In this paper, a class of SEIQV epidemic model with general nonlinear incidence rate is investigated. By constructing Lyapunov function, it is shown that the disease-free equilibrium is globally asymptotically stable ...In this paper, a class of SEIQV epidemic model with general nonlinear incidence rate is investigated. By constructing Lyapunov function, it is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R0 ≤ 1. If R0 〉 1, we show that the endemic equilibrium is globally asymptotically stable by applying Li and Muldowney geometric approach.展开更多
This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are...This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the “Disease-Free Equilibrium” （DFE） and “Endemic Equilibrium” （EE） are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number R0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.展开更多
In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by t...In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.展开更多
In this paper, we study the spreading of infections on complex heterogeneous networks based on an SEIRS epidemic model with nonlinear infectivity. By mathematical analysis, the basic reproduction number R0 is obtained...In this paper, we study the spreading of infections on complex heterogeneous networks based on an SEIRS epidemic model with nonlinear infectivity. By mathematical analysis, the basic reproduction number R0 is obtained. When R0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R0 is greater than one, the disease-free equilibrium becomes unstable and the disease is permanent, and in the meantime there exists a unique endemic equilibrium which is globally attrac- tive under certain conditions. Finally, the effects of various immunization schemes are studied. To verify our theoretical results, the corresponding numerical simulations are also included.展开更多
Age and infection age have significant influence on the transmission of infectious dis- eases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dyna...Age and infection age have significant influence on the transmission of infectious dis- eases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dynamics of the disease spread. The basic reproduction number R0 is defined and used as the threshold parameter to character- ize the disease extinction or persistence. It is shown that the disease-free equilibrium is globally stable if R0 〈 1, and it is unstable if R0 〉 1. When R0 〉 1, there exists an endemic equilibrium, and the disease is uniformly persistent. The stability of the endemic equilibrium is investigated numerically.展开更多
基金The first author was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ14A010004.
文摘In this paper, a class of SEIQV epidemic model with general nonlinear incidence rate is investigated. By constructing Lyapunov function, it is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R0 ≤ 1. If R0 〉 1, we show that the endemic equilibrium is globally asymptotically stable by applying Li and Muldowney geometric approach.
文摘This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the “Disease-Free Equilibrium” （DFE） and “Endemic Equilibrium” （EE） are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number R0 is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.
文摘In this paper, we introduce stochasticity into an SIR epidemic model with vaccina- tion. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number R0. If R0 ≤ 1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If R0 〉 1, there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail.
文摘In this paper, we study the spreading of infections on complex heterogeneous networks based on an SEIRS epidemic model with nonlinear infectivity. By mathematical analysis, the basic reproduction number R0 is obtained. When R0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R0 is greater than one, the disease-free equilibrium becomes unstable and the disease is permanent, and in the meantime there exists a unique endemic equilibrium which is globally attrac- tive under certain conditions. Finally, the effects of various immunization schemes are studied. To verify our theoretical results, the corresponding numerical simulations are also included.
文摘Age and infection age have significant influence on the transmission of infectious dis- eases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dynamics of the disease spread. The basic reproduction number R0 is defined and used as the threshold parameter to character- ize the disease extinction or persistence. It is shown that the disease-free equilibrium is globally stable if R0 〈 1, and it is unstable if R0 〉 1. When R0 〉 1, there exists an endemic equilibrium, and the disease is uniformly persistent. The stability of the endemic equilibrium is investigated numerically.
