媒介传染病在中国传染病中占比较高,构成严重的公共卫生风险。因此有关媒介传染病模型的动力学行为研究受到了国内外学者的广泛关注。针对这类传染病,首先基于异质平均场理论建立了三层无标度关联网络协同传播模型;其次基于所建模型,针对各子系统恢复率均相等、至少有两个不相等两种情况,利用柯西交错定理和扰动理论分析了全局传播阈值和各孤立子网阈值的相对大小,并得到结论:协同传播减小了传播阈值,促进了疾病的传播。
Vector-borne diseases account for a high proportion of the infectious diseases in China, which constitutes a serious public health risk. Thus the research on dynamic behavior of vector-borne disease model has been widely concerned by a number of scholars. Aiming at a kind of vector-borne transmission disease. Firstly, a collaborative communication model of three-layer scale-free associated networks is established based on the heterogeneous mean field theory. Secondly, based on the established model, the relative values of global propagation threshold and each isolated subnetworks threshold are analyzed by Cauchy’s interleaving theorem and perturbation theory under the condition that the recovery rates of each subsystem are equal or at least two are unequal. It was found that collaborative communication reduced the transmission threshold and promoted the spread of the disease.
[1] Watts D J, Strogatz S H. Collective dynamics of ‘small-world’ networks [J]. Nature, 1998, 393(6684):440-442.
[2] Barabá Si A. Emergence of scaling in random networks [J]. Science, 1999, 286(5439):509-512.
[3] 汪小帆. 无标度网络研究纷争:回顾与评述[J]. 电子科技大学学报,2020,49(4):499-510.
Wang Xiaofan. Disputes over scale-free networks: a review and review [J]. Journal of the University of Electronic Science and Technology,2020,49(4):499-510.
[4] Liu X Y, He D B, Yang L F, et al. A novel negative feedback information dissemination model based on online social network[J]. Physical A: Statistical Mechanics and Its Applications, 2019,513(9):371-389.
[5] Zhu G H, Chen G R, Zhang H F, et al. Propagation dynamics of an epidemic model with infective media connecting two separated networks of populations[J]. Communications in Nonlinear Ence & Numerical Simulation, 2015, 20(1):240-249.
[6] Pastor-Satorras R, Vespignani A. Epidemic spreading in scale-free networks[J]. Physical Review Letters, 2001, 86(14): 3200-3203.
[7] Zhou T, Liu J G, Bai W J, et al. Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity[J]. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics,2006,74(5): 1-6.
[8] Gomez-Gardenes J, Latora V, Moreno Y, et al. Spreading of sexually transmitted diseases in heterosexual populations[J]. Proceedings of the National Academy of Sciences of the United States of America,2008,105(5):1399-1404.
[9] Bisanzio D, Bertolotti L, Tomassone L, et al. Modeling the spread of vector-borne diseases on bipartite network[J]. PLoS ONE, 2010,5(11): 1- 6.
[10] Wei X, Chen S H, Wu X Q, et al. A unified framework of interplay between two spreading processes in multiplex networks[J]. EPL, 2016, 114(2):1-6.
[11] 王玲娜,王领弟,傅新楚. 三部图网络上的媒介传染病动力学[J].复杂系统与复杂性科学,2017,14(2):11-18.
Wang Lingna, Wang Lingdi, Fu Xinchu. Dynamics of vector borne infectious diseases on tripartite graph networks[J]. Complex Systems and Complexity Science,2017,14(2):11-18.
[12] Li K Z, Zhang H F, Zhu G H, et al. Suboptimal control and targeted constant control for semi-random epidemic networks[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 99:1-9.
[13] 姜志宽,贾德胜,韩招久. 鼠疫的流行特点与防控对策[J].中华卫生杀虫药械,2020,26(1):8-15.
Jiang Zhikuan, Jia Desheng, Han Zhaojiu. Epidemic characteristics and control strategies of plague[J]. Chinese Sanitary Insecticide,2020,26(1):8-15.
[14] Gomez S, Arenas A, Borge-Holthoefer J, et al. Discrete-time markov chain approach to contact-based disease spreading in complex networks[J]. Europhys Lett, 2010,89(3):1-6.
[15] Hwang S G. Cauchy′s interlace theorem for eigenvalues of hermitian matrices[J]. American Mathematical Monthly, 2004, 111(2):157-159.
[16] Wei X, Wu X Q, Chen S H. Cooperative epidemic on a two-layered interconnected network[J]. Siam Journal on Applied Dynamical Systems, 2018,17(2):1503-1520.
