Browsing by Author "Potgieter, Linke"

Now showing 1 - 4 of 4
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    Allocating epidemic response teams and vaccine deliveries by drone in generic network structures, according to expected prevented exposures
    (Public Library of Science, 2021) Matter, Dean; Potgieter, Linke
    The tumultuous inception of an epidemic is usually accompanied by difficulty in determining how to respond best. In developing nations, this can be compounded by logistical challenges, such as vaccine shortages and poor road infrastructure. To provide guidance towards improved epidemic response, various resource allocation models, in conjunction with a network-based SEIRVD epidemic model, are proposed in this article. Further, the feasibility of using drones for vaccine delivery is evaluated, and assorted relevant parameters are discussed. For the sake of generality, these results are presented for multiple network structures, representing interconnected populations—upon which repeated epidemic simulations are performed. The resource allocation models formulated maximise expected prevented exposures on each day of a simulated epidemic, by allocating response teams and vaccine deliveries according to the solutions of two respective integer programming problems—thereby influencing the simulated epidemic through the SEIRVD model. These models, when compared with a range of alternative resource allocation strategies, were found to reduce both the number of cases per epidemic, and the number of vaccines required. Consequently, the recommendation is made that such models be used as decision support tools in epidemic response. In the absence thereof, prioritizing locations for vaccinations according to susceptible population, rather than total population or number of infections, is most effective for the majority of network types. In other results, fixed-wing drones are demonstrated to be a viable delivery method for vaccines in the context of an epidemic, if sufficient drones can be promptly procured; the detrimental effect of intervention delay was discovered to be significant. In addition, the importance of well-documented routine vaccination activities is highlighted, due to the benefits of increased pre-epidemic immunity rates, and targeted vaccination.
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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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    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.
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    Simulation modelling as a decision support in developing a sterile insect-inherited sterility release strategy for Eldana saccharina (Lepidoptera: Pyralidae)
    (Florida Entomological Society, 2016) Potgieter, Linke; Van Vuuren, Jan H.; Conlong, Des E.
    ENGLISH SUMMARY : A user-friendly simulation tool for determining the impact of the sterile insect technique/inherited sterility technique (SIT/IS) on populations of the African sugarcane stalk borer, Eldana saccharina Walker (Lepidoptera: Pyralidae) is described in this paper. The simulation tool is based on a spatio-temporal model. The design of the simulation tool is such that it is applicable for use in a number of pest/crop and pest control scenarios. It uses 4 interacting subsystems (pest species population dynamics, crop dynamics, environmental dynamics and economics) within a specified spatial domain. Furthermore, the spatial domain describes the layout of the agricultural crop (position, size, shape, crop age and variety of the different fields contained within the crop area). The pest species population subsystem describes E. saccharina population dynamics (but is designed to also include population dynamics of other pest species) under the influence of the IS technique. The E. saccharina module developed utilizes mean-field and spatio-temporal models, and includes dynamics of all E. saccharina life stages under the influence of the control measure. Only temperature and damage caused by E. saccharina are currently included as variables in the sugarcane dynamics subsystem. This subsystem estimates stalk length as a function of time and temperature, and sucrose percentage as a function of damage caused by E. saccharina boring. Interaction between E. saccharina population growth and sugarcane growth is described by a decreasing s-shaped density-dependent mortality function—the older the cane, the higher the carrying capacity (more food resources) and corresponding infestation and damage levels. The only environmental factor considered as an independent variable in the environmental dynamics subsystem is temperature. Possible extensions to this subsystem are discussed. The economics subsystem developed includes the estimation of the recoverable value, percentage, expected revenue and the cost of control. No other farm expenditures are taken into account. As such only profit or loss expected from applying the IS technique is estimated. The profit or loss is defined as the increase in revenue expected less the cost of applying a pest control measure. An example of using the simulation tool is presented in the context of a real field scenario of a simulated SIT/IS program against E. saccharina at a pilot site near the Eston area of KwaZulu-Natal, South Africa.