In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the mo...In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R0. If the basic reproduction number R0〈 1, the disease- free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R0 〉 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.展开更多
In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection a...In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 〈 1, the infection-free equilibrium P0 is globally asymptotically stable. If R1 〈 1 〈 R0, the asymptomatic-carrier equilibrium P1 is globally asymptotically stable. If R1 〉 1, there exists a unique HAM/TSP equilibrium P2. The stability of P2 is changed when the second delay T2 varies, that is there exist stability switches for P2.展开更多
文摘In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R0. If the basic reproduction number R0〈 1, the disease- free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R0 〉 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.
基金Acknowledgments The authors would like to thank the reviewers＇ constructive suggestions which have improved the presentation of the paper. This research is supported by National Natural Science Foundation of China （No. 11371111）, the Research Fund for the Doctoral Program of Higher Education of China （No. 20122302110044） and Shandong Provincial Natural Science Foundation, China （No. ZR2013AQ023）.
文摘In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R0 and R1, basic reproduction numbers for viral infection and for CTL response, respectively. If R0 〈 1, the infection-free equilibrium P0 is globally asymptotically stable. If R1 〈 1 〈 R0, the asymptomatic-carrier equilibrium P1 is globally asymptotically stable. If R1 〉 1, there exists a unique HAM/TSP equilibrium P2. The stability of P2 is changed when the second delay T2 varies, that is there exist stability switches for P2.
