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    Mathematical analysis of a lymphatic filariasis model with quarantine and treatment
    (BioMed Central Ltd., 2017-03) 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.
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    Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions
    (Hindawi Publishing Corporation, 2017) 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.
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    Inequalities of harmonic univalent functions with connections of hypergeometric functions
    (DE GRUYTER OPEN LTD, BOGUMILA ZUGA 32A ST, 01-811 WARSAW, POLAND, 2015) 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.
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    New integral inequalities of hermite-hadamard type for n-times differentiable s-logarithmically convex functions with applications.
    (University of Miskolc, 2015-09) 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.
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    Analysis of binary multivariate longitudinal data via 2-dimensional orbits: An application to the Agincourt Health and Socio-Demographic Surveillance System in South Africa.
    (Public Library of Science, 2015-04) Visaya, M.V.; Sherwell, D.; Sartorius, B.; Cromieres, F.
    We analyse demographic longitudinal survey data of South African (SA) and Mozambican (MOZ) rural households from the Agincourt Health and Socio-Demographic Surveillance System in South Africa. In particular, we determine whether absolute poverty status (APS) is associated with selected household variables pertaining to socio-economic determination, namely household head age, household size, cumulative death, adults to minor ratio, and influx. For comparative purposes, households are classified according to household head nationality (SA or MOZ) and APS (rich or poor). The longitudinal data of each of the four subpopulations (SA rich, SA poor, MOZ rich, and MOZ poor) is a five-dimensional space defined by binary variables (questions), subjects, and time. We use the orbit method to represent binary multivariate longitudinal data (BMLD) of each household as a two-dimensional orbit and to visualise dynamics and behaviour of the population. At each time step, a point (x, y) from the orbit of a household corresponds to the observation of the household, where x is a binary sequence of responses and y is an ordering of variables. The ordering of variables is dynamically rearranged such that clusters and holes associated to least and frequently changing variables in the state space respectively, are exposed. Analysis of orbits reveals information of change at both individual- and population-level, change patterns in the data, capacity of states in the state space, and density of state transitions in the orbits. Analysis of household orbits of the four subpopulations show association between (i) households headed by older adults and rich households, (ii) large household size and poor households, and (iii) households with more minors than adults and poor households. Our results are compared to other methods of BMLD analysis.
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    Recalibration of the limiting antigen avidity EIA to determine mean duration of recent infection in divergent HIV-1 subtypes.
    (Public Library of Science, 2015-02-24) Duong, Y.T.; Kassanjee, R.; Welte, A.; Ampofo, W.; Parekh, B.S.; Morgan, M.; De, A.; Dobbs, T.; Rottinghaus, E.; Nkengasong, J.; Curlin, M.E.; Kittinunvorakoon, C.; Raengsakulrach, B.; Martin, M.; Choopanya, K.; Vanichseni, S.; Jiang, Y.; Qiu, M.; Yu, H.; Hao, Y.; Shah, N.; Le, L.-V.; Kim, A.A.; Nguyen, T.A.
    Background: Mean duration of recent infection (MDRI) and misclassification of long-term HIV-1 infections, as proportion false recent (PFR), are critical parameters for laboratory-based assays for estimating HIV-1 incidence. Recent review of the data by us and others indicated that MDRI of LAg-Avidity EIA estimated previously required recalibration. We present here results of recalibration efforts using >250 seroconversion panels and multiple statistical methods to ensure accuracy and consensus. Methods: A total of 2737 longitudinal specimens collected from 259 seroconverting individuals infected with diverse HIV-1 subtypes were tested with the LAg-Avidity EIA as previously described. Data were analyzed for determination of MDRI at ODn cutoffs of 1.0 to 2.0 using 7 statistical approaches and sub-analyzed by HIV-1 subtypes. In addition, 3740 specimens from individuals with infection >1 year, including 488 from patients with AIDS, were tested for PFR at varying cutoffs. Results: Using different statistical methods,MDRI values ranged from 88-94 days at cutoff ODn = 1.0 to 177-183 days at ODn = 2.0. The MDRI values were similar by different methods suggesting coherence of different approaches. Testing formisclassification among long-terminfections indicated that overall PFRs were 0.6%to 2.5%at increasing cutoffs of 1.0 to 2.0, respectively. Balancing the need for a longer MDRI and smaller PFR (<2.0%) suggests that a cutoff ODn = 1.5, corresponding to an MDRI of 130 days should be used for cross-sectional application. The MDRI varied among subtypes from 109 days (subtype A&D) to 152 days (subtype C). Conclusions: Based on the new data and revised analysis, we recommend an ODn cutoff = 1.5 to classify recent and long-term infections, corresponding to an MDRI of 130 days (118-142). Determination of revised parameters for estimation of HIV-1 incidence should facilitate application of the LAg-Avidity EIA for worldwide use.
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    Intelligent Optimization Algorithms: A Stochastic Closed-Loop Supply Chain Network Problem Involving Oligopolistic Competition for Multiproducts and Their Product Flow Routings.
    (Hindawi Publishing Corporation, 2015-10-26) Zhou, Y.; Chan, C.K.; Wong, K.H.; Lee, Y.C.E.
    Recently, the first oligopolistic competition model of the closed-loop supply chain network involving uncertain demand and return has been established. This model belongs to the context of oligopolistic firms that compete noncooperatively in a Cournot-Nash framework. In this paper, we modify the above model in two different directions. (i) For each returned product from demand market to firm in the reverse logistics, we calculate the percentage of its optimal product flows in each individual path connecting the demand market to the firm. This modification provides the optimal product flow routings for each product in the supply chain and increases the optimal profit of each firm at the Cournot-Nash equilibrium. (ii) Our model extends the method of finding the Cournot-Nash equilibrium involving smooth objective functions to problems involving nondifferentiable objective functions. This modification caters for more real-life applications as a lot of supply chain problems involve nonsmooth functions. Existence of the Cournot-Nash equilibrium is established without the assumption of differentiability of the given functions. Intelligent algorithms, such as the particle swarm optimization algorithm and the genetic algorithm, are applied to find the Cournot-Nash equilibrium for such nonsmooth problems. Numerical examples are solved to illustrate the efficiency of these algorithms.
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    Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis.
    (MDPI AG, 2016-04-26) Freidoonimehr, N.; Rashidi, M.M.; Abelman, S.; Lorenzini, G.
    The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number.
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    Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions.
    (Hindawi Publishing Corporation, 2015) Naz, R.; Mahomed, F.M.
    We study a dynamic fourth-order Euler-Bernoulli partial differential equation having a constant elastic modulus and area moment of inertia, a variable lineal mass density g(x), and the applied load denoted by f(u), a function of transverse displacement u(t,x). The complete Lie group classification is obtained for different forms of the variable lineal mass density g(x) and applied load f(u). The equivalence transformations are constructed to simplify the determining equations for the symmetries. The principal algebra is one-dimensional and it extends to two- and three-dimensional algebras for an arbitrary applied load, general power-law, exponential, and log type of applied loads for different forms of g(x). For the linear applied load case, we obtain an infinite-dimensional Lie algebra. We recover the Lie symmetry classification results discussed in the literature when g(x) is constant with variable applied load f(u). For the general power-law and exponential case the group invariant solutions are derived. The similarity transformations reduce the fourth-order partial differential equation to a fourth-order ordinary differential equation. For the power-law applied load case a compatible initial-boundary value problem for the clamped and free end beam cases is formulated. We deduce the fourth-order ordinary differential equation with appropriate initial and boundary conditions.
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    Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation.
    (Hindawi Publishing Corporation, 2015) Khan, M.; Abelman, S.; Mahomed, F.M.
    The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates.The exact steady-state solution for the nonlinear problem is obtained.Thereduction of the nonlinear initial value problem is carried out by using a similarity transformation.The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.
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    Study of nonlinear MHD tribological squeeze film at generalized magnetic reynolds numbers using DTM.
    (Public Library of Science, 2015-08-12) Rashidi, M.M.; Freidoonimehr, N.; Momoniat, E.; Rostami, B.
    In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.
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    Heat transfer analysis for stationary boundary layer slip flow of a power-law fluid in a Darcy porous medium with plate suction/injection.
    (Public Library of Science, 2015-09-25) Aziz, A.; Ali, Y.; Aziz, T.; Siddique, J.I.
    In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the powerlaw index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined.
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    Steady boundary layer slip flow along with heat and mass transfer over a flat porous plate embedded in a porous medium.
    (Public Library of Science, 2014-12) Aziz, A.; Siddique, J.I.; Aziz, T.
    In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/ injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile.
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    A partial Lagrangian approach to mathematical models of epidemiology.
    (Hindawi Publishing Corporation, 2015) Naz, R.; Naeem, I; Mahomed, F.M.
    This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system.We investigate the SIR and HIV models.We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.