马尔可夫链
统计物理学
不相关
流行病模型
学位(音乐)
马尔可夫过程
数学
人口
马尔科夫蒙特卡洛
蒙特卡罗方法
离散时间和连续时间
统计
马尔可夫性质
应用数学
马尔可夫模型
物理
医学
环境卫生
声学
作者
Chao-Ran Cai,Zhi-Xi Wu,Jiancheng Guan
标识
DOI:10.1103/physreve.90.052803
摘要
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
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