Stability and bifurcation analysis on a fractional model of disease spreading with different time delays
Stability and bifurcation analysis on a fractional model of disease spreading with different time delays
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不同时滞疾病传播分数模型的稳定性和分岔分析
DOI：
10.1007/s11063-021-10715-3
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发表时间：
2022
影响因子：
3.1
通讯作者：
Zunshui Cheng
中科院分区：
文献类型：
--
作者：
Y;an Zhang;Yu Wang;Tianshun Wang;Xue Lin;Zunshui Cheng
本文研究了一类由小世界网络模拟的具有线性和非线性时滞的分数阶疾病传播模型的镇定和Hopf分支问题。值得一提的是，将时滞参数对作为分叉参数的研究是前所未有的。首先，建立了基于Caputo分数导数的分数次疾病传播网络模型，确定了一类时滞，并用另一类时滞作为分叉参数，得到了系统的稳定性和Hopf分叉判据。然后进行数值拟合，得到清晰的稳定区域和分叉边界曲线，当选择的时滞参数对通过分叉边界曲线到达平衡点时，系统在平衡点发生Hopf分叉。最后，通过数值算例验证了理论的有效性。此外，规则格子的仿真实例表明，新模型涵盖了规则网络和随机网络的极端情况，并且比以前的模型表现出更灵活的内部非线性相互作用。
This paper investigates the problem of stabilization and Hopf bifurcation for a fractional order disease spreading model simulated by small-world networks via two types of time delays, that is, the linear and nonlinear time delays. It is worth mentioning that the study of making delay parameter pairs as the bifurcation parameter is unprecedented. Firstly, we build a fractional disease transmission network model based on the Caputo fractional derivative, and fix one type of time delay and use another one as the bifurcation parameter to get criterions of stability and Hopf bifurcation. Then, numerical fitting obtains clear stable region and bifurcation boundary curve, and Hopf bifurcation occurs at the equilibrium when select time delay parameter pairs are in the area through the bifurcation boundary curve. Finally, some numerical examples verify the effectiveness of theories. In addition, simulation examples of regular lattices show that the new model covers the extreme conditions of regula and random networks, and it presents more flexible internal nonlinear interactions than previous models.