具有媒体效应和时滞的反应扩散传染病模型的控制与预测

Control and Prediction of a Reaction-diffusion Epidemic Model with Media Effect and Time Delay

针对媒体效应的传染病建立相应的反应扩散模型,研究平衡点的稳定性、Hopf分岔以及重要参数如时滞、传染率和媒体效应等对模型Turing结构的影响.最后,给出精确Turing失稳的参数条件,并给出相应的数值模拟,得到条状和点状共存的斑图.理论分析与数值模拟揭示了空间动力学复杂性机理,为控制疾病的传播提供了有力理论依据.

In this paper, a reaction diffusion model with media effect is established. The stability of the equilibrium, Hopf bifurcation and important parameters such as time delay,infection rate and media effects on the Turing structure of the model are studied. The Turing structure and the parameters of the exact Turing instability are given with the corresponding numerical simulation. The theoretical analysis and numerical simulation reveal the complexity mechanism of spatial dynamics and provide a powerful theoretical basis for the control of the spread of disease.