首先建立了一类具常恢复率,有效接触率依赖于总人数的SIQS传染病模型,并得到了阈值参数σ的表达式.如果σ≤1,则疾病消除平衡点全局稳定;如果σ>1,则存在唯一的传染病平衡点且是局部渐近稳定的。对于带有双线性传染率和标准传染率的...首先建立了一类具常恢复率,有效接触率依赖于总人数的SIQS传染病模型,并得到了阈值参数σ的表达式.如果σ≤1,则疾病消除平衡点全局稳定;如果σ>1,则存在唯一的传染病平衡点且是局部渐近稳定的。对于带有双线性传染率和标准传染率的两个相应模型,我们进一步证明了当σ>1时传染病平衡点的全局稳定性。其次对于带隔离项修正的传染率的相应模型,我们同样证明了传染病平衡点只要存在唯一就一定全局稳定的结论。上述结果均推广和改进了Hethcote et al.(2002)的相应工作。展开更多
A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are in...A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.展开更多
A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally as...A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.展开更多
We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by th...We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold Ro. If Ro 〈 1, the virusfree equilibrium is globally asymptotically stable, and if R0 〉 1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.展开更多
In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the...In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.展开更多
文摘首先建立了一类具常恢复率,有效接触率依赖于总人数的SIQS传染病模型,并得到了阈值参数σ的表达式.如果σ≤1,则疾病消除平衡点全局稳定;如果σ>1,则存在唯一的传染病平衡点且是局部渐近稳定的。对于带有双线性传染率和标准传染率的两个相应模型,我们进一步证明了当σ>1时传染病平衡点的全局稳定性。其次对于带隔离项修正的传染率的相应模型,我们同样证明了传染病平衡点只要存在唯一就一定全局稳定的结论。上述结果均推广和改进了Hethcote et al.(2002)的相应工作。
基金This work is supported by National Natural Science Foundation of China (10171106)the Special Fund for Major State Basic Research Projects (G1999032805)
文摘A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.
基金Supported by National Natural Science Foundation of China (Grant No. 10971021)the Ministry of Education of China (Grant No. 109051)+1 种基金the Ph.D. Programs Foundation of Ministry of China (Grant No. 200918)the Graduate Innovative Research Project of NENU (Grant No. 09SSXT117)
文摘A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.
文摘We study a proposed model describing the propagation of computer virus in the network with antidote in vulnerable system. Mathematical analysis shows that dynamics of the spread of computer viruses is determined by the threshold Ro. If Ro 〈 1, the virusfree equilibrium is globally asymptotically stable, and if R0 〉 1, the endemic equilibrium is globally asymptotically stable. Lyapunov functional method as well as geometric approach are used for proving the global stability of equilibria. A numerical investigation is carried out to confirm the analytical results. Through parameter analysis, some effective strategies for eliminating viruses are suggested.
基金supported by the National Natural Science Foundation of China (No.12231008 and No.11971185)。
文摘In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.
