具有媒体饱和发生率的SIS时滞模型研究

为了研究媒体报道对传染病动力学性态的影响,通过建立疾病发生率受媒体报道影响的SIS数学模型,确定模型的基本再生数,证明平衡点的存在性以及地方病平衡点的唯一性,并证明无病平衡点的局部渐近稳定性和全局稳定性,以及地方病平衡点的局部渐近稳定性。引入时滞因子对模型进行深入研究,通过数值模拟验证了理论结果的正确性。研究结果表明:当参数满足一定条件时,在地方病平衡点会产生Hopf分支。具有媒体饱和发生率的SIS时滞模型的研究结果,阐释了媒体报道对疾病传播的影响,丰富了饱和发生率的传染病模型结果,为有效实施疾病防控提供了理论依据。

Study of SIS model with media saturation rate and time delay

In order to study the influence of media coverage on the dynamic state of infectious disease models, a SIS mathematical model of the incidence of diseases affected by media coverage is established, the reproduction number of the model is confirmed, the existence of equilibrium point and the uniqueness of endemic equilibrium point are proved, and the local asymptotic stability and global stability of disease-free equilibrium and local asymptotic stability of endemic equilibrium are proved. The delay factor is introduced to study the model in depth, and the correctness of the theoretical results is verified by numerical simulation. The results show that Hopf bifurcation occurs at the equilibrium point of endemic diseases when the parameters satisfy certain conditions. The research results of SIS time-delay model with media saturation rate can enrich the theory of infectious disease model with media saturation rate in theory, and play a positive reference value in the application of media coverage of disease transmission and the implementation of disease prevention measures.