International Journal of Biomathematics

In this paper, we study the effects of heat transfer on the peristaltic magneto-hydrodynamic (MHD) flow of a Bingham fluid through a porous medium in a channel. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large in comparison with the radius of the channel) and low Reynolds number are used to linearize the governing equations. The velocity field for the model of interest is solved by Adomian decomposition method. The expressions for pressure rise, flow rate and frictional force are obtained. The effect of magnetic field, Darcy number, yield stress, amplitude ratio and the temperature on the axial pressure gradient, pumping characteristics and frictional force are discussed through graphs.

In this note we present the Adomian decomposition method for solving a simple model for the diffusion and absorption of oxygen in tissue. The method is examined for computational efficiency and accuracy.

This paper investigate the existence of weak-renormalized solutions of the three species degenerate predator–prey model. The data belong to L¹ and we assume no growth condition on the nonlinearities.

First, we show that the theorem by Hirsch which guarantees the existence of carrying simplex for competitive system on any n-rectangle: {x ∈ Rⁿ : 0 ≤ x_i ≤ k_i, i = 1, …, n} still holds. Next, based on the theorem a competitive system with the linear structure saturation defined on the n-rectangle is investigated, which admits a unique (n - 1)-dimensional carrying simplex as a global attractor. Further, we focus on the whole dynamical behavior of the three-dimensional case, which has a unique locally asymptotically stable positive equilibrium. Hopf bifurcations do not occur. We prove that any limit set is either this positive equilibrium or a limit cycle. If limit cycles exist, the number of them is finite. We also give a criterion for the positive equilibrium to be globally asymptotically stable.

Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ₁, the Froude number Fr, the perturbation parameter δ, the angle of inclination θ and the phase difference ϕ. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.

In this paper, the blood flow through a tapered artery with a stenosis by considering axially non-symmetric but radially symmetric mild stenosis on blood flow characteristics is analyzed, assuming the flow is steady and blood is treated as Williamson fluid. Perturbation solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

This study describes ciliary motion on the transport of fluids in human body with heat transfer. The mathematical model of the flow of a Jeffrey fluid in a tube of finite length is considered due to metachronal wave of cilia motion. Flow equations have been modeled and simplified using similarity variables. Exact solutions of the formulated problem have been obtained for velocity, temperature and pressure gradient and graphs for velocity, pressure rise, pressure gradient and temperature profile have been plotted and studied for different values of specific physical parameters. Trapping phenomena and isotherms are presented at the end of the paper.

In this paper, we consider the solution of the following rational systems of difference equations:

This research is concerned with the mathematical modeling and analysis of blood flow in a tapered artery with stenosis. The analysis has been carried out in the presence of heat and mass transfer. Constitutive equation of Carreau fluid has been invoked in the mathematical formulation. The representation of blood flow is considered through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is given due attention. Solutions have been obtained for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. Graphical illustrations associated with the tapered arteries namely converging, diverging and non-tapered arteries are examined for different parameters of interest. Streamlines have been plotted and discussed.

In this paper, a diffusive three species predator–prey model with two Leslie–Gower terms is considered. The stability of the unique positive constant equilibrium for the reaction–diffusion system is obtained. Sufficient conditions are derived for the global stability of the positive constant equilibrium. In particular, we establish the existence and non-existence of non-constant positive steady states of this system. The results indicate that the large diffusivity is helpful for the appearance of the non-constant positive steady states (stationary patterns).

In this paper, the dynamics of mathematical model for infection of thymus gland by HIV-1 is analyzed by applying some perturbation through two different types of delays such as in terms of Hopf bifurcation analysis. Further, the conditions for the existence of Hopf bifurcation are derived by evaluating the characteristic equation. The direction of Hopf bifurcation and stability of bifurcating periodic solutions are determined by employing the center manifold theorem and normal form method. Finally, some of the numerical simulations are carried out to validate the derived theoretical results and main conclusions are included.

In this paper, by utilizing the comparison theorem and constructing a suitable Lyapunov functional the predator–prey model with modified Leslie–Gower Holling-type II schemes and a deviating argument is studied. Some sufficient conditions are obtained for uniform persistence and global attractivity of positive periodic solutions for this model. Furthermore, an example shows that the obtained criteria are easily verifiable.

This paper presents formulae and explanation about the growth of a convective gas bubble in the blood and other tissues of divers who surface too quickly, concentration distribution around the growing bubble is also presented. The formulae are valid all over the growth stages, i.e. under variable ambient pressure while the diver is ascending, and under constant ambient pressure at diving stops or at sea level. The mathematical model is solved analytically by using the method of combined variables. The growth process is affected by tissue diffusivity, concentration constant and the initial void fraction, which is the dominant parameter. Results show that, the time of the complete growth, in the convective growth model, is shorter than those earlier presented by Mohammadein and Mohamed [Concentration distribution around a growing gas bubble in tissue, Math. Biosci.225(1) (2010) 11–17] and Srinivasan et al. [Mathematical models of diffusion-limited gas bubble dynamics in tissue, J. Appl. Physiol.86 (1999) 732–741] for the growth of a stationary gas bubble, this explains the effect of bubble motion on consuming the oversaturated dissolved gas from the tissue into growing bubble which leads to increment in the growth rate to be more than those presented in the previous stationary models.

The human head is one of the most sensitive parts of human body due to the fact that it contains brain. Any abnormality in the functioning of brain may disturb the entire system. One of the disturbing factors of brain is thermal stress. Thus, it is imperative to study the effects of thermal stress on human head at various environmental conditions. For the thermoregulation process, the human head is considered to be a structure of four layers viz.; brain, cerebrospinal fluid (CSF), skull and scalp. A mathematical model has been formulated to estimate the variation of temperature at these layers. The model is based on radial form of bio-heat equation with the appropriate boundary conditions and has been solved by variational finite element method. The rate of metabolic heat generation and thermal conductivity in this study have been assumed to be heterogeneous. The results were compared with the experimental studies for their coincidence and it has been observed theoretically and experimentally that the human head has greater resistance to compete with the thermal stress up to large extent.