Pure Mathematicshttp://hdl.handle.net/10413/67702018-02-17T09:51:22Z2018-02-17T09:51:22ZApproximation methods for solutions of some nonlinear problems in Banach spaces.http://hdl.handle.net/10413/148432017-11-29T07:17:36Z2017-01-01T00:00:00ZApproximation methods for solutions of some nonlinear problems in Banach spaces.
Abstract available in PDF file.
Doctor of Philosophy in Mathematics. University of KwaZulu-Natal, Durban 2016.
2017-01-01T00:00:00ZMathematical modeling of R5 and X4 HIV : from within host dynamics to the epidemiology of HIV infection.http://hdl.handle.net/10413/130652016-06-15T01:01:14ZMathematical modeling of R5 and X4 HIV : from within host dynamics to the epidemiology of HIV infection.
Most existing models have considered the immunological processes occurring within the host
and the epidemiological processes occurring at population level as decoupled systems. We
present a new model using continuous systems of non linear ordinary differential equations by
directly linking the within host dynamics capturing the interactions between Langerhans cells,
CD4+ T-Cells, R5 HIV and X4 HIV and the without host dynamics of a basic compartmental
HIV/AIDS, susceptible, infected, AIDS model. The model captures the biological theories
of the cells that take part in HIV transmission. The study incorporates in its analysis the
differences in time scales of the fast within host dynamics and the slow without host dynamics.
In the mathematical analysis, important thresholds, the reproduction numbers, were computed
which are useful in predicting the progression of the infection both within the host and without
the host. The study results showed that the model exhibits four within host equilibrium
points inclusive of three endemic equilibria whose effects translate into different scenarios at
the population level. All the endemic equilibria were shown to be globally stable using Lyapunov
functions and this is an important result in linking the within host dynamics to the population
dynamics, because the disease free equilibrium point ceases to exist. The linked models had
no effect on the basic reproduction numbers of the within host dynamics but on the basic
reproduction number of the population dynamics. The effects of linking were observed on
the endemic equilibrium points of both the within host and population dynamics. Therefore,
linking the two dynamics leads to the increase in the viral load within the host and increase in
the epidemic levels in the population dynamics.
M. Sc. University of KwaZulu-Natal, Pietermaritzburg 2015.
On Huppert Conjecture for some quasi-simple groups.http://hdl.handle.net/10413/121222016-05-06T09:50:10Z2015-06-17T00:00:00ZOn Huppert Conjecture for some quasi-simple groups.
Abstract available in PDF file.
M. Sc. University of KwaZulu-Natal, Pietermaritzburg 2014.
2015-06-17T00:00:00ZSpherically symmetric charged Einstein-Maxwell solutions.http://hdl.handle.net/10413/116022016-05-06T08:22:59Z1999-01-01T00:00:00ZSpherically symmetric charged Einstein-Maxwell solutions.
In this thesis we study spherically symmetric spacetimes with a perfect fluid source
which incorporates charge. We seek explicit solutions to the Einstein- Maxwell system
of equations. For nonaccelerating spherically symmetric models a charged, dust
solution is found. With constant pressure the equations reduce to quadratures. Particular
solutions are also found, with no acceleration, with the equation of state
P =( y - 1)u. The Lie analysis is utilised to reduce the Einstein- Maxwell equations
to a syst.em of ordinary differential equations. The evolution of the model depends
on a Riccati equation for this general class of accelerating, expanding and shearing
spacetimes with charge. Also arbitrary choices for the gravitational potentials lead
to explicit solutions in particular cases. With constant gravitational potential A we
generate a simple nonvacuum model. The analysis, in this case, enables us to reduce
the solution to quadratures. With the value y = 2, for a stiff equation of state, we
find that the solution is expressable in terms of elementary functions. Throughout
the thesis we have attempted to relate our results to previously published work, and
to obtain the uncharged perfect fluid limit where appropriate.
Thesis (Ph.D.)-University of Natal, 1999
1999-01-01T00:00:00Z