DYNAMIC FOR A STOCHASTIC MULTI-GROUP AIDS MODEL WITH SATURATED INCIDENCE RATE

In this paper,a stochastic multi-group AIDS model with saturated incidence rate is studied.We prove that the system is persistent in the mean under some parametric restrictions.We also obtain the sufficient condition for the existence of the ergodic stationary distribution of the system by constructing a suitable Lyapunov function.Our results indicate that the existence of ergodic stationary distribution does not rely on the interior equilibrium of the corresponding deterministic system,which greatly improves upon previous results.

含微小颗粒的非牛顿生物Sutterby流体在感应磁场旋转圆盘上的流动性

本研究的主要目标是研究含有微小颗粒的非牛顿Sutterby流体的流动性,以及微生物回旋运动引起感应磁场的影响。流动设置在一对圆盘之间,圆盘间充满了含有微小颗粒和趋旋微生物的Sutterby流体。在流动控制中考虑了Arrhenius动力学和热辐射的影响。利用相关的相似变换将所建立的数学模型修改为非线性常微分方程。为了计算非线性常微分方程的数值解,使用微分变换程序(DTM)。对于非线性问题,积分变换技术执行难度大。因此,使用基于Taylor展开的微分变换方法以获得多项式解作为解析解。为了提高公式化数学建模的收敛性,将Padé近似与微分变换方法相结合。讨论了不同无量纲因子对速度、温度场、浓度分布和运动回旋微生物剖面的影响,用表格形式对两块板上的扭矩进行计算和显示。

DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

In this article, we present a hepatitis B epidemic model with saturated incidence.The dynamic behaviors of the deterministic and stochastic system are studied. To thisend, we first establish the local and global stability conditions of the equilibrium of thedeterministic model. Second, by constructing suitable stochastic Lyapunov functions, thesufficient conditions for the existence of ergodic stationary distribution as well as extinctionof hepatitis B are obtained.

A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we discuss the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations. Our main result is based on a hybrid fixed point theorem for a sum of three operators due to Dhage, and is well illustrated with the aid of an example.

Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas)is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typically,more than one of these procedures may happen in a given circumstance.We use the Cattaneo-Christov(CC)heat flux model instead of the Fourier law of heat conduction to discuss the behavior of heat transportation.A mathematical model is presented for the Cattaneo-Christov double diffusion(CCDD)in the flow of a non-Newtonian nanofluid(the Jeffrey fluid)towards a stretched surface.The magnetohydrodynamic(MHD)fluid is considered.The behaviors of heat and mass transportation rates are discussed with the CCDD.These models are based on Fourier’s and Fick’s laws.The convective transportation in nanofluids is discussed,subject to thermophoresis and Brownian diffusions.The nonlinear governing flow expression is first altered into ordinary differential equations via appropriate transformations,and then numerical solutions are obtained through the built-in-shooting method.The impact of sundry flow parameters is discussed on the velocity,the skin friction coefficient,the temperature,and the concentration graphically.It is reported that the velocity of material particles decreases with higher values of the Deborah number and the ratio of the relaxation to retardation time parameter.The temperature distribution enhances when the Brownian motion and thermophoresis parameters increase.The concentration shows contrasting impact versus the Lewis number and the Brownian motion parameter.It is also noticed that the skin friction coefficient decreases when the ratio of the relaxation to retardation time parameter increases.

ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

By applying the standard fixed point theorems,we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals,supplemented with nonlocal coupled fractional integral boundary conditions.An example is also constructed for the illustration of the obtained results.

EXISTENCE OF HOMOCLINIC ORBITS FOR A CLASS OF FIRST-ORDER DIFFERENTIAL DIFFERENCE EQUATIONS

In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.

The stationary distribution and extinction of a double thresholds HTLV-I infection model with nonlinear CTL immune response disturbed by white noise

This paper investigates the stochastic HTLV-I infection model with CTL immune response,and the corresponding deterministic model has two basic reproduction numbers.We consider the nonlinear CTL immune response for the interaction between the virus and the CTL immune cells.Firstly,for the theoretical needs of system dynamical behavior,we prove that the stochastic model solution is positive and global.In atldition,we obtain the existence of ergodic stationary distribution by stochastic Lyapunov functions.Meanwhile,sufficient condition for the extinction of the stochastic system is acquired.Reasonably,the dynamical behavior of deterministic model is included in our result of stochastic model when the white noise disappears.

The asymptotic behavior of a stochastic multigroup SIS model

In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.

Dynamics of stochastic predator-prey models with distributed delay and stage structure for prey

In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.

Stationary distribution and periodic solution of stochastic chemostat models with single-species growth on two nutrients

In this paper,we consider two chemostat models w th random perturbation,in which single species depends on two perfectly substitutable resources for growth.For the autonomous system,we first prove that the solution of the system is positive and global.Then we establish sufficient conditions for the existence of an ergodic stationary distribu tion by constructing appropriate Lyapunov functions-For the non-autonomous system,by using Mas'minskii theory on periodic Markov processes,we derive it admits a nontriv ial positive periodic solution.Finally,numerical simulations are carried out to illustrate our main results.

Long-Time Behavior and Density Function of a Stochastic Chemostat Model with Degenerate Diffusion

This paper considers a stochastic chemostat model with degenerate diffusion.Firstly,the Markov semigroup theory is used to establish sufficient criteria for the existence of a unique stable stationary distribution.The authors show that the densities of the distributions of the solutions can converge in L^(1)to an invariant density.Then,conditions are obtained to guarantee the washout of the microorganism.Furthermore,through solving the corresponding Fokker-Planck equation,the authors give the exact expression of density function around the positive equilibrium of deterministic system.Finally,numerical simulations are performed to illustrate the theoretical results.

Dynamics of an autonomous Gilpin-Ayala competition model with random perturbation

This paper discusses the dynamics of a Gilpin-Ayala competition model of two interact­ing species perturbed by white noise.We obtain the existence of a unique global positive solution of the system and the solution is bounded in pth moment.Then,we establish sufficient and necessary conditions for persistence and the existence of an ergodic sta­tionary distribution of the model.We also establish sufficient conditions for extinction of the model.Moreover,numerical simulations are carried out for further support of present research.

Stationary distribution and extinction for a stochastic two-compartment model of B-cell chronic lymphocytic leukemia

In this paper,we study the dynamical behavior of a stochastic two-compartment model of B-cell chronic lymphocytic leukemia,which is perturbed by white noise.Firstly,by constructing suitable Lyapunov functions,we establish sufficient conditions for the existence of a unique ergodic stationary distribution.Then,conditions for extinction of the disease are derived.Furthermore,numerical simulations are presented for supporting the theoretical results.Our results show that large noise intensity may contribute to extinction of the disease.