一类带负交叉扩散项的SIR传染病模型的空间Turing斑图

SPATIAL TURING PATTERN IN SIR EPIDEMIC MODEL WITH NEGATIVE CROSS-DIFFUSION

本文研究了带有负交叉扩散项的SIR传染病模型的空间斑图动力学问题.利用稳定性理论和Hopf分支理论,获得了Turing失稳的条件以及Turing斑图的存在区域,并且利用Matlab软件模拟获得了不同类型的Turing斑图,比如点状、条状以及二者共存等Turing斑图.通过负交叉扩散诱导出规则斑图,推广了负扩散效应对空间斑图的形成具有巨大影响的结果.

In this paper,spatial pattern of SIR epidemic model with negative cross di?usion is considered.By performing a linear approach around the positive steady states of the model and Hopf bifurcation theorem,su±cient conditions are obtained for the Turing instability.And Turing region in which there are plenty of complicate spatial patterns is derived.Finally,some numerical simulations are given to certify that Turing patterns,such as spot,stripe and mixture of spot-stripe patterns.The regular pattern is induced by negative cross di?usion,which generalizes the results that negative cross di?usion has great in°uence on the spatial pattern formation.