Exact solutions for different vorticity functions of couple stress fluids

In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).

Modifications of the Optimal Auxiliary Function Method to Fractional Order Fornberg-Whitham Equations

In this paper,we present a new modification of the newly developed semi-analytical method named the Optimal Auxilary Function Method(OAFM)for fractional-order equations using the Caputo operator,which is named FOAFM.The mathematical theory of FOAFM is presented and the effectiveness of this method is proven by using it with well-known Fornberg-Whitham Equations(FWE).The FOAFM results are compared with other method results along with their exact solutions with the help of tables and plots to prove the validity of FOAFM.A rapidly convergent series solution is obtained from FOAFMand is validated by comparison with other results.The analysis proves that ourmethod is simply applicable,contains less computationalwork,and is rapidly convergent to the exact solution at the first iteration.A series solution to the problem is obtained with the help of FOAFM.The validity of FOAFM results is validated by comparing its results with the results available in the literature.It is observed that FOAFM is simply applicable,contains less computational work,and is fastly convergent.The convergence and stability are obtained with the help of optimal constants.FOAFM is very easy in applicability and provides excellent results at the first iteration for complex nonlinear initial/boundary value problems.FOAFM contains the optimal auxiliary constants through which we can control the convergence as FOAFM contains the auxiliary functions D_(1),D_(2),D_(3)...in which the optimal constants G_(1),G_(2),...and the control convergence parameters exist to play an important role in getting the convergent solution which is obtained rigorously.The computational work in FOAFM is less when compared to other methods and even a low-specification computer can do the computational work easily.

Exact Solutions of a Power Law Fluid Model in Posttreatment Analysis of Wire Coating with Linearly Varying Boundary Temperature

In this paper, analysis of post-treatment of wire coating is presented. Coating material satisfies power law fluid model. Exact solutions for the velocity field, volume flow rate and average velocity are obtained. Moreover, the heat transfer results are presented for different cases of linearly varying on the boundaries. The variations of velocity, volume flow rate, radius of coated wire, shear rate and the force on the total wire are presented graphically and discussed.

Optimal Campaign in Leptospirosis Epidemic by Multiple Control Variables

In this paper, we consider a leptospirosis epidemic model to implement optimal campaign by using multiple control variables. First, we show the existence of the control problem. Then we derive the conditions under which it is optimal to eradicate the leptospirosis infection and examine the impact of a possible educatioal/vaccinaction campaign using Pontryagin’s Maximum Principle. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method. The results obtained from the numerical simulations of the model show that a possible educational/vaccinaction combined with effective treatment regime would reduce the spread of the leptospirosis infection appreciably.

Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction R0. The disease-free equilibrium is stable locally and globally whenever R0〈 1. If R0 〉 1, then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented.

Global stability and vaccination of an SEIVR epidemic model with saturated incidence rate

This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R0. If the basic reproduction number R0〈 1, the disease- free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R0 〉 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology

In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For R0〈1, the disease-free equilibrium is stable both locally and globally and for R0〉1, the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.