带有非线性传染率的具有阶段结构的SI传染病模型

对带有非线性传染率的具有阶段结构的SI传染病模型进行了讨论,得到了传染病最终消除和成为地方病的条件.     

一类时滞SIS传染病模型的讨论

对一类具有生理阶段结构的SIS传染病模型进行了分析，得到了传染病最终消除和成为地方病的阈值．     

具有阶段结构的SI传染病模型

本文对一类具有两个阶段结构的SI传染病模型进行了分析，得到了传染病最终消除和成为地方病的阈值。     

一类具有时滞传染病模型的稳定性

讨论了具有双时滞的SIS传染病模型.研究了一个边界平衡点的全局稳定性和正平衡点的局部稳定性,得到了传染病最终消失和成为地方病的阈值.     

离散的SI和SIS传染病模型的研究

为了描述个体的死亡、染病者的恢复以及疾病的传染,引入了相应的概率.基于总种群中个体数量为常数的假设,根据染病者能否恢复分别建立了具有生命动力学的离散SI和SIS传染病模型.所得到的结果显示:它们具有与相应连续模型相同的动力学性态,并确定了各自的阈值.在它们的阈值之下,传染病最终将灭绝;在它们的阈值之上,传染病将会发展成为地方病,染病者的数量将趋向于一确定的正常数.     

一类具有垂直传染率的SIS模型的稳定性分析

研究了一类具有垂直传染率的SIS模型,首先计算出该模型的基本再生数和平衡点,其次分析了该模型在无病平衡点处的局部渐近稳定性和全局稳定性;然后构造Lyapunov函数证明了地方病平衡点的全局稳定性;最后得到当基本再生数小于1时,传染病会逐渐消失;基本再生数大于1时,传染病将会流行并最终形成一种地方病.     

一类具有非线性传染率的阶段结构传染病模型

讨论了一类带有非线性传染率的阶段结构传染病模型,得到了各类平衡点存在的阈值条件.借助Hurwitz判据、Lasalle不变集原理和Bendixson法则,找到了疾病消除平衡点,及在无因病死亡时,地方病平衡点全局渐近稳定的充要条件.     

一类带有非线性传染率的SEIR传染病模型的全局分析

通过假设被传染的易感者一部分经过一段潜伏期后才具有传染性,而另一部分被感染的易感者直接成为传染者,建立了一类带有非线性传染率的SEIR传染病模型,得到了确定疾病是否成为地方病的基本再生数以及无病平衡点和地方病平衡点的全局稳定性.     

具有免疫接种且总人口规模变化的SIR传染病模型的稳定性

讨论一类具有预防免疫接种且有效接触率依赖于总人口的SIR传染病模型,给出了决定疾病灭绝和持续生存的基本再生数σ的表达式,在一定条件下证明了疾病消除平衡点的全局稳定性,得到了唯一地方病平衡点的存在性和局部渐近稳定性条件.最后研究了具有双线性传染率和标准传染率的两个具体模型,并证明了当σ>1时该模型地方病平衡点的全局渐近稳定性.     

一类非线性SEIR传染病模型的全局稳定性

研究了一类具有一般形式非线性发生率g(S)h(I)的SEIR传染病模型.利用Liapunov函数方法,证明了当R_0≤1时,无病平衡点P_0在G内全局渐近稳定,疾病最终消失.利用周期轨道稳定性和Poincare-Bendixson性质理论,证明了当R_01时,地方病平衡点P~*在G的内部全局渐近稳定,疾病流行形成地方病.     

Spreading of epidemics on scale-free networks with nonlinear infectivity

In this paper, we study the spreading of epidemics on scale-free networks with infectivity which is nonlinear in the connectivity of nodes. We will show that the nonlinear infectivity is more appropriate than constant or linear ones, and give the epidemic threshold of the SIS model on a scale-free network with nonlinear infectivity. In addition, we compare the effects of nonlinear infectivity on the epidemic threshold with two other cases on infinite and finite scale-free networks, and find some new results, such as: with unit recovery rate and nonlinear irrational infectivity, the epidemic threshold is always positive; and the epidemic threshold can increase with network size on finite networks, contrary to the findings in all previous work.     

Competing spreading processes and immunization in multiplex networks

Epidemic spreading on physical contact network will naturally introduce the human awareness information diffusion on virtual contact network, and the awareness diffusion will in turn depress the epidemic spreading, thus forming the competing spreading processes of epidemic and awareness in a multiplex networks. In this paper, we study the competing dynamics of epidemic and awareness, both of which follow the SIR process, in a two-layer networks based on microscopic Markov chain approach and numerical simulations. We find that strong capacities of awareness diffusion and self-protection of individuals could lead to a much higher epidemic threshold and a smaller outbreak size. However, the self-awareness of individuals has no obvious effect on the epidemic threshold and outbreak size. In addition, the immunization of the physical contact network under the interplay between of epidemic and awareness spreading is also investigated. The targeted immunization is found performs much better than random immunization, and the awareness diffusion could reduce the immunization threshold for both type of random and targeted immunization significantly.     

The threshold of a stochastic SIRS epidemic model with saturated incidence

In this paper, we investigate the dynamics of a stochastic SIRS epidemic model with saturated incidence. When the noise is small, we obtain a threshold of the stochastic system which determines the extinction and persistence of the epidemic. Besides, we find that large noise will suppress the epidemic from prevailing.     

Threshold behaviour of a stochastic SIR model

In this paper, we investigate the threshold behaviour of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation. When the noise is small, we show that the threshold determines the extinction and persistence of the epidemic. Compared with the corresponding deterministic system, this value is affected by white noise, which is less than the basic reproduction number of the deterministic system. On the other hand, we obtain that the large noise will also suppress the epidemic to prevail, which never happens in the deterministic system. These results are illustrated by computer simulations.     

Assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of HIV/AIDS in heterosexual settings

A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of the disease in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. The epidemic threshold and equilibria for the model are determined and stabilities are investigated. Comprehensive qualitative analysis of the model including invariance of solutions and permanence are carried out. The epidemic threshold known as the basic reproductive number suggests that heterosexuality, homosexuality, and bisexuality influence the growth of the epidemic in HIV/AIDS affected populations and the partial reproductive number (homosexuality induced or heterosexuality and bisexuality induced) with the larger value influences the overall dynamics of the epidemic in a setting. Numerical simulations of the model show that as long as one of the partial reproductive numbers is greater than unity, the disease will exist in the population. We conclude from the study that homosexuality and bisexuality enlarge the epidemic in a heterosexual setting. The theoretical study highlights the need to carry out substantial research to map homosexuals and bisexuals as it has remained unclear as to what extent this group has contributed to the epidemic in heterosexual settings especially in southern Africa, which has remained the epidemiological locus of the epidemic.     

Threshold dynamics in a stochastic SIRS epidemic model with nonlinear incidence rate

We discuss the dynamic of a stochastic Susceptible-Infectious-Recovered-Susceptible (SIRS) epidemic model with nonlinear incidence rate.The crucial threshold $\tilde{R}_0$ is identified and this will determine the extinction and persistence of the epidemic when the noise is small. We also discuss the asymptotic behavior of the stochastic model around the endemic equilibrium of the corresponding deterministic system. When the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it dies out. Finally, these results are illustrated by computer simulations.     

具周期性潜伏期的SEIR传染病模型的动力学

研究了一类具有周期性潜伏期的常微分SEIR传染病模型.首先借助于染病年龄分布函数导出了模型.紧接着定义了模型的基本再生数R_0并利用耗散动力系统的相关理论证明R_0是决定疾病是否继续流行的阈值.最后,利用数值方法进一步验证了结论,并分析了忽略潜伏期的周期性对估计疾病传播能力的影响.