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In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Furthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission. [ABSTRACT FROM AUTHOR]

In this paper, regarding the time delay as a bifurcation parameter, the stability and Hopf bifurcation of the model of competition between two species in a turbidostat with Beddington-DeAngelis functional response and discrete delay are studied. The Hopf bifurcations can be shown when the delay crosses the critical value. Furthermore, based on the normal form and the center manifold theorem, the type, stability and other properties of the bifurcating periodic solutions are determined. Finally, some numerical simulations are given to illustrate the results. [ABSTRACT FROM AUTHOR]

This article is concerned with the optimal harvesting of a predator-prey model with a prey refuge and imprecise biological parameters. We consider the model under impreciseness and introduce a parametric functional form of an interval which differs from those of models with precise biological parameters. The existence of all possible equilibria and stability of system are discussed. The bionomic equilibrium of the model is analyzed. Also, the optimal harvesting policy is derived using Pontryagin's maximal principle. Numerical simulations are presented to verify the feasibilities of our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamic behaviors of a non-autonomous single-species model subject to impulsive and random perturbations. We first investigate the existence and uniqueness of the globally positive solution of the model. Secondly, a good understanding of the extinction, non-persistence in the mean, weak persistence, persistence in the mean and stochastic permanence of the model is obtained. Thirdly, we further examine the asymptotic pathwise estimation. Fourthly, it is shown that the model is globally attractive under some appropriate conditions. Finally, numerical simulations are presented to justify the analytical results. [ABSTRACT FROM AUTHOR]

Co-injection molding (CIM) is an advanced technology which was developed to meet quality requirements and to reduce the material cost. Theoretical investigations concerning it are very limited, especially for simultaneous CIM. The interactions of air, skin and core polymer melt in the process are very complex, which makes it more challenging to simulate free surface flows in the mold. Thus, this article presents a mathematical model for it. The extended Pom-Pom (XPP) model is selected to predict the viscoelastic behavior of polymer melt. The free surface is captured by the level set method. The article vividly shows the simultaneous CIM process by means of a visual numerical simulation technique. Both two-dimensional (2D) and 3D examples are presented to validate the model and illustrate its capabilities. The 3D flow behaviors of simultaneous CIM process are hard to predict numerically. To our knowledge, this is the first attempt at simulating melt flow behaviors in 3D simultaneous CIM based on the XPP constitutive equation and visual technique. The numerical results are in good agreement with the available experiment results, which establish the capability of the multiphase flow model presented in this article to simulate the flow behaviors of polymer melt in simultaneous CIM process. [ABSTRACT FROM AUTHOR]

This paper is concerned with a nonautonomous single-species model, in which the population dynamics is affected by impulsive perturbations and environmental noise. Sufficient conditions for the extinction, stochastic permanence, and global attractivity of system are obtained, respectively. The above results reveal that the white noise plays a very important role in the dynamic behaviors. However, it is found that the bounded impulse does not affect the above properties. Some numerical simulation results are presented to support the analytical findings. [ABSTRACT FROM AUTHOR]

A randomized discrete competitive system is investigated and the maximum likelihood estimation (MLE) of the parameters of the system is obtained. Also, a corresponding numerical simulation is offered to support our theoretical results. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of positive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an almost periodic system of impulsive differential equations used in modeling two-species in competition is considered. By the comparison between the solutions of impulsive system and the corresponding non-impulsive system and constructing Lyapunov function, sufficient conditions ensuring the uniformly asymptotic stability of a unique positive almost periodic solution of the system are derived. Finally, an example and its corresponding numerical simulations are presented to explain our theoretical results. [Copyright &y& Elsevier]

A simplified model using a modified effectiveness–Number of Transfer Units (NTU) method for thermal performance simulation of indirect evaporative heat exchangers is presented and then validated utilizing experimental data from the literature. The objective of this model is to facilitate efficient computer simulation of indirect evaporative cooling or hybrid indirect evaporative cooling/direct expansion vapor compression systems, both of which include an indirect evaporative heat exchanger as a core component. Through some approximations, the governing differential equations that describe indirect evaporative heat exchanger heat/mass transfer behavior are modified to produce a methodology that is analogous to the effectiveness–NTU method for sensible-only heat exchangers. The simplified set of equations can then be solved within short computation times and with numerical stability. An examination of the Lewis factor impact on evaporation processes using this model indicates that the approximation of unity for the Lewis factor may not be valid when the inlet air to the wet side is cold and dry. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the dynamic behavior of an impulsive delay differential equation model with the effects of interspecific allelopathic interaction. A good understanding of the permanence, extinction and the existence of positive periodic solutions is gained. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results. [Copyright &y& Elsevier]

Abstract: In this paper, the smoothed particle hydrodynamics (SPH) method is extended to deal with three-dimensional (3D) non-Newtonian flows with complex free surfaces, in which the viscosity is modeled using the Cross model. In order to alleviate the so-called tensile instability which leads to particle clustering and unphysical fracture in fluid stretching, an artificial stress term is particularly incorporated into the momentum equation. For convenience in implementation of wall boundary condition in 3D, an enhanced treatment of solid boundaries is proposed to improve the computational performance. Parallelization is also developed to ensure affordable computational time of simulations involving millions of particles. The proposed SPH algorithm is validated by solving the Hagen–Poiseuille flow and comparing the SPH results with the available analytical solutions. To demonstrate the ability of the numerical method in simulating 3D non-Newtonian flows with free surfaces, three challenging engineering applications, including the impacting droplet, molding injection of a thin plate mold and a Z-shaped mold, and jet buckling, are investigated. It is found that the shear-thinning behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and fairly accurate and agrees well with the available data. [Copyright &y& Elsevier]