In this paper, we consider two nonlinear models for viral infection with humoraL immu- nity. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cel...In this paper, we consider two nonlinear models for viral infection with humoraL immu- nity. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The second model is a modification of the first one by including the latently infected cells. The incidence rate, removal rate of infected cells, production rate of viruses and the latent-to-active conversion rate are given by more general nonlinear functions. We have established a set of conditions on these general functions and determined two threshold parameters for each model which are sufficient to determine the global dynamics of the models. The global asymptotic stability of all equilibria of the models has been proven by using Lyapunov theory and applying LaSalle＇s invariance principle. We have performed some numerical simulations for the models with specific forms of the general functions. We have shown that, the numerical results are consistent with the theoretical results.展开更多
A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attracti...A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attractivity of the model is studied using Lyapunov functions and LaSalle＇s invariance principle. By the uniform persistence theories, the permanence of the system and the existence of the positive equilibrium are obtained. Moreover, by the normal form theory and the center manifold presented by Hassard, a stability and Hopf bifurcation analysis of the system around positive equilibrium from a local perspective are performed. Numerical simulation is carried out to illustrate our results.展开更多
This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance pri...This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.展开更多
文摘In this paper, we consider two nonlinear models for viral infection with humoraL immu- nity. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The second model is a modification of the first one by including the latently infected cells. The incidence rate, removal rate of infected cells, production rate of viruses and the latent-to-active conversion rate are given by more general nonlinear functions. We have established a set of conditions on these general functions and determined two threshold parameters for each model which are sufficient to determine the global dynamics of the models. The global asymptotic stability of all equilibria of the models has been proven by using Lyapunov theory and applying LaSalle＇s invariance principle. We have performed some numerical simulations for the models with specific forms of the general functions. We have shown that, the numerical results are consistent with the theoretical results.
文摘A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attractivity of the model is studied using Lyapunov functions and LaSalle＇s invariance principle. By the uniform persistence theories, the permanence of the system and the existence of the positive equilibrium are obtained. Moreover, by the normal form theory and the center manifold presented by Hassard, a stability and Hopf bifurcation analysis of the system around positive equilibrium from a local perspective are performed. Numerical simulation is carried out to illustrate our results.
基金supported by the National Natural Science Fundation of China under Grant No.60874006
文摘This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.
