一种新型复杂社会网络谣言随机模型：分布收敛到最终谣言规模。
A novel complex social network rumor stochastic model: Convergence in distribution to a final rumor size.
作者信息
Wanduku Divine
机构信息
Department of Mathematical Sciences, Georgia Southern University, 65 Georgia Ave, Room 3309, Statesboro, GA, 30460, USA.
出版信息
Heliyon. 2023 Mar 30;9(4):e15125. doi: 10.1016/j.heliyon.2023.e15125. eCollection 2023 Apr.
We introduce a chain-binomial model in a heterogeneous complex social network (HCSN) to investigate the spread of a rumor. A novel formulation of the state of the Markov chain (MC) for the SEIR (susceptible-exposed-infected-removed) rumor epidemic model is obtained, where two discrete time measures represent individuals in their disease states both instantaneously, and also the total time duration in each state. The general MC is characterized in the HCSN, for both the mean-field and global levels of the network rumor epidemic dynamics. The convergence in distribution of the MC to the final size of the rumor epidemic random variable is fully characterized. Moreover, the algorithm to obtain the expected final number of nodes that ever hear the rumor is given. An example to demonstrate the algorithm is presented.
我们在异构复杂社会网络（HCSN）中引入一个链二项式模型来研究谣言传播。针对SEIR（易感-暴露-感染-移除）谣言传播模型，我们得到了马尔可夫链（MC）状态的一种新颖表述，其中两个离散时间度量既即时表示处于疾病状态的个体，也表示在每个状态下的总持续时间。针对网络谣言传播动态的平均场和全局层面，在HCSN中对一般的MC进行了刻画。充分刻画了MC在分布上收敛到谣言传播随机变量的最终规模。此外，给出了获取最终听到谣言的节点预期数量的算法。还给出了一个示例来演示该算法。
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