A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium ...A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.展开更多
In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqu...In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.展开更多
文摘A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.
基金This work is supported by the National Natural Science Foundation of China(Nos.12001090 and 11871473)Shandong Provincial Natural Science Foundation(No.ZR2019MA010)the Fundamental Research Funds for the Central Universitiesof China(No.2412020QD024).
文摘In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.
