Showing papers by "Oluwole Daniel Makinde published in 2014"

A co-infection model of malaria and cholera diseases with optimal control.

Abstract: In this paper we formulate a mathematical model for malaria–cholera co-infection in order to investigate their synergistic relationship in the presence of treatments. We first analyze the single infection steady states, calculate the basic reproduction number and then investigate the existence and stability of equilibria. We then analyze the co-infection model, which is found to exhibit backward bifurcation. The impact of malaria and its treatment on the dynamics of cholera is further investigated. Secondly, we incorporate time dependent controls, using Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the disease. We found that malaria infection may be associated with an increased risk of cholera but however, cholera infection is not associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time also include cholera control.

MHD Boundary Layer Slip Flow and Heat Transfer of Nanofluid Past a Vertical Stretching Sheet with Non-Uniform Heat Generation/Absorption

Abstract: An investigation of the magnetohydrodynamics (MHD) boundary layer slip flow over a vertical stretching sheet in nanofluid with non-uniform heat generation/absorbtion in the presence of a uniform transverse magnetic field has been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the surface of the sheet. The results show that there are significant effects of various pertinent parameters on velocity and temperature profiles.

Entropy generation in couple stress fluid flow through porous channel with fluid slippage

Abstract: In this paper, entropy generation in couple stress fluid flowing steadily through a porous channel with slip at the isothermal walls is considered. The Navier slip model is employed at both walls. Analytical solutions for the governing nonlinear boundary-value problems are constructed using Adomian decomposition method (ADM). Important flow properties are presented and discussed including the entropy generation and irreversibility ratio.

Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.

Abstract: A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

Optimal control analysis of hepatitis C virus with acute and chronic stages in the presence of treatment and infected immigrants

Abstract: In this paper, we consider a deterministic hepatitis C virus (HCV) model and study the impact of optimal control on the screening of immigrants and treatment of HCV on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles. First, we derived the condition in which disease-free equilibrium is locally asymptotically stable and established that a stable disease-free equilibrium can only be achieved in the absence of infective immigrants. Second, we investigated the impact of each control mechanism individually and the combinations of these strategies in the control of HCV. The costs associated with each of these strategies are also investigated by formulating the costs function problem as an optimal control problem, and we then use the Pontryagin's Maximum Principle to solve the optimal control problems. From the numerical simulations we found that the optimal combination of treatment of acute-infected and chronic-infected individuals control strategy produced the same results as the combination of the three strategies (combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals). By our model and these results, we suggest the treatment of acute-infected and chronic-infected individuals control strategy should be optimized where resources are scarce, because the implementation of the three strategies (combination of screening of immigrants, treatment of acute-infected and chronic-infected individuals) would imply additional cost.

Thermal analysis of a reactive generalized Couette flow of power law fluids between concentric cylindrical pipes

Abstract: In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton’s law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.

Computational Dynamics of Arterial Blood Flow in the Presence of Magnetic Field and Thermal Radiation Therapy

Abstract: We conduct a numerical study to determine the influence of magnetic field and thermal radiation on both velocity and temperature distributions in a single blood vessel. The model here assumes that blood is a Newtonian incompressible conducting fluid with radially varying viscosity due to hematocrit variation. The transient equations of momentum and energy transport governing the flow in an axisymmetric configuration are solved numerically using a semi-implicit finite difference method. Results are presented graphically and discussed both qualitatively and quantitatively from the physiological point of view. The results of this work may enhance current understanding of the factors that determine the effects of hyperthermia treatment on tumor tissues.

Axisymmetric slip flow on a vertical cylinder with heat transfer

Abstract: The paper is aimed at studying fluid flow heat transfer in the axisymmetric boundary layer flow of a viscous incompressible fluid, along the axial direction of a vertical stationary isothermal cylinder in presence of uniform free stream with momentum slip. The equations governing the flow i.e. continuity, momentum and energy equation are transformed into non-similar boundary layer equations and are solved numerically employing asymptotic series method with Shanks transformation. The numerical scheme involves the Runge-Kutta fourth order scheme along with the shooting technique. The flow is analyzed for both assisting and opposing buoyancy and the effect of different parameters on fluid velocity, temperature distribution, heat transfer and shear stress parameters is presented graphically.

Second law analysis for MHD permeable channel flow with variable electrical conductivity and asymmetric Navier slips

Abstract: CITATION: Eegunjobi, A. S. & Makinde, O. D. 2014. Second law analysis for MHD permeable channel flow with variable electrical conductivity and asymmetric Navier slips. Open Physics, 13(1):100-110, doi:10.1515/phys-2015-0014.

Axisymmetric Slip Flow on a Vertical Cylinder with Heat Transfer (Aliran Gelincir Simetri Sepaksi pada Silider Menegak dengan Pemindahan Haba)

Abstract: The paper is aimed at studying fluid flow heat transfer in the axisymmetric boundary layer flow of a viscous incompressible fluid, along the axial direction of a vertical stationary isothermal cylinder in presence of uniform free stream with momentum slip. The equations governing the flow i.e. continuity, momentum and energy equation are transformed into non-similar boundary layer equations and are solved numerically employing asymptotic series method with Shanks transformation. The numerical scheme involves the Runge-Kutta fourth order scheme along with the shooting technique. The flow is analyzed for both assisting and opposing buoyancy and the effect of different parameters on fluid velocity, temperature distribution, heat transfer and shear stress parameters is presented graphically.

On MHD unsteady reactive Couette flow with heat transfer and variable properties

Abstract: This study is devoted to investigate the effect of magnetic field on a reactive unsteady generalized Couette flow with temperature dependent viscosity and thermal conductivity. It is assumed that conducting incompressible fluid is subjected to an exothermic reaction under Arrhenius kinetics, neglecting the consumption of the material. The model nonlinear differential equations governing the transient momentum and energy balance are obtained and tackled numerically using a semi-discretization finite difference technique coupled with Runge-Kutta Fehlberg integration scheme. Important properties of the velocity and temperature fields including thermal stability conditions are presented graphically and discussed quantitatively.

Thermodynamic Analysis of Variable Viscosity MHD Unsteady Generalized Couette Flow with Permeable Walls

Abstract: The thermodynamic first and second law analyses of a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls is investigated. The transient model problem for momentum and energy balance is tackled numerically using a semi-discretization method while the steady state boundary value problem is solved by shooting method together with Runge-Kutta-Fehlberg integration scheme. The velocity and the temperature profiles are obtained and are utilized to compute the skin friction coefficient, Nusselt number, entropy generation rate and the Bejan number. Pertinent results are presented graphically and discussed quantitatively.

Unsteady Hydromagnetic Flow of Radiating Fluid Past a Convectively Heated Vertical Plate with the Navier Slip

Abstract: This paper investigates the unsteady hydromagnetic-free convection of an incompressible electrical conducting Boussinesq’s radiating fluid past a moving vertical plate in an optically thin environment with the Navier slip, viscous dissipation, and Ohmic and Newtonian heating. The nonlinear partial differential equations governing the transient problem are obtained and tackled numerically using a semidiscretization finite difference method coupled with Runge-Kutta Fehlberg integration technique. Numerical data for the local skin friction coefficient and the Nusselt number have been tabulated for various values of parametric conditions. Graphical results for the fluid velocity, temperature, skin friction, and the Nusselt number are presented and discussed. The results indicate that the skin friction coefficient decreases while the heat transfer rate at the plate surface increases as the slip parameter and Newtonian heating increase.

Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling

Abstract: Heat transfer characteristics of a Berman flow of water based nanofluids containing copper (Cu) and alumina (Al2O3) as nanoparticles in a porous channel with Navier slip, viscous dissipation, and convective cooling are investigated. It is assumed that the exchange of heat with the ambient surrounding takes place at the channel walls following Newton’s law of cooling. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop, and Nusselt numbers are presented graphically and discussed quantitatively.

Application of Successive Linearisation Method to Squeezing Flow with Bifurcation

Abstract: This paper employs the computational approach known as successive linearization method (SLM) to tackle a fourth order nonlinear differential equation modelling the transient flow of an incompressible viscous fluid between two parallel plates produced by a simple wall motion. Numerical and graphical results obtained show excellent agreement with the earlier results reported in the literature. We obtain solution branches as well as a turning point in the flow field accurately. A comparison with numerical results generated using the inbuilt MATLAB boundary value solver, bvp4c, demonstrates that the SLM approach is a very efficient technique for tackling highly nonlinear differential equations of the type discussed in this paper.

Computational Modelling of Couette Flow of Nanofluids with Viscous Heating and Convective Cooling

Abstract: The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base nanofluids containing Copper Oxide (CuO) and Alumina (Al2O3) as nanoparticles is investigated. It is assumed that the nanofluid flows in a channel between two parallel plates with the channel’s upper plate accelerating and exchange heat with the ambient surrounding following the Newton’s law of cooling, while the lower plate is stationary and maintained at a constant temperature. Using appropriate similarity transformation, the governing Navier-Stokes and the energy equations are reduced to a set of nonlinear ordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement technique and numerically by an efficient Runge-Kutta-Fehlberg integration technique coupled with shooting method. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop and Nusselt number are presented graphically, and discussed quantitatively.

Computational Modelling and Optimal Control of HIV/AIDS Transmission in a Community with Substance Abuse Problem

Abstract: Abuse of substances continues to be ubiquitous in communities leading to high-risk sexual behaviour mainly due to impaired decision-making capacity. The abuse may also have numerous effects on neurocognitive function resulting in HIV infection and ultimately AIDS. In this paper, a compartmental deterministic model for the transmission dynamics of HIV/AIDS in a community plagued with substance abuse is proposed. The nonlinear problem is tackled using stability theory of differential equations and a basic reproduction number for the elimination of HIV infection is determined. The implementation of optimal control strategies involving treatment of substance-abusing susceptibles, counselling and prevention to combat the spread of HIV infection is determined using Pontryagin’s maximum principle. Numerical simulations are performed and the pertinent results are presented graphically and discussed quantitatively.

Computational Dynamics of Solid Waste Generation and Treatment in the Presence of Population Growth

Abstract: Solid waste management is a global challenge and the situation is worse in urban areas of the developing countries where, in most cases, there are no data of how much solid waste is generated over a specific period of time. Worse still, solid waste continues to pile up as population continues to grow and authorities in developing countries are increasingly becoming unable to manage the waste. This calls for a means for anticipating the solid waste to be generated in order for the authorities to take proactive actions in managing the solid waste. In this paper, a deterministic compartmental mathematical model that can be used to predict the amount of solid waste generation and treatment needed with population growth as major factor is proposed and analysed qualitatively using the stability theory of differential equations. Numerical simulation is performed to validate the qualitative results.

Estimating sustainable harvests of lake victoria fishery

Abstract: A study was conducted to develop an environmentally sound strategy for sustainable harvesting of fish species of the Lake Victoria fishery. Its objectives were: firstly, to estimate current harvesting rates of fish species; secondly to show how the biomass stock is changing in response to growth rates and harvesting rates; and finally, using a mathematical model, to predict sustainable levels of harvesting the fish species. Lake wide catch data from year 2005 to 2011 were used for various fish species and were analyzed using Least square method with the aid of MAPLE. Harvesting efforts were computed; 0.2805 for the Nile perch representing a maximum sustainable harvest of 74412.8447 tonnes per year; 0.0593 for the Nile tilapia representing a maximum sustainable harvest of 4834.4503 tonnes per year; 0.5334 for the small pelagic silver fish representing 259538.9165 tonnes per year; 0.1158 for the Haplochromines representing a maximum sustainable harvest of 12569.7240 tonnes per year and 0.0108 for the other fish species representing a maximum sustainable harvest of 87.1936 tonnes per year. Further the study revealed that the lake Victoria Received: July 14, 2014 c © 2014 Academic Publications Correspondence author 408 J.P. Mpele, Y. Nkansah-Gyekye, O.D. Makinde fishery is yet sustainable however its sustanability is under 50% for most of fish species. AMS Subject Classification: 65P99, 92B05, 37N25

Analysis of Turbulent Hydromagnetic Flow with Radiative Heat over a Moving Vertical Plate in a Rotating System

Abstract: In this paper, the combined effects of magnetic fields, buoyancy force, thermal radiation, viscous and Ohmic heating on turbulent hydromagnetic flow of an incompressible electrically conducting fluid over a moving vertical plate in a rotating system is investigated numerically. The governing equations are reduced to non-linear ordinary differential equations using the time-averaged approach known as Reynolds-averaged Navier–Stokes equations (or RANS equations) and tackled by employing an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. Graphical results showing the effects of various thermophysical parameters on the velocity, temperature, local skin friction and local Nusselt number are presented and discussed quantitatively.

A dynamic model for a three species open-access fishery with taxation as a control instrument of harvesting efforts the case of Lake Victoria

Abstract: The Lake Victoria fishery is dominated by three commercial fish species namely Nile perch, Nile tilapia and small pelagic silver fish.The current excessive use of fishing efforts in the lake have devastating consequences to the extent of diminishing these fish species. The purpose of this study is to propose a bioeconomic mathematical model based on Lotka-Volterra dynamics by introducing taxes to the profit per unit biomass of the harvested fish of each species with the intention of controlling fishing efforts.The results of the formulated model showed that the co-existence steady state with taxation was both locally and globally assymptotically stable.The optimal harvesting policy was established using Pontryagin’s maximum principle. The numerical example illustrated that imposition of optimal taxations resulted into optimal harvesting efforts and hence optimal harvesting levels which favour the sustainability of fish species.

Nonlinear Fluid Flow and Heat Transfer

Abstract: Please cite as follows: Makinde, O. D., Moitsheki, R. J., Jana, R. N., Bradshaw-Hajek, B. H. & Khan, W. A. 2014. Nonlinear fluid flow and heat transfer. Advances in Mathematical Physics, 2014:1-2 (Article ID 719102), doi:10.1155/2014/719102.