Cao Shengli, Feng Peihua, Wang Wei, Shi Yayun, Zhang Jiazhong
School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, 710049 China.
State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of China.
Nonlinear Dyn. 2021;106(2):1557-1572. doi: 10.1007/s11071-021-06519-8. Epub 2021 May 11.
Pandemic with mutation and permanent immune spreading in a small-world network described is studied by a modified SIR model, with consideration of mutation-immune mechanism. First, a novel mutation-immune model is proposed to modify the classical SIR model to simulate the transmission of mutable viruses that can be permanently immunized in small-world networks. Then, the influences of the size, coordination number and disorder parameter of the small-world network on the spread of the epidemic are analyzed in detail. Finally, the influences of mutation cycle and infection rate on epidemic transmission in small-world network are investigated further. The results show that the structure of the small-world network and the virus mutation cycle have an important impact on the spread of the epidemic. For viruses that can be permanently immunized, virus mutation is equivalent to making the immune cycle of human beings from infinite to finite. The dynamical behavior of the modified SIR epidemic model changes from an irregular, low-amplitude evolution at small disorder parameter to a spontaneous state of wide amplitude oscillations at large disorder parameter. Moreover, similar transition can also be found in increasing mutation cycle parameter. The maximum valid variation mutation decreases with the increase of disorder parameter and coordination number, but increase with respect to system size. In addition above, as the infection rate increases, the fraction of the infected increases and then decreases. As the mutation cycle increases, the time-average fraction of the infected and the infection rate corresponding to the maximum time-average fraction of the infected also decrease. As one conclusion, the results could give a deep understanding Pandemic with mutation and permanent immune spreading, from viewpoint of small-world network.
本文通过一个改进的SIR模型，考虑突变-免疫机制，研究了在小世界网络中描述的具有突变和永久免疫传播的大流行情况。首先，提出了一种新颖的突变-免疫模型来修改经典的SIR模型，以模拟在小世界网络中可永久免疫的可变病毒的传播。然后，详细分析了小世界网络的规模、配位数和无序参数对疫情传播的影响。最后，进一步研究了突变周期和感染率对小世界网络中疫情传播的影响。结果表明，小世界网络的结构和病毒突变周期对疫情传播有重要影响。对于可永久免疫的病毒，病毒突变相当于使人类的免疫周期从无限变为有限。改进后的SIR疫情模型的动力学行为从无序参数较小时的不规则、低振幅演化转变为无序参数较大时的宽振幅振荡的自发状态。此外，在增加突变周期参数时也能发现类似的转变。最大有效变异突变随无序参数和配位数的增加而减小，但随系统规模的增加而增加。除此之外，随着感染率的增加，感染部分先增加后减少。随着突变周期的增加，感染部分的时间平均值以及对应感染部分时间平均值最大时的感染率也会降低。作为一个结论，这些结果可以从小世界网络的角度深入理解具有突变和永久免疫传播的大流行情况。
