http://hdl.handle.net/10386/65 2013-05-20T15:21:24Z 2013-05-20T15:21:24Z Mfumadi, Komane Boldwin http://hdl.handle.net/10386/613 2012-12-22T22:02:20Z 2008-01-01T00:00:00Z

Title: Variable viscosity arterial blood flow: its nature and stability Authors: Mfumadi, Komane Boldwin Abstract: Understanding the effects of blood viscosity variation plays a very crucial role in hemodynamics, thrombosis and inflammation and could provide useful information for diagnostics and therapy of (cardio) vascular diseases. Blood viscosity, which arises from frictional interactions between all major blood constituents, i.e. plasma, plasma proteins and red blood cells, constitutes blood inherent resistance to flow in the blood vessel. Generally, blood viscosity in large arteries is lower near the vessel wall due to the presence of plasma layer in this peripheral region than the viscosity in the central core region which depends on the hematocrit. In this dissertation, the flow of blood in a large artery is investigated theoretically using the fluid dynamics equations of continuity and momentum. Treating artery as a rigid channel with uniform width and blood as a variable viscosity incompressible Newtonian fluid, the basic flow structure and its stability to small disturbances are examined. A fourth-order eigenvalue problem which reduces to the well known Orr–Sommerfeld equation in some limiting cases is obtained and solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials implemented in MATLAB. Graphical results for the basic flow axial velocity, disturbance growth rate and marginal stability curve are presented and discussed. It is worth pointing out that, a decrease in plasma viscosity near the arterial wall has a stabilizing effect on the flow. Description: Thesis (M.Sc. (Applied Mathematics)) -- University of Limpopo, 2008

2008-01-01T00:00:00Z Kgasago, Tshepo Matenatena Blessings http://hdl.handle.net/10386/347 2012-05-11T13:33:39Z 2008-01-01T00:00:00Z

Title: Modelling the transmission dynamics of infectious diseases with vaccination and temporary immunity Authors: Kgasago, Tshepo Matenatena Blessings Abstract: In this dissertation, two non-linear mathematical models are proposed and analyzed to investigate the spread of infectious diseases in a variable size population through horizontal transmission in the presence of preventive or therapeutic vaccines which are capable of inducing temporary immunity and wane in time. In modeling the transmission dynamics, the population is divided into three subclasses namely; Susceptibles, Infectives and Vaccinated groups. It is assumed that both Vaccinated and Susceptible individuals are recruited into the community and can only become infected via contacts with the infectives group but the rate at which the vaccinated group may contract the diseases is extremely very low depending on the efficacy of the vaccine. All infectives are assumed to move at a constant rate to both Vaccinated and Susceptible groups. These models are analyzed by using the stability theory of differential equations and numerical simulation. The models exhibit two equilibria namely; the disease-free and the endemic equilibria. It is shown that if the vaccination reproduction number R0 < 1, the disease-free equilibrium is always globally asymptotically stable and in such a case the endemic equilibrium does not exist and the disease can be totally eliminated in the community. However, if R0 > 1, a unique endemic equilibrium exists that is locally asymptotically stable and consequently the equilibrium values of infective, vaccinated and susceptible population can be maintained at desired levels. Numerical simulations implemented on MAPLE using both Adomian decomposition technique and Runge-Kutta integration schemes, support our analytical conclusions and illustrate possible behaviour scenarios of the models. Description: Thesis (M.Sc.) (Applied Mathematics) --University of Limpopo, 2008.

2008-01-01T00:00:00Z