Browsing by Author "Van Schalkwyk, Helene"

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    The development of a spatio-temporal model for water hyacinth biological control strategies
    (University of Georgia, 2016) Van Schalkwyk, Helene; Potgieter, Linke; Hui, Cang
    A reaction-diffusion model for a temporally variable and spatially heterogeneous environment is developed to mathematically describe the spatial dynamics of water hyacinth and the interacting populations of the various life stages of the Neochetina eichhorniae weevil as a biological control agent on a bounded two-dimensional spatial domain. Difficulties encountered during the implementation of the model in MATLAB are discussed, including the implementation of time delays and spatial averaging. Conceptual validation tests indicate that the model may succeed in describing the spatio-temporal dynamics of the water hyacinth and weevil interaction. A modelling framework is thereby provided to evaluate the effectiveness of different biological control release strategies, providing guidance towards the optimal magnitude, timing, frequency and distribution of agent releases. Numerical results confirm the hypothesis that the seasonal timing of releases have a significant influence on the success of the control achieved. However, in order to ascertain the degree to which the model output realistically represent the real life water hyacinth and weevil interaction, predictive validation tests are proposed for further research.
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    The development of a spatio-temporal model for water hyacinth, Eichhornia crassipes (Martius) Solms-Laubach (Pontederiaceae), biological control strategies
    (Stellenbosch : Stellenbosch University, 2016-12) Van Schalkwyk, Helene; Potgieter, Linke; Hui, Cang; Stellenbosch University. Faculty of Economic and Management Science. Dept. of Logistics.
    ENGLISH SUMMARY : The sustainable and cost-effective management of the notorious water hyacinth weed remains a challenge in South Africa. In this study, a reaction-diffusion model, consisting of a system of delayed partial differential equations, is developed to mathematically describe the population growth and dispersal of water hyacinth and the interacting populations of the various life stages of the Neochetina eichhorniae weevil as a biological control agent (BCA) in a temporally variable and spatially heterogeneous environment, subject to homogeneous Neumann boundary conditions on a bounded two-dimensional spatial domain. The primary objectives are to establish a spatio-temporal model which may be used to investigate the efficiency of different biological control release strategies, providing guidance towards the optimal magnitude, frequency, timing and distribution of BCA releases, and to evaluate the cost-effectiveness of local mass rearing programmes in biological control. Although previous studies have started to examine the influence of temperature on the population dynamics of the two species and the control of the weed under constant conditions, the model developed in this study is the first to evaluate the effect of introducing spatial dynamics. In addition, for the first time in research of water hyacinth management, different BCA release strategies are compared by means of mathematical modelling to provide practical recommendations for efficient and cost-effective biological control of water hyacinth in South Africa without having to conduct formal field experiments. Numerical solutions emphasize the benefit of frequent releases of Neichhorniae compared to a once-off release in the long term, as well as the advantage of more distributed releases along the edges of an infested water body. Furthermore, releases commencing in summer appear to be significantly more efficient and cost-effective than releases commencing in winter. The model is applied to a real-world release site in order to illustrate how the model may be utilized to provide guidance towards suitable BCA release strategies, which may minimize costs while maximizing the benefit for a specific site.