共查询到20条相似文献，搜索用时 15 毫秒
1.
《Mathematical Methods in the Applied Sciences》2018,41(5):1966-1987
In this paper, we propose a host‐vector model for malaria transmission by incorporating infection age in the infected host population and nonlinear incidence for transmission from infectious vectors to susceptible hosts. One novelty of the model is that the recovered hosts only have temporary immunity and another is that successfully recovered infected hosts may become susceptible immediately. Firstly, the existence and local stability of equilibria is studied. Secondly, rigorous mathematical analyses on technical materials and necessary arguments, including asymptotic smoothness and uniform persistence of the system, are given. Thirdly, by applying the fluctuation lemma and the approach of Lyapunov functionals, the threshold dynamics of the model for a special case were established. Roughly speaking, the disease‐free equilibrium is globally asymptotically stable when the basic reproduction number is less than one and otherwise the endemic equilibrium is globally asymptotically stable when no reinfection occurs. It is shown that the infection age and nonlinear incidence not only impact on the basic reproduction number but also could affect the values of the endemic steady state. Numerical simulations were performed to support the theoretical results. 相似文献
2.
Jianquan Li Yali Yang Yanni Xiao Shuo Liu 《Journal of Applied Analysis & Computation》2016,6(1):38-46
In this paper, by investigating an SIR epidemic model with nonlinear incidence, we present a new technique for proving the global stability of the endemic equilibrium, which consists of introducing a variable transformation and constructing amore general Lyapunov function. For the model we obtain the following results. The disease-free equilibrium is globally stable in the feasible region as the basic reproduction number is less than or equal to unity, and the endemic equilibrium is globally stable in the feasible region as the basic reproduction number is greater than unity.The generality of the technique is illustrated by considering certain nonlinear incidences and SIS and SIRS epidemic models. 相似文献
3.
In this article,we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlinear incidence rates and distributed... 相似文献
4.
In this paper, we perform global stability analysis of a multi‐group SEIR epidemic model in which we can consider the heterogeneity of host population and the effects of latency and nonlinear incidence rates. For a simpler version that assumes an identical natural death rate for all groups, and with a gamma distribution for the latency, the basic reproduction number is defined by the theory of the next generation operator and proved to be a sharp threshold determining whether or not disease spread. Under certain assumptions, the disease‐free equilibrium is globally asymptotically stable if R0≤1 and there exists a unique endemic equilibrium which is globally asymptotically stable if R0>1. The proofs of global stability of equilibria exploit a matrix‐theoretic method using Perron eigenvetor, a graph‐theoretic method based on Kirchhoff's matrix tree theorem and Lyapunov functionals. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
Qiang Hou 《Journal of Applied Analysis & Computation》2016,6(4):1023-1040
The transmission mechanism of some animal diseases is complex because of the multiple transmission pathways and multiple-group interactions, which lead to the limited understanding of the dynamicsof these diseases transmission. In this paper, a delay multi-group dynamic model is proposed in which time delay is caused by the latency of infection. Under the biologically motivated assumptions, the basic reproduction number $R_0$ is derived and then the global stability of the disease-free equilibrium and the endemic equilibrium is analyzed by Lyapunov functionals and a graph-theoretic approach as for time delay. The results show the global properties of equilibria only depend on the basic reproductive number $R_0$: the disease-free equilibrium is globally asymptotically stable if $R_0leq 1$; if $R_0>1$, the endemic equilibrium exists and is globally asymptotically stable, which implies time delay span has no effect on the stability of equilibria. Finally, some specific examples are taken to illustrate the utilization of the results and then numerical simulations are used for further discussion. The numerical results show time delay model may experience periodic oscillation behaviors, implying that the spread of animal diseases depends largely on the prevention and control strategies of all sub-populations. 相似文献
6.
Yuming Chen Jianquan Li Shaofen Zou 《Mathematical Methods in the Applied Sciences》2019,42(4):1283-1291
On the basis of a basic SIR epidemic model, we propose and study an epidemic model with nonlinear incidence. The model also incorporates many features of the recovered such as relapse and with/without immunity. A threshold dynamics is established, which is completely determined by the basic reproduction number. The global stability of the disease‐free equilibrium is proved by means of the fluctuation lemma. To prove the global stability of the endemic equilibrium, we need some novel techniques including the transformation of variables, the construction of a new type of Lyapunov functions, and the seeking of an appropriate positively invariant set of the model. 相似文献
7.
An infection‐age virus dynamics model for human immunodeficiency virus (or hepatitis B virus) infections with saturation effects of infection rate and immune response is investigated in this paper. It is shown that the global dynamics of the model is completely determined by two critical values R 0, the basic reproductive number for viral infection, and R 1, the viral reproductive number at the immune‐free infection steady state (R 1<R 0). If R 0<1, the uninfected steady state E 0 is globally asymptotically stable; if R 0>1 > R 1, the immune‐free infected steady state E ? is globally asymptotically stable; while if R 1>1, the antibody immune infected steady state is globally asymptotically stable. Moreover, our results show that ignoring the saturation effects of antibody immune response or infection rate will result in an overestimate of the antibody immune reproductive number. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
讨论了一类具有非线性传染力的阶段结构 SI传染病模型 ,确定了各类平衡点存在的阈值条件 ,得到了各类平衡点局部稳定和全局稳定的条件 . 相似文献
9.
In this paper, a class of three delayed viral dynamics models with immune response and saturation infection rate are proposed and studied. By constructing suitable Lyapunov functionals, we derive the basic reproduction number R0 and the corresponding immune response reproduction numbers for the viral infection models, and establish that the global dynamics are completely determined by the values of the related basic reproduction number and immune response reproduction numbers. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
10.
Zhang Hai~ 《Annals of Differential Equations》2007,23(4):564-569
The global exponential stability of the zero solution to a class of differential system with delay is considered.By constructing a suitable type of Lyapunov functional and using some analytical techniques,we derive some criteria to check exponential stability of this system.The results establish a relation between the delay time and the parameters of the system.Two examples are also given to illustrate the validity of the results. 相似文献
11.
This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions. 相似文献
13.
STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH DELAYS 总被引：4，自引：0，他引：4
１ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓｈａｖｅｂｅｎｗｉｄｅｌｙａｐｐｌｉｅｄｉｎｓｏｌｖｉｎｇｐａｔｅｒｎｒｅｃｏｇｎｉｔｉｏｎ，ａｎｄｓｉｇｎａｌａｎｄｉｍａｇｅｐｒｏｃｅｓｉｎｇ，ａｎ... 相似文献
14.
Yoshiaki Muroya Yoichi Enatsu 《Journal of Difference Equations and Applications》2013,19(9):1463-1482
15.
Liming Cai Jinliang Liu Gaoxu Fan Huidong Chen 《Journal of Applied Analysis & Computation》2019,9(5):1731-1749
To understand V.Cholera transmission dynamics, in this paper, a mathematical model for the dynamics of cholera with reinfection is formulated that incorporates the duration time of the recovery individuals (age-of-immunity). The basic reproduction number $Re_0$ for the model is identified and the threshold property of $Re_0$ is established. By applying the persistence theory for infinite-dimensional systems, we show that the disease is uniformly persistent if the reproductive number $ Re_0>1$. By constructing a suitable Lyapunov function, the global stability of the infection-free equilibrium in the system is obtained for $Re_0<1$; the unique endemic equilibrium of the system is globally asymptotically stable for $Re_0>1$. 相似文献
16.
In the presence of external forces depending only on the time and space variables,the Boltzmann-Enskog equation formally conserves only the mass of the system,and its entropy functional is also nonincr... 相似文献
17.
Xiaomei Feng Kai Wang Fengqin Zhang Zhidong Teng 《Mathematical Methods in the Applied Sciences》2017,40(7):2762-2771
The global stability of equilibria is investigated for a nonlinear multi‐group epidemic model with latency and relapses described by two distributed delays. The results show that the global dynamics are completely determined by the basic reproduction number under certain reasonable conditions on the nonlinear incidence rate. Moreover, compared with the results in Michael Y. Li and Zhisheng Shuai, Journal Differential Equations 248 (2010) 1–20, it is found that the two distributed delays have no impact on the global behaviour of the model. Our study improves and extends some known results in recent literature. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
A delayed periodic Lotka–Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the model. Numerical simulation is presented to illustrate the feasibility of our main results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptoticstability of the zero solution of a certain fourth order functional differential equations.The resultgeneralizes the well known results. 相似文献
20.
研究了具有Beddington-DeAngelis发生率和细胞免疫反应的HIV模型的全局性.得到模型的基本再生数R_0和免疫基本再生数R_1.通过建立适当的Lyapunov函数,得出无病平衡点E_0,无免疫平衡点E_1和免疫平衡点E_2是全局渐近稳定的. 相似文献