The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells.The existence of steady states is determined by the basic reproduction number of virus.Wit...The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells.The existence of steady states is determined by the basic reproduction number of virus.With the Lyapunov's direct method,they establish a threshold dynamics of the model with the basic reproduction number of virus as the threshold parameter.To achieve it,a novel procedure is proposed.Its novelties are two-folded.On one hand,the coefficients involved in the specific forms of the used Lyapunov functionals for the two feasible steady states are determined by the same set of inequalities.On the other hand,for the infection steady state,a new approach is proposed to check whether the derivative of the Lyapunov functional candidate along solutions is negative(semi-)definite or not.This procedure not only simplifies the analysis but also exhibits the relationship between the two Lyapunov functionals for the two feasible steady states.Moreover,the procedure is expected to be applicable for other similar models.展开更多
In this paper, the sharp threshold properties of a （2n ＋ 1）-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells a...In this paper, the sharp threshold properties of a （2n ＋ 1）-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells and nonlinear incidence rate h（x,v）. Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model.展开更多
This paper is devoted to the study of the stability of a CD4^＋ T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analy...This paper is devoted to the study of the stability of a CD4^＋ T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value R0 ≤1; the endemic equilibrium is globally asymptotically stable if R0 〉 1 and du^＊ - δw^＊ ≥0. Finally, we give an application and numerical simulations to illustrate the main results.展开更多
In this paper, we investigate global dynamics for a distributed time delayed HCV infec tion model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic re...In this paper, we investigate global dynamics for a distributed time delayed HCV infec tion model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. By employing the method of Lyapunov functional, we prove that the uninfected equilibrium is global asymptotically stable if the basic reproduction number is less than one, it is unsta ble and the infected equilibrium is global asymptotically stable if the basic reproduction number is larger than one. The simulations results are in good accordance with our analytic results.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11971281,12071268,12071418)the NSERC of Canada(No.RGPIN-2019-05892)+1 种基金the Natural Science Basic Research Program of Shaanxi(Nos.2022JM-029,2023-JC-QN-0090)the Scientific Research Fund of Xi’an Medical University(No.2022JG-53)。
文摘The authors propose and analyze a viral infection model with defectively infected cells and age of the latently infected cells.The existence of steady states is determined by the basic reproduction number of virus.With the Lyapunov's direct method,they establish a threshold dynamics of the model with the basic reproduction number of virus as the threshold parameter.To achieve it,a novel procedure is proposed.Its novelties are two-folded.On one hand,the coefficients involved in the specific forms of the used Lyapunov functionals for the two feasible steady states are determined by the same set of inequalities.On the other hand,for the infection steady state,a new approach is proposed to check whether the derivative of the Lyapunov functional candidate along solutions is negative(semi-)definite or not.This procedure not only simplifies the analysis but also exhibits the relationship between the two Lyapunov functionals for the two feasible steady states.Moreover,the procedure is expected to be applicable for other similar models.
基金The authors would like to thank the anonymous referees and the editor for very helpful suggestions and comments which led to improvements of our orig- inal paper. J. Wang was supported by National Natural Science Foundation of China （Nos. 11401182 and 11471089）, Natural Science Foundation of Heilongjiang Province （No. A201415）, Science and Technology Innovation Team in Higher Edu- cation Institutions of Heilongjiang Province （No. 2014TD005）, Project funded by China Postdoctoral Science Foundation （No. 2014M552295） and Project funded by Chongqing Postdoctoral Foundation （No. Xm2014024）. X. Wang is supported by the National Natural Science Foundation of China （No. 11301453）, Postdoctoral Science Foundation of China （No. 2014M562366）, Postdoctoral Science Foundation of Shaanxi Province （No. 2014010）, the Universities Young Teachers Program of Henan Province （No. 2014GGJS-093）.
文摘In this paper, the sharp threshold properties of a （2n ＋ 1）-dimensional delayed viral infection model are investigated. This model combines with n classes of uninfected tar- get cells, n classes of infected cells and nonlinear incidence rate h（x,v）. Two kinds of distributed time delays are incorporated into the model to describe the time needed for infection of uninfected target cells and virus replication. Under certain conditions, it is shown that the basic reproduction number is a threshold parameter for the existence of the equilibria, uniform persistence, as well as for global stability of the equilibria of the model.
文摘This paper is devoted to the study of the stability of a CD4^＋ T cell viral infection model with diffusion. First, we discuss the well-posedness of the model and the existence of endemic equilibrium. Second, by analyzing the roots of the characteristic equation, we establish the local stability of the virus-free equilibrium. Furthermore, by constructing suitable Lyapunov functions, we show that the virus-free equilibrium is globally asymptotically stable if the threshold value R0 ≤1; the endemic equilibrium is globally asymptotically stable if R0 〉 1 and du^＊ - δw^＊ ≥0. Finally, we give an application and numerical simulations to illustrate the main results.
文摘In this paper, we investigate global dynamics for a distributed time delayed HCV infec tion model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. By employing the method of Lyapunov functional, we prove that the uninfected equilibrium is global asymptotically stable if the basic reproduction number is less than one, it is unsta ble and the infected equilibrium is global asymptotically stable if the basic reproduction number is larger than one. The simulations results are in good accordance with our analytic results.
