Research Repository :: Browsing by Author "Makinde, Oluwole D."

Browsing by Author "Makinde, Oluwole D."

Now showing 1 - 12 of 12

Computational Dynamics of Hydromagnetic Stagnation Flow towards a Stretching Sheet
(2010) Makinde, Oluwole D.; Charles, Wilson M.
This paper investigates the hydromagnetic stagnation flow of an incompressible viscous, electrically conducting fluid, towards a stretching sheet in the presence of axially increasing free stream velocity. The newton-Raphson shooting method, along with fourth-order Runge-Kutta integration algorithm, are employed to tackle the third order, nonlinear boundary layer equation governing the problem. The variational iteration method (VIM), coupled with Padé technique is also applied for a reliable treatment of the problem. The study shows that the series solution is obtained without restrictions on the nonlinearity behavio. The solutions are compared with the other available results in the literature, and a good agreement is found.
Computational Modelling of Cholera Bacteriophage with Treatment
(Scientific Research, 2015) Mgonja, Daniel S.; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the computational modelling of cholera bacteriophage with treatment. A nonlinear mathematical model for cholera bacteriophage and treatment is formulated and analysed. The effective reproduction number of the nonlinear model system is calculated by next generation operator method. By using the next generation matrix approach, the disease-free equilibrium is found to be locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium point is not stable due to existence of forward bifurcation at threshold parameter equal to unity. Stability analysis and numerical simulations suggest that the combination of bacteriophage and treatment may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of bacteriophage virus and treatment, cholera is self-limiting in nature.
Mathematical Analysis of Control Strategies of HCV in a Community with Inflow of Infected Immigrants
(Scientific Research, 2015-01) Ainea, Neterindwa; Massawe, Estomih S.; Makinde, Oluwole D.; Namkinga, Lucy
In this paper, we derive and analyse rigorously a mathematical model of control strategies (screening, education, health care and immunization) of HCV in a community with inflow of infected immigrants. Both qualitative and quantitative analysis of the model is performed with respect to stability of the disease free and endemic equilibria. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Using Lyapunov method, endemic equilibrium is globally stable under certain conditions. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the HCV model in a community with inflow of infected immigrants. However, analysis shows that screening, education, health care and immunization have the effect of reducing the transmission of the disease in the community.
Modeling Laminar Flow between a Fixed Impermeable Disk and a Porous Rotating Disk
(Academic Journals, 2009) Kavenuke, D. P.; Massawe, Estomih S.; Makinde, Oluwole D.
We formulate a mathematical model that governs operations of many engineering systems particularly the ceiling fan to explain the fluid flow between the fixed impermeable and the porous rotating disks. The model is based on the continuity and the Navier-Stokes equations which are reduced into a set of coupled ordinary differential equations through transformation by similarity variables. The coupled ordinary differential equations are solved using perturbation techniques and the series solution obtained is improved by Paté’s approximation. Our results meet the supposition that, with laminar flow regime, suction increases with increasing speed of rotation of the rotating porous disk and these are shown on the graphical representations.
Modelling the Effect of Screening on the Spread of HIV Infection in a Population with Variable Inflow of Infective Immigrants
(Scientific Research, 2011) Shabani, Issa; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the combined effects of screening and variable inflow of infective immigrants on the spread of HIV/AIDS (human immunodeficiency virus/acquired immune deficiency syndrome) in a population of varying size. A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. The results show that the reproductive number R0 >1 as the rate of inflow of infective immigrants increases leading to persistence of the disease in the population. However, the presence of screening greatly reduces the spread of HIV/AIDS. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the spread of the disease.
Modelling the Effect of Treatment and Infected Immigrants on the Spread of Hepatitis C Virus Disease with Acute and Chronic Stages
(2012) Ainea, Neterindwa; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the effect of Treatment and Infected Immigrants on the spread of Hepatitis C Virus (HCV) disease with Acute and Chronic stages. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However the disease becomes more endemic due to the presence of infected immigrants in the community. It is also shown that in the presence of treatment, the rate of infected immigrants (acute and chronic) decreases and consequently the treated in-fected individuals decreases continuously. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the treatment and infected immigrants on the spread of the disease with acute and chronic stages.
Modelling the Optimal Control of Transmission Dynamics of Mycobacterium ulceran Infection
(Scientific Research, 2015) Kimaro, Magreth A.; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.
Modelling the Pyrolysis and Combustion of Wood
(2012) Massawe, Estomih S.; Salim, Said S.; Makinde, Oluwole D.
This paper examines the chemical kinetics of cellulosic material with fixed and varying temperatures. The combustion kinetics of wood together with Arrhenius equation is used in derivation of the model. The governing nonlinear ordinary differential equations with initial conditions are solved numerically. The results obtained are presented graphically for the purpose of showing the pyrolysis and combustion of wood and impact of wood burning for both fixed and varying temperatures. It is observed that charcoal and gases yields are the end products formed during the processes. However it is observed that gases are highly produced at varying temperatures. However for both fixed and varying temperatures, the decomposition reaction of wood (cellulose) in the system leads to the separation of the components of wood giving charcoal and gases as end products, but the gases are highly produced at moderate temperatures.
On the Boundary Layer Flow over a Moving Surface in a Fluid with Temperature-Dependent Viscosity
(2012-12) Mureithi, Eunice; Mwaonanji, J. J.; Makinde, Oluwole D.
This paper examines a boundary layer flow over a continuously moving heated flat surface with velocity in a streaming flow with velocity and with temperature dependent viscosity,. The momentum and the energy equations are coupled through the viscous dissipation term. The coupled boundary layer equations are transformed into a self-similar form using an appropriate similarity variable. An efficient numerical technique is used to solve the self-similar boundary layer equations. It is shown that at low enough values for the velocity ratio, an increase in viscous dissipation enhances greatly the local heat transfer leading to temperature overshoots adjacent to the wall. The viscosity variation parameter is shown to have significant effects on the temperature dependent viscosity and the velocity and temperature distribution within the boundary layer.
Temporal Model for Dengue Disease with Treatment
(Scientific Research, 2015) Massawe, Laurencia N.; Massawe, Estomih S.; Makinde, Oluwole D.
This paper examines the effect of treatment of Dengue fever disease. A non linear mathematical model for the problem is proposed and analysed quantitatively using the stability theory of the differential equations. The results show that the disease-free equilibrium point is locally andglobally asymptotically stable if the reproduction number (R ) 0 is less than unity. The additive compound matrices approach is used to show that the dengue fever model’s endemic equilibrium point is locally asymptotically stable when trace, determinant and determinant of second additive compound matrix of the Jacobian matrix are all negative. However, treatment will have a control of dengue fever disease. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the dengue fever disease with treatment.
Transmission Dynamics of Infectious Diseases by Immigrants in a Vaccinated and Temporary Immune Protected Population
(Academic Journals, 2011) Mlyashimbi, Helikumi; Massawe, Estomih S.; Makinde, Oluwole D.
In this paper, a mathematical model of infectious diseases by immigrants in a vaccinated and temporary immune protected population has been investigated. The model incorporates the assumption that immigrant individuals enter in the respective population with an immunity received from either vaccination or recover from the disease. The stability of the system has been analyzed for the existence of the disease-free and endemic equilibrium points, and it has been shown that the disease free equilibrium point is asymptotically stable when an effective reproduction number is less than unity and unstable when an effective reproduction number is greater than unity. From the analysis of the model, it is shown that vaccination coverage is greater than the vaccination; otherwise the disease will persist within the community. It is also shown that the increase of immigrants in a population tends to lower the first dose-vaccination coverage, hence the disease become endemic in the population. Numerical simulations of the model showed that in the absence of the immigrants, the disease can be eradicated in a population with a single-dose vaccination only.
Unsteady Convection with Chemical Reaction and Radiative Heat Transfer past a Flat Porous Plate Moving Through a Binary Mixture
(Springer, 2011) Makinde, Oluwole D.; Olanrewaju, Philip O.; Charles, Wilson M.
In this paper, the problem of unsteady convection with chemical reaction and radiative heat transfer past a flat porous plate moving through a binary mixture in an optically thin environment is presented. The dimensionless governing equations for this investigation are solved numerically by the fourth-order Runge–Kutta integration scheme along with shooting technique. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions. Graphical results for velocity, temperature and concentration profiles based on the numerical solutions are presented and discussed.

Browsing by Author "Makinde, Oluwole D."

Results Per Page

Sort Options