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A mathematical model for studying the impact of climate variability on malaria epidemics in South Africa
(University of the Western Cape, 2017)
Malaria is most prevalent in tropical climates, where there are sufficient rainfall
for mosquitoes to breed and conducive temperatures for both the mosquito and
protozoa to live. A slight change in temperature can ...
Mathematical modeling and analysis of HIV/AIDS control measures
(University of the Western Cape, 2012)
In this thesis, we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyse a math-
ematical model that describes the dynamics of HIV infection among the ...
Efficient numerical methods to solve some reaction-diffusion problems arising in biology
(2013)
In this thesis, we solve some time-dependent partial differential equations, and systems of such equations, that governs reaction-diffusion models in biology. we design and implement some novel exponential time differencing ...
Robust computational methods to simulate slow-fast dynamical systems governed by predator-prey models
(University of the Western Cape, 2019)
Numerical approximations of multiscale problems of important applications in ecology
are investigated. One of the class of models considered in this work are singularly perturbed
(slow-fast) predator-prey systems which ...
A mathematical modeling of optimal vaccination strategies in epidemiology
(2010)
We review a number of compartmental models in epidemiology which leads to a
nonlinear system of ordinary differential equations. We focus an SIR, SEIR and
SIS epidemic models with and without vaccination. A threshold ...
On the numerical integration of singularly perturbed Volterra integro-differential equations
(University of the Western Cape, 2017)
Efficient numerical approaches for parameter dependent problems have been an inter-
esting subject to numerical analysts and engineers over the past decades. This is due
to the prominent role that these problems play in ...
High Accuracy Fitted Operator Methods for Solving Interior Layer Problems
(University of the Western Cape, 2020)
Fitted operator finite difference methods (FOFDMs) for singularly perturbed
problems have been explored for the last three decades. The construction of
these numerical schemes is based on introducing a fitting factor ...