Global Stability in a Graph p-Laplacian SIR Epidemic ModelS

A p-Laplacian ( p > 2 ) reaction-diffusion system on weighted graphs is introduced to a networked SIR epidemic model. After overcoming difficulties caused by the nonlinear p-Laplacian, we show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number r0 is greater than 1, while the disease-free equilibrium is globally asymptotically stable if r0 is lower than 1. We extend the stability results of SIR models with graph Laplacian ( p = 2 ) to general graph p-Laplacian.

Global Stability of An Eco-epidemiological Model with Beddington-DeAngelis Functional Response and Delay

In this paper,an eco-epidemiological model with Beddington-DeAngelis functional response and a time delay representing the gestation period of the predator is studied.By means of Lyapunov functionals and Laselle’s invariance principle,sufficient conditions are obtained for the global stability of the interior equilibrium and the disease-free equilibrium of the system,respectively.

Fuzzy Global Stability Analysis of the Dynamics of Malaria with Fuzzy Transmission and Recovery Rates

In this paper, fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (), we reach the model disease-free equilibrium. Using Choquet integral, the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible, Exposed, Infected, Recovered, susceptible-Susceptible, Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium is globally asymptotically stable if or if the basic reproduction number is less than one (). When and , there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set . Finally, the numerical simulation has been done for showing the effectiveness of our analytical results.

GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D MAGNETIC BéNARD PROBLEM

In this paper,we consider the 3D magnetic Bénard problem.More precisely,we prove that the large solutions are stable under certain conditions.And we obtain the equivalent condition with respect to this stability condition.Finally,we also establish the stability of 2 D magnetic Bénard problem under 3D perturbations.

Impulsive efects on global stability of models based on impulsive diferential equations with “supremum” and variable impulsive perturbations

Sufcient conditions are investigated for the global stability of the solutions to models based on nonlinear impulsive diferential equations with "supremum" and variable impulsive perturbations. The main tools are the Lyapunov functions and Razumikhin technique. Two illustrative examples are given to demonstrate the efectiveness of the obtained results.

Global Stability in Dynamical Systems with Multiple Feedback Mechanisms

A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C1 functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.

Global Stability for a Diffusive System with Time Delay and Functional Response

In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.

Global Stability of a Three-Species System with Attractive Prey-Taxis

This paper reports the global asymptotic stability of a three-species predator-prey system involving the prey-taxis. With the assumptions, we establish the global asymptotic stability results of its equilibria, respectively. Our results illustrate that 1) the global asymptotic stability of the semi-trivial equilibrium does not involve the prey-taxis coefficients χ, ξ;2) the global asymptotic stability of two boundary equilibria relies on a single prey-taxis coefficient χ and ξ, respectively;3) the global asymptotic stability of the unique positive equilibrium depends on two prey-taxis coefficients χ and ξ.

Global Stability and Hopf Bifurcation for a Virus Dynamics Model with General Incidence Rate and Delayed CTL Immune Response

In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E*0, CTL-inactivated infection equilibrium E*1 and CTL-activated infection equilibrium E*2. We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R0 and R1, if R0 ≤ 1, E*0 is globally asymptotically stable, if R1 ≤ 1 < R0, E*1 is globally asymptotically stable and if R1 >1, E*2 is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E*2 changes completely, although R1 > 1, a Hopf bifurcation at E*2 is established. In the end, we present some numerical simulations.

The global stability and optimal control of the COVID-19 epidemic model

This paper considers stability analysis of a Susceptible-Exposed-Infected-Recovered-Virus(SEIRV)model with nonlinear incidence rates and indicates the severity and weakness of control factors for disease transmission.The Lyapunov function using Volterra-Lyapunov matrices makes it possible to study the global stability of the endemic equilibrium point.An optimal control strategy is proposed to prevent the spread of coronavirus,in addition to governmental intervention.The objective is to minimize together with the quantity of infected and exposed individuals while minimizing the total costs of treatment.A numerical study of the model is also carried out to investigate the analytical results.

Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate

A four-dimensional delay differential equations(DDEs)model of malaria with standard incidence rate is proposed.By utilizing the limiting system of the model and Lyapunov direct method,the global stability of equilibria of the model is obtained with respect to the basic reproduction number R_(0).Specifically,it shows that the disease-free equilibrium E^(0)is globally asymptotically stable(GAS)for R_(0)<1,and globally attractive(GA)for R_(0)=1,while the endemic equilibrium E^(*)is GAS and E^(0)is unstable for R_(0)>1.Especially,to obtain the global stability of the equilibrium E^(*)for R_(0)>1,the weak persistence of the model is proved by some analysis techniques.

Global stability of bistable traveling wavefronts for a three-species Lotka-Volterra competition system with nonlocal dispersal

This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.

Global stability and optim al control of a two-patch tuberculosis epidemic model using fractional-order derivatives

In this paper,we propose a fractional-order and two-patch model of tuberculosis(TB)epidemic,in which susceptible,slow latent,fast latent and infectious individuals can travel freely between the patches,but not under treatment infected individuals,due to medical reasons.We obtain the basic reproduction number Ro for the model and extend the classical LaSalle's invariance principle for fractional differential equations.We show that if R0<1,the disease-free equilibrium(DFE)is locally and globally asymptotically stable.If Ro>l,we obtain sufficient conditions under which the endernic equilibrium is unique and globally asymptotically stable.We extend the model by inclusion the time-dependent controls(effective treatment controls in both patches and controls of screening on travel of infectious individuals between patches),and formulate a fractional optimal control problem to reduce the spread of the disease.The numerical results show that the use of all controls has the most impact on disease control,and decreases the size of all infected compartments,but increases the size of susceptible compartment in both patches.We,also,investigate the impact of the fractional derivative order a on the values of the controls(0.7≤α≤1).The results show that the maximum levels of effective treatment controls in both patches increase when a is reduced from l,while the maximum level of the travel screening control of infectious individuals from patch 2 to patch 1 increases when o limits to 1.

Global Stability of a Mumps Transmission Model with Quarantine Measure

In this paper,a model of mumps transmission with quarantine measure is proposed and then the control reproduction number Rc of the model is obtained.This model admits a unique endemic equilibrium P*if and only if Rc>1,while the disease-free equilibrium P0 always exists.By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem,we first show that the equilibrium P0 is globally asymptotically stable(GAS)if Rc≤1;second,we prove that the equilibrium P*is GAS if Rc>1.Our results reveal that mumps can be eliminated from the community for Rc≤1 and it will be persistent for Rc>1,and quarantine measure can also effectively control the mumps transmission.

Almost Periodic Solution and Global Stability for Cooperative L-V Diffusion System

In this paper a nonautonomous two-species n-patches system is studied.Within each patch,there are two cooperative species and their dynamics are described by the LotkaVolterra model.Each species can diffuse independently and discretely between its interpatch and intrapatch.By constructing a suitable Liapunov function,some sufficient conditions are obtained for the existence of a unique globally asymptotically stable positive almost periodic solution.

PERMANENCE AND GLOBAL STABILITY OF A DISCRETE COOPERATION SYSTEM

In this paper,a discrete cooperation system is studied. Sufficient conditions which guarantee the permanence and global stability of such system are obtained.

PERMANENCE AND GLOBAL STABILITY OF POSITIVE SOLUTIONS TO TWO PREDATORSONE PREY SYSTEM WITH A DISCRETE TIME RATIO-DEPENDENT

A three-species ratio-dependent predator-prey discrete model is studied.As a result,sufficient conditions which guarantee the permanence of the model are obtained. In addition,by constructing a suitable Lyapunov function,we derive some sufficient conditions,which ensure that the positive solution of the model is stable and attracts all positive solutions.To illustrate the feasibility of the main results,we introduce an example with corresponding numeric simulations.

PERMANENCE AND GLOBAL STABILITY OF A DELAYED RATIO-DEPENDENT PREDATOR-PREY MODEL WITH STAGE STRUCTURE

A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.

GLOBAL STABILITY FOR MICHAELIS-MENTEN SINGLE-SPECIES GROWTH EQUATIONS

Consider the so-called Michaelis-Menten single-species growth equation with.ai,ti∈(0,+∞),ci∈(0,1),r(t)∈C([0,∞),(0,+∞)),ai(1+ci)-1=1and n is a positive integer. We establish a new sufficient condition for the global stability of the positive equilibrium N*=1. This condition generalizes and improves some known results and is different from a recent result of Yu J.S..

Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .