Research Articles https://hdl.handle.net/10539/20395 2021-10-27T02:28:22Z Mathematical analysis of a lymphatic filariasis model with quarantine and treatment https://hdl.handle.net/10539/23390 Mathematical analysis of a lymphatic filariasis model with quarantine and treatment Mwamtobe, P.M.; Simelane, S.M.; Abelman, S.; Tchuenche, J.M. Background: Lymphatic filariasis is a globally neglected tropical parasitic disease which affects individuals of all ages and leads to an altered lymphatic system and abnormal enlargement of body parts. Methods: A mathematical model of lymphatic filariaris with intervention strategies is developed and analyzed. Control of infections is analyzed within the model through medical treatment of infected-acute individuals and quarantine of infected-chronic individuals. Results: We derive the effective reproduction number, R 0 , $\mathcal {R}_{0},$ and its interpretation/investigation suggests that treatment contributes to a reduction in lymphatic filariasis cases faster than quarantine. However, this reduction is greater when the two intervention approaches are applied concurrently. Conclusions: Numerical simulations are carried out to monitor the dynamics of the filariasis model sub-populations for various parameter values of the associated reproduction threshold. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance on the disease transmission. 2017-03-01T00:00:00Z Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions https://hdl.handle.net/10539/23389 Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions Jooma, R.; Harley, C. A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions. 2017-01-01T00:00:00Z Inequalities of harmonic univalent functions with connections of hypergeometric functions https://hdl.handle.net/10539/21105 Inequalities of harmonic univalent functions with connections of hypergeometric functions Sokol, Janusz; Ibrahim, Rabha W.; Ahmad, M. Z; Al-Janaby, Hiba F. Let SH be the class of functions f = h + (g) over bar that are harmonic univalent and sense-preserving in the open unit disk U = {z : vertical bar z vertical bar < 1} for which f(0) = f'(0) - 1 = 0. In this paper, we introduce and study a subclass H(alpha, beta)of the class SH and the subclass NH(alpha, beta) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H(alpha, beta) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions. 2015-01-01T00:00:00Z New integral inequalities of hermite-hadamard type for n-times differentiable s-logarithmically convex functions with applications. https://hdl.handle.net/10539/20862 New integral inequalities of hermite-hadamard type for n-times differentiable s-logarithmically convex functions with applications. Latif, M.A.; Dragomir, S.S. In this paper, some new integral inequalities of Hermite-Hadamard type are presented for functions whose nth derivatives in absolute value are s-logarithmically convex. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are s-logarithmically convex functions as special cases. Our results may provide refinements of some results for s-logarithmically convex functions already exist in literature. Finally, applications to special means of the established results are given. 2015-09-01T00:00:00Z