Shirley Abelman | University of the Witwatersrand (original) (raw)

Papers by Shirley Abelman

$Research paper thumbnail of Research Article Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change$

Copyright © 2014 H. Abelman and S. Abelman.This is an open access article distributed under the C... more Copyright © 2014 H. Abelman and S. Abelman.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in anymedium, provided the originalwork is properly cited. Unacceptable principal powers in well-centred lenses may require a toric over-refraction which differs in nature from the one where correct powers have misplaced meridians.This paper calculates residual (over) refractions and their natures.Themagnitude of the power of the over-refraction serves as a general, reliable, real scalar criterion for acceptance or tolerance of lenses whose surface relative curvatures change or whose meridians are rotated and cause powers to differ. Principal powers and meridians of lenses are analogous to eigenvalues and eigenvectors of symmetric matrices, which facilitates the calculation of powers and their residuals. Geometric paths in symmetric power space link intended refractive correction and these...

Results in Physics, 2017

This article examines the effects of melting heat transfer and thermal radiation in stagnation po... more This article examines the effects of melting heat transfer and thermal radiation in stagnation point flow towards a stretching/shrinking surface. Mathematical formulation is made in the presence of mass transfer and second order slip condition. Numerical solutions to the resulting nonlinear problems are obtained by Runge-Kutta fourth fifth order method. Physical quantities like velocity, temperature, concentration, skin friction, Nusselt and Sherwood number are analyzed via sundry parameters for stretching/shrinking, first order slip, second order slip, radiation, melting, Prandtl and Schmidt. A comparative study with the previously published results in limiting sense is made.

International Journal of Heat and Mass Transfer, 2017

The objective of present attempt is to investigate electric field effect in Fe3O4–ethylene glycol... more The objective of present attempt is to investigate electric field effect in Fe3O4–ethylene glycol nanomaterial force convective heat transfer. Viscosity of nanomaterial depends upon electric field effect. Relevant mathematical formulation is completed. Control volume based finite element method (CVFEM) is employed for the numerical simulation. Emphasis is given to the outcomes of nanofluid volume fraction, supplied voltage and Reynolds number. Clearly flow pattern depends upon supplied voltage and such effect for low Reynolds number is more sensible. Thermal layer thickness close to bottom is thinner for larger Reynolds number. Heat transfer rate is increasing function of both supplied voltage and Reynolds number.

Journal of Inequalities and Applications, 2013

Let {X n , n ≥ 1} be a sequence of strictly stationary φ-mixing positive random variables which a... more Let {X n , n ≥ 1} be a sequence of strictly stationary φ-mixing positive random variables which are in the domain of attraction of the normal law with EX 1 = μ > 0, possibly infinite variance and mixing coefficient rates φ(n) satisfying n≥1 φ 1/2 (2 n) < ∞. Under suitable conditions, we here give an almost sure central limit theorem for self-normalized products of partial sums, i.e., lim n→∞ 1 D n n m=1 d m I m k=1 S k kμ μ/(βV m) ≤ x = F(x) a.s. for any x ∈ R, where F is the distribution function of the random variable e √ 2N and N is a standard normal random variable. MSC: 60F15

Acta Biotheoretica, 2022

Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public ... more Schistosomiasis, a vector-borne chronically debilitating infectious disease, is a serious public health concern for humans and animals in the affected tropical and sub-tropical regions. We formulate and theoretically analyze a deterministic mathematical model with snail and bovine hosts. The basic reproduction number [Formula: see text] is computed and used to investigate the local stability of the model's steady states. Global stability of the endemic equilibrium is carried out by constructing a suitable Lyapunov function. Sensitivity analysis shows that the basic reproduction number is most sensitive to the model parameters related to the contaminated environment, namely: shedding rate of cercariae by snails, cercariae to miracidia survival probability, snails-miracidia effective contact rate and natural death rate of miracidia and cercariae. Numerical results show that when no intervention measures are implemented, there is an increase of the infected classes, and a rapid decline of the number of susceptible and exposed bovines and snails. Effects of the variation of some of the key sensitive model parameters on the schistosomiasis dynamics as well as on the initial disease transmission threshold parameter [Formula: see text] are graphically depicted.

Acta Biotheoretica, 2019

 The stability analysis is carried out for infection-free and infection equilibrium.  Local sta... more  The stability analysis is carried out for infection-free and infection equilibrium.  Local stability is demonstrated by Routh-Hurwitz criterion.  Global stability is verified by Lyapunov's and the geometric approach method.

International Journal of Biomathematics, 2018

A model which incorporates some of the basic epidemiological features of the co-dynamics of malar... more A model which incorporates some of the basic epidemiological features of the co-dynamics of malaria and tuberculosis (TB) is formulated and the effectiveness of current intervention strategies of these two diseases is analyzed. The malaria-only and TB-only models are considered first. Global stability disease-free steady states of the two sub-models does not hold due to the co-existence of stable disease-free with stable endemic equilibria, a phenomenon known as backward bifurcation. The dynamics of the dual malaria–TB model with intervention strategies are also analyzed. Numerical simulations of the malaria–TB model are carried out to determine whether the two diseases can co-exist. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance to disease transmission.

Acta Biotheoretica, 2017

An analytical investigation into compressible gas flow with slight rarefactions through the insec... more An analytical investigation into compressible gas flow with slight rarefactions through the insect trachea and tracheoles during the closed spiracle phase is undertaken, and a complete set of asymptotic analytical solutions is presented. We first obtain estimates of the Reynolds and Mach numbers at the channel terminal ends where the tracheoles directly deliver respiratory gases to the cells, by comparing the magnitude of the different forces in the compressible gas flow. The 2D Navier-Stokes equations with a slip boundary condition are used to investigate compressibility and rarefied effects in the trachea and tracheoles. Expressions for the velocity components, pressure gradients and net flow inside the trachea are then presented. Numerical simulations of the tracheal compressible flow are performed to validate the analytical results from this study. This work extends previous work of Arkilic et al. (J Microelectromech Syst 6(2):167-178, 1997) on compressible flows through a microchannel. Novel devices for microfluidic compressible flow transport may be invented from results obtained in this study.

Applied Mathematics and Computation, 2016

Rift Valley fever (RVF) is a vector-borne viral disease with pronounced health and economic impac... more Rift Valley fever (RVF) is a vector-borne viral disease with pronounced health and economic impacts on domestic animals and humans in much of sub-Saharan Africa. Using techniques of uncertainty and sensitivity analysis (both local derivatives and samplingbased methods) of a mathematical model for RVF transmission in livestock by two population of mosquitoes (Aedes and Culex). We systematically investigate the relative importance of each model parameter for both disease epidemic and endemic activities. The relationship between vertical transmission and basic reproduction number reveals that during epidemic activities vertical transmission accelerates the course of the outbreak as it increases the size of infected vectors and reduces the duration of the outbreak. However, during endemic activities, vertical transmission exceeding 20% highly influences the basic reproduction number and disease persistence. Results of both local and global sensitivity analysis agrees that R 0 is most sensitive to vertical transmission, probability of transmission from Aedes mosquitoes to host, vector initial density and number of bites an Aedes mosquito would want to bite a host and number of bites that a host can sustain. This suggests that reducing vector population and enhancing control intervention in livestock is a viable preventive strategy. Both time varying and time invariant sensitivity analysis of disease prevalence governed by both asymptomatic and symptomatic state variables indicate that the most significant parameters are: number of bites that an Aedes mosquito would want to bite a host, number of bites a host can sustain, probability of transmission from host to an Aedes mosquito and the host death rate. Furthermore, time varying sensitivity analysis provides a comprehensive overview of the effects of each model input parameter at all important stages of the epidemic.

BMC Public Health, 2017

Background: Lymphatic filariasis is a globally neglected tropical parasitic disease which affects... more 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 , 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.

Mathematical and Computational Applications, 2010

Acta Biotheoretica, 2016

In this paper two models for movement of respiratory gases in the insect trachea are presented. O... more In this paper two models for movement of respiratory gases in the insect trachea are presented. One model considers the tracheal system as a single flexible compartment while the other model considers the trachea as a single flexible compartment with gas exchange. This work represents an extension of Ben-Tal's work on compartmental gas exchange in human lungs and is applied to the insect tracheal system. The purpose of the work is to study nonlinear phenomena seen in the insect respiratory system. It is assumed that the flow inside the trachea is laminar, and that the air inside the chamber behaves as an ideal gas. Further, with the isothermal assumption, the expressions for the tracheal partial pressures of oxygen and carbon dioxide, rate of volume change, and the rates of change of oxygen concentration and carbon dioxide concentration are derived. The effects of some flow parameters such as diffusion capacities, reaction rates and air concentrations on net flow are studied. Numerical simulations of the tracheal flow characteristics are performed. The models developed provide a mathematical framework to further investigate gas exchange in insects.

Ce document est protégé par la loi sur le droit d'auteur. L'utilisation des services d'Érudit (y ... more Ce document est protégé par la loi sur le droit d'auteur. L'utilisation des services d'Érudit (y compris la reproduction) est assujettie à sa politique d'utilisation que vous pouvez consulter en ligne.

The standard fourth-order non-linear PDE modelling the flow of thin fluid film subject to surface... more The standard fourth-order non-linear PDE modelling the flow of thin fluid film subject to surface tension is studied. The Lie group method is used to reduce the model equation from a fourth-order PDE to a fourth-order ODE. Analytical solutions are obtained for certain cases. Where analytical progress cannot be made, we determine numerical solutions.

In this study combined heat and mass transfer by mixed convective flow along a moving vertical fl... more In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, C f x x , local Nusselt number, Nu x x , and local Sherwood number Sh x x are shown and explained through tables.

PloS one, 2014

This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Q... more This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Qualitative analysis have been used to explore the stability dynamics of the equilibrium points while visualization techniques such as bifurcation diagrams, Poincaré maps, maxima return maps and largest Lyapunov exponents are numerically computed to confirm further complexity of these dynamics induced by the seasonal forcing on the mosquitoes oviposition rates. The obtained results show that ordinary differential equation models with external forcing can have rich dynamic behaviour, ranging from bifurcation to strange attractors which may explain the observed fluctuations found in RVF empiric outbreak data, as well as the non deterministic nature of RVF inter-epidemic activities. Furthermore, the coexistence of the endemic equilibrium is subjected to existence of certain number of infected Aedes mosquitoes, suggesting that Aedes have potential to initiate RVF epidemics through transovaria...

Abstract and Applied Analysis, 2014

This paper explores the dynamics of respiratory gases interactions which are accompanied by the l... more This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect’s spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analysis is carried out in continuous time. The purpose of the research is to determine bounds for the gas volumes and to discuss the complexity and stability of the equilibria. Numerical simulations also demonstrate the dynamics of our model utilizing the new conditions for stability and instability.