A delayed SEIR epidemic model with vertical transmission and non-inonotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. Th...A delayed SEIR epidemic model with vertical transmission and non-inonotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. The local stability of disease-free equilib- rium and endemic equilibrium is established by analyzing the corresponding character- istic equations. By comparison arguments, it is proved that, if Ro 〈 1, the disease-free equilibrium is globally asymptotically stable. Whereas, the disease-free equilibrium is unstable if R0 〉 1. Moreover, we show that the disease is permanent if the basic repro- duction number is greater than one. Furthermore, the sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium when R0 〉 1.展开更多
文摘A delayed SEIR epidemic model with vertical transmission and non-inonotonic incidence is formulated. The equilibria and the threshold of the model have been determined on the bases of the basic reproduction number. The local stability of disease-free equilib- rium and endemic equilibrium is established by analyzing the corresponding character- istic equations. By comparison arguments, it is proved that, if Ro 〈 1, the disease-free equilibrium is globally asymptotically stable. Whereas, the disease-free equilibrium is unstable if R0 〉 1. Moreover, we show that the disease is permanent if the basic repro- duction number is greater than one. Furthermore, the sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium when R0 〉 1.
