A Thesis submitted to the Faculty of Science in ful lment of the requirements for the degree of Doctor of Philosophy, School of Computer Science and Applied Mathematics. Johannesburg, 2016. / In this thesis in order to study the complex dynamics of Rift Valley fever (RVF) we
combine two modelling approaches: equation-based and simulation-based modelling.
In the first approach we first formulate a deterministic model that includes two
vector populations, Aedes and Culex mosquitoes with one host population (livestock),
while considering both horizontal and vertical transmissions. An easy
applicable expression of the basic reproduction number, R0 is derived for both
periodic and non-periodic environment. Both time invariant and time varying
uncertainty and sensitivity analysis of the model is carried out for quantifying
the attribution of model output variations to input parameters over time and
novel relationships between R0 and vertical transmission are determined providing
important information useful for improving disease management.
Then, we analytically derive conditions for stability of both disease-free and endemic
equilibria. Using techniques of numerical simulations we perform bifurcation
and chaos analysis of the model under periodic environment for evaluating the
effects of climatic conditions on the characteristic pattern of disease outbreaks.
Moreover, extending this model including vectors other than mosquitoes (such as
ticks) we evaluate the possible role of ticks in the spread and persistence of the
disease pointing out relevant model parameters that require further attention from
experimental ecologists to further determine the actual role of ticks and other biting
insects on the dynamics of RVF. Additionally, a novel host-vector stochastic model
with vertical transmission is used to analytically determine the dominant period
of disease outbreaks with respect to vertical transmission efficiency. Then, novel
relationships among vertical transmission, invasion and extinction probabilities
and R0 are determined.
In the second approach a novel individual-based model (IBM) of complete mosquito
life cycle built under daily temperature and rainfall data sets is designed and
simulated. The model is applied for determining correlation between abundance of
mosquito populations and rainfall regimes and is then used for studying disease
inter-epidemic activities. We find that indeed rainfall is responsible for creating
intra- and inter-annual variations observed in the abundance of adult mosquitoes
and the length of gonotrophic cycle, number of eggs laid per blood meal, adults
age-dependent survival and
fight behaviour are among the most important features
of the mosquito life cycle with great epidemiological impacts in the dynamics of
RVF transmission. These indicators could be of great epidemiological significance
by allowing disease control program managers to focus their e orts on specific
features of vector life cycle including vertical transmission ability and diapause.
We argue that our IBM model is an ideal extendible framework useful for further
investigations of other relevant host-vector ecological and epidemiological questions
for providing additional knowledge important for improving the length and quality
of life of humans and domestic animals. / LG2017
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/21716 |
| Date | January 2016 |
| Creators | Pedro, Sansao Agostinho |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (xxii, 218 leaves), application/pdf, application/pdf |
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