Thesis (PhD)--Stellenbosch University, 2013. / 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. / AFRIKAANSE OPSOMMING: Twee wiskundige modelle word in hierdie proefskrif vir die populasiegroei van ’n Eldana saccha-
rina Walker infestasie van suikerriet onder die invloed van gedeeltelik steriele, vrygelate insekte
daargestel. Die eerste model beskryf die populasiegroei van en -interaksie tussen normale en
steriele E. saccharina motte in ’n dinamiese, maar ruimtelik-homogene omgewing. Die model is
’n stelsel deterministiese verskilvergelykings onderhewig aan streng positiewe aanvangswaardes.
Die primˆere doelstelling met hierdie model is om geskikte parameters te bepaal in terme waarvan
die bogenoemde groei en interaksie gekwantifiseer kan word, en waarvolgens E. saccharina
infestasievlakke en die gepaardgaande suikerrietskade gemeet kan word.
Die tweede model beskryf hierdie groei en interaksie onder die invloed van gedeeltelik steriele
insekte wat in ’n dinamiese en ruimtelik-heterogene omgewing vrygelaat word. Die model
is ’n gediskretiseerde stelsel reaksie-diffusievergelykings met veranderlike diffusieko¨effisi¨ente
onderhewig aan streng positiewe aanvangswaardes en zero-vloei Neumann-randwaardes op ’n
begrensde ruimtelike gebied. Die primˆere doelstellings in hierdie geval is om ’n model tot stand
te bring wat in ’n area-wye, ge¨ıntegreerde pesbestrydingsprogram vir E. saccharina gebruik
kan word om die doeltreffendheid van verskillende steriele motvrylatingstrategie¨e te bepaal
sonder om daadwerklik veldeksperimente uit te voer, en om riglyne daar te stel waarvolgens
vrylatingsverhoudings, -frekwensies en -verspreidings bepaal kan word wat na verwagting na ’n
onderdrukking van die pes sal lei.
Bykomend tot die wiskundige modelle in hierdie proefskrif, word twee praktiese toepassings
van die modelle ook beskryf. In die eerste toepassing word ’n gebruikersvriendelike simulasie
hulpmiddel ontwikkel om E. saccharina infestasie onder die invloed van steriele insekvrylatings
in verskillende ruimtelike gebiede te simuleer. Hierdie toepassing fasiliteer ’n dieper begrip van
wat ter sprake is in die toepassing van wiskundige modelle, soos die twee modelle in hierdie
tesis, tot werklike scenario’s. In die tweede toepassing word ’n optimale diversifisering van
suikerriet habitats as ’n opsie vir die vermindering van die gemiddelde E. saccharina infestasie
vlakke beskou, en gevolglik word die verbetering van die koste-doeltreffendheid van steriele
insekvrylatings afgeskat. Alhoewel verskeie spesiale gevalle van die bogenoemde twee klasse van modelle reeds in die
verlede gebruik is om die doeltreffendheid van die steriele-insektegniek te modelleer, beskryf
weinig van hierdie modelle die tegniek vir Lepidopteriese spesies met meer as een lewensfase en
waar F1-steriliteit ter sprake is. Verder beskryf geen van hierdie modelle die tegniek waar algeheel
steriele wyfies en gedeeltelik steriele mannetjies vrygelaat word nie. Die modelle in hierdie
tesis is ook die eerste waar die tegniek spesifiek op E.saccharina toegepas word, en waar die
ekonomiese lewensvatbaarheid van die tegniek vir hierdie spesie oorweeg word. Verder bestaan
daar min voorbeelde van soortgelyke modelle wat verder gaan as ’n teoretiese beskrywing en
wiskundige ontleding na praktiese, werklike toepassings, soos in hierdie proefskrif ge¨ıllustreer.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/85865 |
| Date | 12 1900 |
| Creators | Potgieter, Linke |
| Contributors | Van Vuuren, J. H ., Conlong, D. E., Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Logistics. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 164 p. : ill. |
| Rights | Stellenbosch University |
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