Tian-Chuan Sun’s research while affiliated with Huzhou University and other places

Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impact of immunization, and the waning of the vaccine on coronavirus infection disease. We analyze the model under their equilibrium points. The model under the equilibrium points is discussed and proven that it is locally asymptotically stable if Rv is lesser than unity. We present the backward bifurcation hypothesis of the model and show that there is a parameter β2 that causes the backward bifurcation in the imperfect vaccine model. We show certain assumptions when ψ=1 for the imperfect vaccine case; the model is both stable globally asymptotically at the disease-free (R0≤1) and endemic cases (R0>1). By using infected cases from the recent wave throughout Pakistan, we shall estimate the model parameters and calculate the numerical value of the basic reproductive number R0≈1.2591. We present the comprehensive graphical results for the realistic parameter values and show many useful suggestions regarding the elimination of the infection from society. The vaccination efficacy that provides an important role in disease elimination is discussed in detail.

Thermal and mass transport in the Carreau Yasuda fluid stagnation point MHD flow is addressed through a stretchable surface in this study. Thermal and solutal stratifications are analyzed. They occur due to temperature and concentration variation. The activation energy in the mass transfer is used to enhance the results. It is the initial input of energy due to which reaction proceeds. The velocity slip effect is implemented at the boundary for the momentum equation. Soret and Dufour’s impact on a given flow is also studied. The entropy generation rate is computed mathematically and the results are presented through different plots for pertinent flow parameters. The governing PDE system is changed into an ordinary one by appropriate transformations. The obtained system is tackled through the ND-Solve MATHEMATICA for numerical results. It is seen that the concentration, temperature, and velocity distributions are diminished against rising values of thermal and solutal stratified parameters and slip. Also, we have seen that stratification is very useful in entropy generation minimization.

The parametric analyses for the Darcy-Forchheimer CNTs hybrid nanofluid (HNF) flow over a permeable spinning disc have been elaborated in this article. The effect of thermal slip and viscous dissipation on the surface of a spinning disc has been evaluated. The HNF is synthesized in the presence of an inorganic compound namely ferric oxide and carbon nanotubes. The nanofluid flow phenomena have been modeled in the form of the system of PDEs along with the Maxwell equation. Using a similarity strategy, the nonlinear PDEs system is simplified to ODEs. The ordinary set of ODEs are then computed using the parametric continuation approach (PCM). The outcomes are evaluated by comparing to boundary value solver (bvp4c) package, for reliability and validity purposes. Multiple flow parameters have been displayed and addressed in relation to energy, mass, and velocity profiles. The superparamagnetic property of magnetic nanoparticles and week van der Waals force interactions between CC atoms make the current study more plausible. It has been perceived that the use of CNTs and magnetic nanoparticles in the water significantly enhances its thermophysical properties and heat transition properties. The energy profile accelerates with the effect of Eckert number, Forchheimer term, and volume friction parameters. ARTICLE HISTORY

In this study, the Fokas system which represents the spread of irregular pulse in monomode optical fibers is investigated via the Jacobi elliptic function expansion (JEFE) method. This method is the most powerful technique to explore solutions for a wide range of various models. As a result, different solutions such as dark-bright, singular, bright, Jacobi elliptic function, and exponential solutions are obtained. In addition, 3D and 2D graphics for the obtained solutions are investigated with the assist of a computer program by assigning particular values to the parameters involved.

In today’s sophisticated global marketplace, supply chains are complex nonlinear systems in the presence of different types of uncertainties, including supply-demand and delivery uncertainties. Though up to now, some features of these systems are studied, there are still many aspects of these systems which need more attention. This necessitates more research studies on these systems. Hence, in this study, we propose a variable-order fractional supply chain network. The dynamic of the system is investigated using the Lyapunov exponent and bifurcation diagram. It is demonstrated that a minor change in the system’s fractional-derivative may dramatically affect its behavior. Then, distributed consensus tracking of the multi-agent network is studied. To this end, a control technique based on the sliding concept and Chebyshev neural network estimator is offered. The system’s stability is demonstrated using the Lyapunov stability theorem and Barbalat’s lemma. Finally, through numerical results, the proposed controller’s excellent performance for distributed consensus tracking of multi-agent supply chain network is demonstrated.

The analysis of thin liquid film over a horizontal rotating disk has attained fabulous attention in the field of the coating industry. Therefore , the present study aims to communicate the nature of the thin-film flow of Maxwell magnetized nanomaterials over the surface of the rotating disk. The important aspects of nano liquid known as the Brownian motion and thermophoresis are considered. This liquid film is explored under the influence of a heat source/sink. Dimen-sionless variables have been implemented to acquire the nonlinear system of ODEs. The obtained system has been tackled numerically via Lobatto IIIA technique for the variation of unsteadiness parameter ranging from 0.3 to 0.45, thin-film thickness parameter ranging 2.20-2.35, rotation parameter ranging 0.7-1.0, magnetic parameter ranging 4.0-7.0, Prandtl number ranging 1.3-1.6, and radiation parameter ranging 0.5-0.8. The outcomes for the flow problem have been estimated against various embedding variables. In addition, tables are made for sundry cases of different scenarios, mesh points, maximum residual errors, Nusselt and Sherwood numbers. Analysis elaborates that an increase in rotation parameter causes a reduction in the azimuthal component of velocity while the temperature is enhancing the function of the radiation parameter. ARTICLE HISTORY

This analysis reports an unsteady and incompressible flow of Williamson nanoliquid in presence of variable thermal characteristics are persuaded by a permeable stretching cylinder. The flow field investigation is established with the effect of mixed convection and non-uniform heat source/sink on flow and heat transfer. On the cylinder surface, the analysis is inspected with utilization of zero mass flux constraints. By using the appropriate similarity variables, the framed equations for the energy, momentum and mass is converted into non-linear ODEs. The numerical communication of the boundary value problem is successfully implemented using a computer algorithm programmed into the fifth Runge-Kutta scheme. Additionally, the wall shear factor and rate of heat transfer are calculated in two different cases namely, with curvature and without curvature. In addition, the results obtained are confirmed by making comparisons with previously published articles and we found an excellent match that guarantees the indemnity of current communication. A comprehensive change in velocity, temperature and concentration is examined for involved parameters like local Weissenberg number, space dependent heat source constant, magnetic number, curvature constant, thermophoretic parameter, buoyancy parameter, Brownian motion parameter, Prandtl number, Schmidt number, unsteadiness parameter, reaction rate parameter, activation energy parameter and temperature difference parameter. A reduction in velocity is observed for unsteady parameter and buoyancy constant. An enhanced nanofluid temperature is noted for space dependent heat source parameter, time dependent heat source parameter and unsteady parameter. Moreover, the nanofluid concentration is increases for temperature difference parameter while reverse observations are noticed for chemical reaction rate.

The nanoparticles play a vital role in the enhancement heat transfer process which is substantial in many industrial and engineering phenomenon's. Moreover, the suspension of nanoparticles with microorganisms is another motivating research area which referred importance in the biotechnology, health sciences and biomedical applications. The aim of this investigation is to present analysis of bioconvection phenomenon for Darcy-Forchheimer flow of Reiner-Philippoff nanofluid induced by a stretched a surface. The contribution of slip via higher relations is dissected for the flow. The radiative pattern is examined for the thermally developed flow. The heat and mass assessment has been examined with help of modified CattaneoChristov expressions. The flow equations associated with momentum, volumetric friction and motile microorganism density is transformed into dimensionless form. Transmuted dimensionless non-linear equations are tracked with shooting technique and results of prominent parameters are sketched via different graphs by using computational software MATLAB. Numerical and graphical tests across macroscopic particles, such as velocity temperature, and the profile of microorganisms, are accessed behind the influence of prominent physical parameters.

In recent years, the research for enhanced thermal transportation is centered around the utilization of nanostructures to avail the prospective benefits in areas of biomedical, metallurgy, polymer processing, mechanical and electrical engineering applications, food processing, ventilation, heat storage devices, nuclear systems cooling, electronic devices, solar preoccupation, magnetic sticking, bioengineering applications, etc. The thermal aspects of nanoliquids and associated dynamics properties are still necessary to be explored. In this thermal contribution, the flow of Casson nanofluid configured by an infinite disk is analyzed. The significance of Marangoni flow with activation energy, thermal and exponential space-dependent heat source, nonlinear thermal radiation and Joule heating impacts is also incorporated. Similarly, variables are affianced to recast the governing flow expressions into highly coupled nonlinear ODEs. The numerical simulation for the prevailing model is elucidated by applying the bvp4c built-in function of computational commercial software MATLAB. Consequences of sundry parameters, namely, magnetic parameter, Prandtl number, radiation parameter, exponential space-dependent heat source parameter, thermal-dependent heat source parameter, Eckert number, Dufour parameter, Soret number, Schmidt number, Marangoni number and Marangoni ratio parameter, mixed convection parameter, buoyancy ratio parameter, bioconvection Rayleigh number, activation energy parameter, thermophoresis parameter, Brownian motion parameter, bioconvection Lewis number, Peclet number microorganisms difference variable versus involved flow profiles like velocity, temperature, concentration of nanoparticles and microorganism field are obtained and displayed through graphs and tabular data.

Magnetohydrodynamic axisymmetric flow of viscous nanoliquid towards a variable stretching sheet is scrutinized. Flow is generated due to nonlinear stretching. Joule heating, heat flux and dissipation are analyzed in heat expression. Random and thermophoresis diffusions are considered. Physical description of entropy generation is also accounted. Entropy generation and heat transfer analysis are scrutinized through thermodynamics laws. Furthermore chemical reaction along with Arrhenius activation energy is addressed. Ordinary differential system is obtained through suitable variables. Homotopic convergent solutions for nonlinear system is developed. Influence of flow variables on entropy rate, velocity, Bejan number, concentration and temperature are analyzed. Further velocity gradient and heat and mass transfer rates are discussed. Reduction in velocity is noticed for magnetic variable. Thermal field has an enhancing trend for magnetic and Eckert number. Larger thermophoresis variable rises the temperature. An increment in entropy rate is observed for magnetic parameter. An increment in drag force is seen for magnetic variable.