Optimal control of a vector borne disease with horizontal transmission

The paper presents the optimal control applied to a vector borne disease with direct transmission in host population. First, we show the existence of the control problem and then use both analytical and numerical techniques to investigate that there are cost effective control efforts for prevention of direct and indirect transmission of disease. In order to do this three control functions are used, one for vector-reduction strategies and the other two for personal (human) protection and blood screening, respectively. We completely characterize the optimal control and compute the numerical solution of the optimality system using an iterative method.     

Approximate conservation laws of nonlinear perturbed heat and wave equations

We construct approximate conservation laws for non-variational nonlinear perturbed (1+1) heat and wave equations by utilizing the partial Lagrangian approach. These perturbed nonlinear heat and wave equations arise in a number of important applications which are reviewed. Approximate symmetries of these have been obtained in the literature. Approximate partial Noether operators associated with a partial Lagrangian of the underlying perturbed heat and wave equations are derived herein. These approximate partial Noether operators are then used via the approximate version of the partial Noether theorem in the construction of approximate conservation laws of the underlying perturbed heat and wave equations.     

How changes in cell mechanical properties induce cancerous behavior

Tumor growth and metastasis are ultimately mechanical processes involving cell migration and uncontrolled division. Using a 3D discrete model of cells, we show that increased compliance as observed for cancer cells causes them to grow at a much faster rate compared to surrounding healthy cells. We also show how changes in intercellular binding influence tumor malignancy and metastatic potential. These findings suggest that changes in the mechanical properties of cancer cells is the proximate cause of uncontrolled division and migration and various biochemical factors drive cancer progression via this mechanism.     

Efficient catalytic effect of CuO nanostructures on the degradation of organic dyes

An efficient catalytic effect of petals and flowers like CuO nanostructures (NSs) on the degradation of two organic dyes, methylene blue (MB) and rhodamine B (RB) were investigated. The highest degradation of 95% in CuO petals and 72% in flowers for MB is observed in 24 h. For RB, the degradation was 85% and 80% in petals and flowers, respectively for 5 h. It was observed that CuO petals appeared to be more active than flowers for degradation of both dyes associated to high specific surface area. The petals and flower like CuO NSs were synthesized using the chemical bath method at 90 °C. The grown CuO NSs were characterized using scanning electron microscopy (SEM), high resolution transmission electron microscopy (HRTEM), and X-ray diffraction (XRD).     

Diffraction of SH-waves across a mixed boundary in a plate

The diffraction of SH-waves in an infinite elastic plate is studied under general boundary conditions using the Wiener-Hopf technique. A mixed interface boundary value problem is solved as an illustration.     

Stability techniques in SIR epidemic models

In biological communities interaction among different species affect their stability. In this paper, we consider a nonlinear SIR model, which describes the dynamics of the interaction between susceptible and infected individuals in population. We establish stability techniques to find out the equilibria for the model and their numerical results are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recent advances in biopolymer based electrospun nanomaterials for drug delivery systems

Drug delivery systems, including liposomes, gels, prodrugs, and so forth, are used to enhance the tissue benefit of a pharmaceutical drug or conventional substance at a specific diseased site with little toxicological impact. Nanotechnology can be a rapidly developing multidisciplinary science that enables the production of polymers at the manometer scale for different medical applications. The use of biopolymers in drug delivery systems provides compatibility, biodegradability and low immunogenicity biologically. Large-scale and smaller-than-expected medication particles can be delivered using biopolymers such as silk fibroins, collagen, gelatine, and others that are easily formed into suspensions. These drug carrier systems are functional at improving drug delivery and can be used in intranasal, transdermal, dental, and ocular delivery systems. This study discusses the latest developments in drug delivery methods based on nanomaterials, mainly using biopolymers like proteins and polysaccharides.     

Effect of polyethylene oxide on the viscosity of dispersions of charged silica particles: interplay between rheology, adsorption, and surface charge

In this study a systematic investigation on the adsorption of polyethylene oxide (PEO) onto the surface of silica particles and the viscosity behavior of concentrated dispersions of silica particles with adsorbed PEO has been performed. The variation of shear viscosity with the adsorbed layer density, concentration of free polymer in the solution (depletion forces), polymer molecular weight, and adsorbed layer thickness at different salt concentrations (range of the electrostatic repulsion between particles) is presented and discussed. Adsorption and rheological studies were performed on suspensions of silica particles dispersed in solutions of 10⁻² M and 10⁻⁴ M NaNO₃ containing PEO of molecular weights 7,500 and 18,500 of different concentrations. Adsorption measurements gave evidence of a primary plateau in the adsorption density of 7,500 MW PEO at an electrolyte concentration of 10⁻² M NaNO₃. Results indicate that the range of the electrostatic repulsion between the suspended particles affects both adsorption density of the polymer onto the surface of the particles and the viscosity behavior of the system. The adsorbed layer thickness was estimated from the values of zeta potential in the presence and absence of the polymer and was found to decrease with decreasing the range of the electrostatic repulsive forces between the particles. Experimental results show that even though there is a direct relation between the viscosity of the suspension and the adsorption density of the polymer onto the surface of the particles, variation of viscosity with adsorption density, equilibrium concentration of the polymer, and range of the electrostatic repulsion cannot be explained just in term of the effective volume fraction of the particles and needs to be further investigated. Received: 15 February 2000/Accepted: 26 June 2000     

Facile synthesis of zirconia supported nanomaterials for efficient photocatalytic applications

The recent study enlightens the synthesis and characterization of zirconia (ZrO₂), Fe-doped ZrO₂ (Fe@ZrO₂), and Ni-doped ZrO₂ (Ni@ZrO₂) catalysts having new-fangled morphology with tuned band gap as photocatalysts for degradation of textile wastewater dyes methylene blue (MB), malachite green (MG), and their mixtures. SEM imaging of Fe@ZrO₂ and Ni@ZrO₂ is interestingly varied from ZrO₂ as well as doping of transition metals greatly affects the morphology of composites. The optimization study depicts that the pH, time (min) and catalyst amount (g) have a direct relation with degradation efficiency, while the dye concentration (mg/L) has an indirect relation as well. The photocatalytic studies depict that the degradation of MB and MG follows oxidation pathway via hydroxyl radicals (OH^•) and holes. Reusability of catalysts corresponds to a little decrease in degradation efficiency in the first two cycles and decreases to about ∼10% (Ni@ZrO₂) and ∼12% (Fe@ZrO₂) in next three cycles.