具有急慢性阶段SEIVR流行病模型的全局稳定性分析

研究了具有急慢性阶段SEIVR流行病模型.首先,给出了基本再生数R0,证明了:当R0<1时,无病平衡点P0是全局稳定的;否则,P0不稳定.其次,当R0>1时,利用LaSalle不变原理证明了唯一地方病平衡点P*的全局稳定性.

Global stability of SEIVR epidemic model with generalized incidence and preventive vaccination

In this paper, an SEIVR epidemic model with generalized incidence and preventive vaccination is considered. First, we formulate the model and obtain its basic properties. Then, we find the equilibrium points of the model, the disease-free and the endemic equilibrium. The stability of disease-free and endemic equilibrium is associated with the basic reproduction number R0. If the basic reproduction number R0〈 1, the disease- free equilibrium is locally as well as globally asymptotically stable. Moreover, if the basic reproduction number R0 〉 1, the disease is uniformly persistent and the unique endemic equilibrium of the system is locally as well as globally asymptotically stable under certain conditions. Finally, the numerical results justify the analytical results.

新媒体环境下具有多目标导向性的信息细化模型研究——基于传染病模型

[目的/意义]网民在新媒体环境下的信息细化存在障碍,为深化新媒体环境下信息细化理论研究提供新的视角,对从实践角度有效提高网民信息利用效率和创造力具有重要意义。[方法/过程]基于国内外学者的信息细化研究成果及相关理论,构建新媒体环境下具有多目标导向性的信息细化SEIVR模型,以新浪微博英国脱欧话题数据为基础,使用Matlab进行仿真实验对模型进行验证并分析目标导向权重变化对信息细化的影响。[结果/结论]实验结果验证了模型的有效性,分析表明我国网民信息细化水平偏低,应采取有效措施促进信息细化的深入发展。

Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction R0. The disease-free equilibrium is stable locally and globally whenever R0〈 1. If R0 〉 1, then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented.