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Title: Modelling the transmission dynamics of bluetongue disease with controls, stochasticity and migration in patchy environments
Authors: Mugabi, Francis 
Issue Date: 2021
In this thesis, a single serotype (j = 1) and patch (i = 1) ordinary difference equation (ODE)
model is formulated and analysed for the effects of direct and transplacental transmission on
the probability of bluetongue virus (BTV) persistence. Using the next generation approach,
the basic reproduction number (R0) is determined. When R0 < 1, the model exhibits a backward bifurcation indicating that the virus persists. When R0 > 1, a continuous-time Markov
chain (CTMC) model derived from the ODE model is used to estimate the probability of
BTV persistence. By approximating the CTMC model with a multitype branching process, it
is shown that both direct and transplacental transmission can have a large effect on the probability of persistence in regions with temperature T < 12◦C and a small effect for those with
T > 12◦C. The ODE and CTMC models are extended to include r serotypes and n patches
with the aim of determining the effects of midge movement on the outbreak and coexistence
of multiple BTV serotypes in an environment divided into patches depending on the risk of
infection. An estimate for the probability of a major outbreak of two BTV serotypes in two
patches is obtained by approximating the CTMC model with a multitype branching process.
It is shown that without movement a major outbreak occurs in the high-risk patch, but with
cattle or midge movement it occurs in both patches. When a major outbreak occurs, numerical simulations of the ODE model illustrate possible coexistence in both patches if the
patches are connected by midge or cattle movement. The multi-patch single-serotype ODE
model is then modified as an optimal control problem to evaluate the effectiveness of vaccination, quarantine, insecticide spraying and the use of repellent control strategies in reducing
the within- and between-patches transmission. By using optimal control theory, the effectiveness of these strategies is established. In a single patch, vaccination, insecticide spraying and
the use of a repellent are all highly effective in minimising transmission, but the most costeffective is vaccination. In patches connected by host and midge movements, if any of these
controls is applied in the high-risk patch, a disease-free status is achieved in both patches,
but if implemented in the low-risk patch, it is not attained in any patch. If hosts and midges
move, quarantine has no effect, but for no midge movement, the effect can be large in the
low-risk patch if it’s internally imposed.
Thesis submitted in fulfilment of the requirements for the Degree of Doctor of Applied Sciences in the Faculty of Applied Sciences at Durban University of Technology, 2021.
Appears in Collections:Theses and dissertations (Applied Sciences)

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