Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynami...Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynamical behavior of this model and define the basic reproductive number R0. The authors also prove that the diseased-free equilibrium is globally asymptotically stable if R0 〈 1. The endemic equilibrium is locally asymptotically stable if K1 〉 α and R0 〉 1.展开更多
An age-structured SEIR epidemic model of a vertically as well as horizontally transmitted disease is investigated. Threshold results for the existence of endemic states are established for most cases. Under certain co...An age-structured SEIR epidemic model of a vertically as well as horizontally transmitted disease is investigated. Threshold results for the existence of endemic states are established for most cases. Under certain conditions, uniqueness is also shown. Threshold used are explicitly computable in term of demographic and epiderniological parameters of the model.展开更多
Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonline...Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.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 National Natural Sciences Foundation of China (10471040)the University Foundation of Yuncheng University (20060218)
文摘Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynamical behavior of this model and define the basic reproductive number R0. The authors also prove that the diseased-free equilibrium is globally asymptotically stable if R0 〈 1. The endemic equilibrium is locally asymptotically stable if K1 〉 α and R0 〉 1.
基金Supported by the Natural Science Foundation of Henan Province(No.0312002000 and No.0211044800)the National Natural Science Foundation of China(No.10371105).
文摘An age-structured SEIR epidemic model of a vertically as well as horizontally transmitted disease is investigated. Threshold results for the existence of endemic states are established for most cases. Under certain conditions, uniqueness is also shown. Threshold used are explicitly computable in term of demographic and epiderniological parameters of the model.
基金Supported by the NSF of China(No.10971178No.10911120387)+1 种基金the Sciences Foundation of Shanxi(20090110053)the Sciences Exploited Foundation of Shanxi(20081045)
文摘Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.
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.
