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

Unsteady MHD Flow of Non-Newtonian Fluid in a Channel Filled with a Saturated Porous Medium with Asymmetric Navier Slip and Convective Heating

This paper aims to computationally study the effects of Navier slip on an unsteady hydromagnetic flow of a pressure driven, reactive, variable viscosity, electrically conducting third-grade fluid through a porous saturated medium with asymmetrical convective boundary conditions. It is assumed that the chemical kinetics in the flow system is exothermic and that the asymmetric convective heat exchange with the surrounding medium at the surfaces follows Newtons law of cooling. The coupled nonlinear partial differential equations governing the flow and heat transfer are derived and solved numerically using a semi-implicit finite difference scheme. The flow and heat transfer characteristics are analyzed graphically and discussed for different values of the parameters embedded in the system. It is observed that the lower wall slip parameter increases the fluid velocity profiles. The upper wall slip parameter is seen to retard the velocity profiles while it increases the fluid temperature profiles. The wall slip parameters increase the skin friction and the Nusselt number. The wall slip parameters as well as the variable viscosity parameter, the viscous heating parameter and the numerical exponent m reduce the thermal criticality values of the reaction parameter