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The ferromagnetic flow of Maxwell nanoliquid past a stretching surface is the focus of this endeavor. The flow is modeled in a porous medium obeying Darcy's law and is also subjected to the effects of magnetic dipole, nonlinear radiative heat flux, and activation energy. Using proper transformation, the governing system of partial differential equations (PDEs) transforms into ordinary differential equations (ODEs). The solution process employs a shooting approach. For nanofluid concentration, temperature, velocity, skin fraction, Sherwood number, and Nusselt number, the effects of relevant non-dimensional flow parameters and numbers are explored. The results show that the porosity, elastic, and ferromagnetic parameters all reduce nanofluid velocity. The nanofluid temperature drops as the ferromagnetic and Prandtl numbers increase, while the nanofluid temperature rises to enhance the temperature ratio and radiative heat parameters. The nanofluid concentration profile rises due to the non-dimensional activation energy and falls as the Schmidt number increases. [ABSTRACT FROM AUTHOR]

In this article, we extend the notion of double Laplace transformation to triple and fourth order. We first develop theory for the extended Laplace transformations and then exploit it for analytical solution of fractional order partial differential equations (FOPDEs) in three dimensions. The fractional derivatives have been taken in the Caputo sense. As a particular example, we consider a fractional order three dimensional homogeneous heat equation and apply the extended notion for its analytical solution. We then perform numerical simulations to support and verify our analytical calculations. We use Fox-function theory to present the derived solution in compact form. [ABSTRACT FROM AUTHOR]

In this article, convection, radiation and internal heat generation for entropy generation in the moving exponential porous fin are investigated. We have considered fins of fixed dimension with insulated tip and convective coefficient at fin's tip. The second law of thermodynamics for one-dimensional heat transfer is applied to study the entropy generation in the exponential porous fins. The shooting method is applied to solve the system numericaly. The amount of entropy generation depends on the porosity parameter, temperature distribution, and temperature ratio of the exponential porous fin which is observed. It is also observed that the highest generation of entropy exists at the fin's base when the temperature difference is increased, at particular values of temperature ratio and porosity parameter. The data also reveal that the effect of porosity parameter on entropy generation number is substantially stronger than the influence of temperature ratio, with an increase in Porosity from 1 to 80 resulting in a 15-time increase in average entropy generation number. However, an increase in temperature ratio from 1.1 to 1.9 results an average of 30% increase in entropy generation number. [ABSTRACT FROM AUTHOR]

The performance and thermal properties of convective–radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by 30 % approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation. [ABSTRACT FROM AUTHOR]

Main concern of current research is to develop a novel mathematical model for stagnation-point flow of magnetohydrodynamic (MHD) Prandtl–Eyring fluid over a stretchable cylinder. The thermal radiation and convective boundary condition are also incorporated. The modeled partial differential equations (PDEs) with associative boundary conditions are deduced into coupled non-linear ordinary differential equations (ODEs) by utilizing proper similarity transformations. The deduced dimensionless set of ODEs are solved numerically via shooting method. Behavior of controlling parameters on the fluid velocity, temperature fields as well as skin friction and Nusselt number are highlighted through graphs. Outcome declared that dimensionless fluid temperature boosts up for both the radiation parameter and Biot number. It is also revealed that the magnitude of both heat transfer rate and skin friction enhance for higher estimation of curvature parameter. Furthermore, comparative analysis between present and previous reports are provided for some specific cases to verify the obtained results. [ABSTRACT FROM AUTHOR]

Infection of hepatitis B virus (HBV) is a global health problem. We provide the study about hepatitis B virus dynamics that can be controlled by education campaign (awareness), vaccination, and treatment. Initially we bring constant controls in considerations for treatment, vaccination, and education campaign (awareness). In the case of constant controls, we study the stability and existence of the disease-free and endemic equilibria model's solutions. Afterwards, we take time as a control and formulate the suitable optimal control problem, acquire optimal control strategy in order to reduce the number of humans that are infected and the costs associated. At the end, results of numerical simulations show that the optimal combination of education campaign (awareness), treatment, and vaccination is the most efficient way to control the infection of hepatitis B virus (HBV) infection. [ABSTRACT FROM AUTHOR]

We discussed anthroponotic cutaneous leishmania transmission in this article, due to its large effect on the community in the recent years. The mathematical model is developed for anthroponotic cutaneous leishmania transmission, and its qualitative behavior is taken under consideration. The threshold number R 0 of the model is derived using the next-generation method. In the disease-free case, local and global stability is carried out with the condition that R 0 will be less than one. The global stability at the disease-free equilibrium point has been derived by utilizing the Castillo–Chavez method. On the other hand, at the endemic equilibrium point, the local and global stability holds with some conditions, and R 0 is greater than unity. The global stability at the endemic equilibrium point is established with the help of a geometrical approach which is the generalization of Lyapunov theory, by using the third additive compound matrix. The sensitivity analysis of the threshold number with other parameters is also taken into account. Several graphs of important parameters are discussed in the last section. [ABSTRACT FROM AUTHOR]

The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new mathematical model, the threshold quantity reproduction number $$R_0$$ is investigated by using the well known approach i.e. next generation matrix and investigate the possible equilibriums such as disease free and endemic equilibria. Then for the local and global behavior of the proposed problem, the local asymptotic stability analysis as well as global asymptotic stability analysis are proved. To prove the global asymptotic stability at disease free equilibrium, the classic Lyapunov function theory is considered. Similarly to show global asymptotic stability at endemic equilibria, the geometrical approach is used, which is the generalization of Lyapunov theory. Finally, numeric of the proposed problem are carried out to show the feasibility of the obtained results and the role of saturated incidence rate. [ABSTRACT FROM AUTHOR]

A mathematical model for HIV-1 infection with multiple delays is proposed. These delays account for (i) the delay in contact process between the uninfected cells virus, (ii) a latent period between the time target cells which are contacted by the virus particles and the time the virions enter the cells, and (iii) a virus production period for new virions to be produced within and released from the infected cells. For this model, the basic reproductive number is identified and its threshold property is discussed. The uninfected and infected steady states are shown to be locally as well as globally asymptotically stable. The value of the basic reproductive number shows that increasing any one of these delays will decrease this number. This may suggest a new direction for new drugs that can prolong the infection process and spreading of virus. The proved results have potential applications in HIV-1 therapy. [ABSTRACT FROM AUTHOR]

SULF1/SULF2 enzymes regulate the activities of several growth factors by selective hydrolysis of 6- O-sulphates of heparan sulphate proteoglycan co-receptors, the sulfation of which is essential for signal transduction of some ligand/receptor interactions but not others. This study demonstrates the existence of SULF1 variants with a wide spectrum of splicing patterns in mammalian tumours. The levels and relative proportions of SULF1/SULF2 splice variants markedly vary in different tumours with a potential to regulate cell growth differentially. Although mammalian Sulf1 compared with Sulf2 gene generates a much larger number of splice variants, both enzymes follow generally similar distribution and signalling association trends in hepatocellular carcinomas. [ABSTRACT FROM AUTHOR]

The mechanical behavior of non-Newtonian fluids can be modeled by several constitutive differential equations. The Oldroyd model is viewed as one of the successful models for describing the response of a subclass of polymeric liquids, in particular the non-Newtonian behavior exhibited by these fluids. In this paper, we are concerned with the study of the unsteady flows of an incompressible viscoelastic fluid of an Oldroyd-B type in a blood vessel acting on a Brownian force. First we derive the orientation stress tensor considering Hookean dumbbells on Brownian configuration fields. Then we reformulate the three-dimensional Oldroyd-B model with the total stress tensor which consists of the isotropic pressure stress tensor, the shear stress tensor, and the orientation stress tensor. Finally we present the numerical simulations of the model and analyze the effect of the orientation stress tensor in the vessel. [ABSTRACT FROM AUTHOR]

Smoking is a large problem in the entire world. Despite overwhelming facts about the risks, smoking is still a bad habit widely spread and socially accepted. Many people start smoking during their gymnasium period. The main purpose of this paper is to determine the asymptotic behavior of a mathematical model using for giving up smoking. Our interest here is to derive and analysis the model taking into account the occasional smokers compartment in the giving up smoking model. Analysis of this model reveals that there are four equilibria, one of them is the smoking-free and the other three correspond to presence of smoking. We also present the global stability and parameter estimates that characterize the natural history of this disease with numerical simulations. [ABSTRACT FROM AUTHOR]

Pairs of 17-day embryonic chick tibiotarsi were removed and maintained in organ culture. One of each pair was subjected to a single 20-minute period of intermittent loading at 0.4 Hz, producing peak longitudinal compressive strains of 650 microstrain (mu epsilon). In the 18-hour culture period following loading, alkaline phosphatase levels in the osteoblasts of the loaded tibiotarsi were maintained whereas in controls they declined. In situ hybridization using a collagen type I cRNA riboprobe showed a substantial increase in expression of mRNA for collagen type I in the periosteal tissue of bones that were cultured for 18 hours after loading compared with that in similarly cultured controls and bones cultured for 4 hours. These results demonstrate that appropriate loading of embryonic chick bones in organ culture elicits adaptive regulation of matrix synthesis as evidenced by increased expression of the gene for type I collagen and alkaline phosphatase activity. This model may be useful as it must contain all the obligatory steps between strain change in the matrix and modified osteogenic activity. [ABSTRACT FROM AUTHOR]

The strain imposed by mechanical loading on bone tissue normally stimulates a response by bone cells that results in an adjustment of bone architecture that enables the bone to withstand reasonable loads. But it is unclear why this process should become less effective in some 50 per cent of postmenopausal women, who suffer fractures as a result. Here we show that bone in vivo undergoes an adaptive response to loading that is less effective in the absence of the a-form of the oestrogen receptor (ER-a) and that osteoblast-like cells require ER-a to proliferate in response to mechanical strain in vitro. As ER-a expression in osteoblasts and osteocytes depends on oestrogen concentration, a failure to maintain bone strength after the menopause might be due to a reduction in the activity of ER-a in bone cells, thereby limiting their anabolic response to mechanical loading and allowing a loss of bone tissue comparable to that associated with disuse. [ABSTRACT FROM AUTHOR]