In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
This paper formulates an SEIRSHM epidemic model with general birth rate,media report and limited medical resources.Firstly,the well-posedness of the solutions and the extinction of the disease are discussed.Then,the e...This paper formulates an SEIRSHM epidemic model with general birth rate,media report and limited medical resources.Firstly,the well-posedness of the solutions and the extinction of the disease are discussed.Then,the existence of the endemic equilibrium is discussed and we find when R^(*)>1 and R0=1,there exhibits a backward bifurcation,if R^(*)<1 and R0=1,there exhibits a forward bifurcation.Finally,numerical simulations are carried out to illustrate the main results and show that media report and limited medical resources have a great impact on disease transmission.展开更多
In this paper,we investigate the global dynamics of a predator-prey model with a general growth rate function and carrying capacity.We prove that the origin is unstable using the blow-up method.Also,by constructing a ...In this paper,we investigate the global dynamics of a predator-prey model with a general growth rate function and carrying capacity.We prove that the origin is unstable using the blow-up method.Also,by constructing a new Lyapunov function and using LaSalle’s invariance principle,we obtain the global stability of the positive equilibrium state of the system.In addition,the system undergoes the Hopf bifurcation at the positive equilibrium point when the predator birth rateδis used as the bifurcation parameter.Finally,two examples are given to verify the feasibility of the theoretical results.One example is given to reconsider the global stability of the positive equilibrium of a Leslie-Gower predator-prey model with prey cannibalism,and the obtained results confirm the conjecture proposed by Lin et al.(Adv Differ Equ 2020,153,2020).The other example is given to verify the occurrence of the Hopf bifurcation of a Leslie-Gower predator-prey model with a square root response function,and obtain the Hopf bifurcation diagram by the numerical simulation.展开更多
In this paper we study the stability analysis of two within-host Chikungunya virus （CHIKV） dynamics models. The incidence rate between the CHIKV and the uninfected mouocytes is modeled by a general nonlinear functio...In this paper we study the stability analysis of two within-host Chikungunya virus （CHIKV） dynamics models. The incidence rate between the CHIKV and the uninfected mouocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes （i） latently infected monocytes which do not generate CHIKV and （ii） actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.展开更多
In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then t...In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then the ergodicity of these processes is proved.展开更多
Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unb...Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.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
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
基金supported by the National Natural Science Foundation(12201540)the Natural Science Foundation of Xinjiang Uygur Autonomous Region,China(2022D01C64)the Doctoral Research Initiation Fund of Xinjiang University,China(620320024).
文摘This paper formulates an SEIRSHM epidemic model with general birth rate,media report and limited medical resources.Firstly,the well-posedness of the solutions and the extinction of the disease are discussed.Then,the existence of the endemic equilibrium is discussed and we find when R^(*)>1 and R0=1,there exhibits a backward bifurcation,if R^(*)<1 and R0=1,there exhibits a forward bifurcation.Finally,numerical simulations are carried out to illustrate the main results and show that media report and limited medical resources have a great impact on disease transmission.
基金supported by the National Natural Science Foundation of China(11672074)the Natural Science Foundation of Fujian Province,China(2022J01192).
文摘In this paper,we investigate the global dynamics of a predator-prey model with a general growth rate function and carrying capacity.We prove that the origin is unstable using the blow-up method.Also,by constructing a new Lyapunov function and using LaSalle’s invariance principle,we obtain the global stability of the positive equilibrium state of the system.In addition,the system undergoes the Hopf bifurcation at the positive equilibrium point when the predator birth rateδis used as the bifurcation parameter.Finally,two examples are given to verify the feasibility of the theoretical results.One example is given to reconsider the global stability of the positive equilibrium of a Leslie-Gower predator-prey model with prey cannibalism,and the obtained results confirm the conjecture proposed by Lin et al.(Adv Differ Equ 2020,153,2020).The other example is given to verify the occurrence of the Hopf bifurcation of a Leslie-Gower predator-prey model with a square root response function,and obtain the Hopf bifurcation diagram by the numerical simulation.
文摘In this paper we study the stability analysis of two within-host Chikungunya virus （CHIKV） dynamics models. The incidence rate between the CHIKV and the uninfected mouocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes （i） latently infected monocytes which do not generate CHIKV and （ii） actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.
基金Ying-Tung Fok Education Foundation and NSFCNSFC and by Anhui Education Commitee..
文摘In this paper,a class of reaction diffusion processes with general reaction rates is studied.A necessary and sufficient condition for the reversibility of this calss of reaction diffusion processes is given,and then the ergodicity of these processes is proved.
基金Supported by National Natural Science Foundation of China （Grant No. 11001091） and Chinese University Research Foundation （Grant No. 2010MS129）
文摘Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence^and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.
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.
