In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotica...In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.展开更多
In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system...In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.展开更多
A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-fr...A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-free and infection equilibria is discussed, respectively. Further, the existence of an orbitally asymptotically stable periodic orbit is also studied. By means of the theory of competitive systems and compound matrices, sufficient conditions are derived for the global stability of the infection-free and infection equilibria, respectively. At last, numerical simulations are carried out to illustrate the main results.展开更多
基金Supported by the National Natural Science Foundation of China(11101323)Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2014JQ1038)Supported by the Xi’an Polytechnic University Innovation Fund for Graduate Students(CX201608)
文摘In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.
基金This work was supported by the National Natural Science Foundation of China （11371368）, the Nature Science Foundation for Young Scientists of Hebei Province, China （A2013506012） and Basic Courses Department of Mechanical Engineering College Foundation （JCKY1507）.
文摘In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.
文摘A hepatitis B virus （HBV） model with standard incidence and the uninfected cells growing logistically is investigated. By analyzing the corresponding characteristic equations, the local stability of the infection-free and infection equilibria is discussed, respectively. Further, the existence of an orbitally asymptotically stable periodic orbit is also studied. By means of the theory of competitive systems and compound matrices, sufficient conditions are derived for the global stability of the infection-free and infection equilibria, respectively. At last, numerical simulations are carried out to illustrate the main results.
