Modelling the spread of HIV/AIDS epidemic in the presence of irresponsible infectives

In this study, a non-linear mathematical model was proposed and analyzed to study the effect of irresponsible infectives in the spread of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) in a variable size population. The population was divided into four subclasses, of susceptibles (HIV negatives who can contract the disease), irresponsible infectives (people who are infected with the virus but do not know or live irresponsible life styles) , responsible infectives (HIV positives who know they are infected and are careful) and full-blown AIDS patients. Susceptibles were assumed to be infected through sexual contact with infectives and all infectives develop AIDS at a constant rate. Stability analysis and numerical simulations of the resulting model are presented. The model analysis shows that the disease-free equilibrium is always locally asymptotically stable and in such a case the basic reproductive number R0<1 and the endemic equilibrium does not exist. The disease is thus eliminated from the system. If R0>1, the endemic equilibrium exists and the disease remains in the system. It is shown that the endemicity of the disease is reduced when irresponsible infectives become responsible.Keywords: Vertical transmission, stability, simulation, irresponsible infective

On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

In this paper, the temporal development of small disturbances in a pressure-driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth-order eigenvalue problem, which reduces to the well-known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials

On thermal stability of a reactive third-grade fluid in a channel with convective cooling the walls

On this paper, the thermal stability of a reactive third-grade liquid flowing steadily between two parallel plates with symmetrical convective cooling at the walls is investigated. The system is assumed to exchange heat with the ambient following Newton’s cooling law and the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. Approximate solutions are constructed for the governing nonlinear boundary value problem using regular perturbation techniques together with a special type of Hermite-Padé approximants and important properties of the velocity and temperature fields including bifurcations and thermal criticality conditions are discussed. It is observed that a combined increase in non-Newtonian parameter and convective cooling enhances the thermal stability of the material

On MHD boundary‐layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux

Purpose – The hydromagnetic mixed convection flow of an incompressible viscous electrically conducting fluid and mass transfer over a vertical porous plate with constant heat flux embedded in a porous medium is investigated. Design/methodology/approach – Using the Boussinesq and boundary‐layer approximations, the fluid equations for momentum, energy balance and concentration governing the problem are formulated. These equations are solved numerically by using the most effective Newton–Raphson shooting method along with fourth‐order Runge–Kutta integration algorithm. Findings – It was found that for positive values of the buoyancy parameters, the skin friction increased with increasing values of both the Eckert number (Ec) and the magnetic field intensity parameter (M) and decreased with increasing values of both the Schmidt number (Sc) and the permeability parameter (K). Practical implications – A very useful source of information for researchers on the subject of hydromagnetic flow in porous media. Originality/value – This paper illustrates the effects of magnetic field on mixed convective boundary layer flow past a vertical plate embedded in a saturated porous medium with mass transfer and a constant heat flux

MHD mixed-convection interaction with thermal radiation and nTH order chemical reaction past a vertical porous plate embedded in a porous medium

This article investigates the hydromagnetic mixed convection heat and mass transfer flow of an incompressible Boussinesq fluid past a vertical porous plate with constant heat flux in the presence of radiative heat transfer in an optically thin environment, viscous dissipation, and an nth order homogeneous chemical reaction between the fluid and the diffusing species. 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 plate surface temperature, 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

On non-pertubative approach to transmission dynamics of infectious diseases with waning immunity

On this paper, a mathematical model that describes the dynamics of re-infection under the assumption that the vaccine induced immune protection may wane over time is presented. The qualitative analysis reveals that the disease eradication depends on vaccination coverage as well as on vaccine efficacy. Using an appropriate Lyapunov function, we establish that the disease free equilibrium is globally asymptotically stable if the vaccination coverage level exceeds a certain threshold value. Numerical algorithm based on Adomian decomposition method (ADM) coupled with Padé approximation technique and He's variational iteration method (VIM) are developed and implemented in MAPLE to approximate the solution of the governing non-linear systems. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model

On MHD convection with Soret and Dufour effects past a vertical plate embedded in a porous medium

The paper studies the mixed convection flow of an incompressible Boussinesq fluid under the simultaneous action of buoyancy and transverse magnetic field with Soret and Dufour effects over a vertical porous plate with constant heat flux embedded in a porous medium. Under suitable nondimensionalization, the governing non-linear coupled differential equations are solved numerically using shooting quadrature. Tabular and graphical results are presented and discussed quantitatively. Results obtained which compare favourably well with published data show that the local skin friction is enhanced by the Sorets and Dufour effects.National Research Foundation of South Africa Thuthuk

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

Please cite as follows: Seidu, B. & Makinde, O. D. 2014. Optimal control of HIV/AIDS in the workplace in the presence of careless individuals. Computational and Mathematical Methods in Medicine, 2014:1-19 (Article ID 831506), doi:10.1155/2014/831506.The original publication is available at http://www.hindawi.com/journals/cmmmA 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.http://www.hindawi.com/journals/cmmm/2014/831506/Publisher's versio