to real-life scenarios. In the second application, an optimal diversification of sugarcane habitats is considered as an option for minimising average E. saccharina infestation levels, and as a further consequence, improving the cost-efficiency of sterile insect releases. Although many special cases of the above model classes have been used to model the sterile insect technique in the past, few of these models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these models consider the technique when fully sterile females and partially sterile males are being released. The models formulated in this dissertation are also the first to describe the technique applied specifically to E. saccharina, and to consider the economic viability of applying the technique to this species. Furthermore, very few examples exist of such models which go beyond a theoretical description and analysis towards practical, real-life applications as illustrated in this dissertation.