A multi-group epidemic model with a variables separated incidence rate and delays is analyzed. For strongly and non-strongly connected networks, the basic reproductive number Ro is calculated, respectively. By applyin...A multi-group epidemic model with a variables separated incidence rate and delays is analyzed. For strongly and non-strongly connected networks, the basic reproductive number Ro is calculated, respectively. By applying the Lyapunov functionals and the LaSalle invariance principle, we prove the global asymptotic stability of infection-free equilibrium P0 when Ro 〈 1 and the endemic equilibrium P＊ when Ro 〉 1.展开更多
In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vacc...In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investi- gated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.展开更多
In this paper, a susceptible-exposed infective-recovered-susceptible （SEIRS） epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group ...In this paper, a susceptible-exposed infective-recovered-susceptible （SEIRS） epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.展开更多
基金Supported by Weihai Science and Technology Development Plan Project(Grant No.2013DXGJ06)the Natural Science Foundation of Shandong Province(Grant No.ZR2015AM018)
文摘A multi-group epidemic model with a variables separated incidence rate and delays is analyzed. For strongly and non-strongly connected networks, the basic reproductive number Ro is calculated, respectively. By applying the Lyapunov functionals and the LaSalle invariance principle, we prove the global asymptotic stability of infection-free equilibrium P0 when Ro 〈 1 and the endemic equilibrium P＊ when Ro 〉 1.
基金This research was supported by grants from the Shandong Provincial Natural Science Foundation of China （No. ZR2015AM018）, and Chinese NSF Grants （Nos. 11671110 and 11201097）.
文摘In this paper, a multi-group SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible after the vaccine loses its protective properties, and the vaccination classes satisfy first-order the partial differential equations structured by vaccination age. Combining the Lyapunov functional method with a graph-theoretic approach, we show that the global stability of endemic equilibrium for the strongly connected system is determined by the basic reproduction number. In addition, the dynamics for non-strongly connected model are also investi- gated, depending on the basic reproduction numbers corresponding to each strongly connected component. Numerical simulations are carried out to support the theoretical conclusions.
基金This research is supported by National Natural Science Foundation of China （No. 11371111）, Weihai Science and Technology Development Plan Project （No. 2013DXGJ06） and Shandong Provincial Natural Science Foundation of China （No. ZR2015AM018）.
文摘In this paper, a susceptible-exposed infective-recovered-susceptible （SEIRS） epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.
