PhD (Mathematics) / Department of Mathematics and Applied Mathematics / In this study, we developed multiscale models of vector-borne diseases. In general, the transmission
of vector-borne diseases can be considered as falling into two categories, i.e. direct transmission
and environmental transmission. Two representative vector-borne diseases, namely; malaria
which represents all directly transmitted vector-borne diseases and schistosomiasis which represents
all environmentally transmitted vector-borne diseases were studied. Based on existing
mathematical modelling science base, we established a new multiscale modelling framework
that can be used to evaluate the effectiveness of vector-borne diseases treatment and preventive
interventions. The multiscale models consisted of systems of nonlinear ordinary differential
equations which were studied for the provision of solutions to the underlying problem of the
disease transmission dynamics. Relying on the fact that there is still serious lack of knowledge
pertaining to mathematical techniques for the representation and construction of multiscale
models of vector-bone diseases, we have developed some grand ideas to placate this gap. The
central idea in multiscale modelling is to divide a modelling problem such as a vector-bone disease
system into a family of sub-models that exist at different scales and then attempt to study
the problem at these scales while simultaneously linking the sub-models across these scales.
For malaria, we formulated the multiscale models by integrating four submodels which are: (i)
a sub-model for the mosquito-to-human transmission of malaria parasite, (ii) a sub-model for
the human-to-mosquito transmission of malaria parasite, (iii) a within-mosquito malaria parasite
population dynamics sub-model and (iv) a within-human malaria parasite population dynamics
sub-model. For schistosomiasis, we integrated the two subsystems (within-host and between-host
sub-models) by identifying the within-host and between-host variables and parameters associated
with the environmental dynamics of the pathogen and then designed a feedback of the variables
and parameters across the within-host and between-host sub-models. Using a combination of analytical
and computational tools we adequately accounted for the influence of the sub-models in
the different multiscale models. The multiscale models were then used to evaluate the effectiveness
of the control and prevention interventions that operate at different scales of a vector-bone
disease system. Although the results obtained in this study are specific to malaria and schistosomiasis,
the multiscale modelling frameworks developed are robust enough to be applicable to
other vector-borne diseases. / NRF
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:univen/oai:univendspace.univen.ac.za:11602/1252 |
| Date | 21 September 2018 |
| Creators | Mathebula, Dephney |
| Contributors | Garira, W., Moyo, S. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (xi, 208 leaves : color illustrations) |
| Rights | University of Venda |
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