Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks

A new Markov chain (MC) model for rumor epidemic dynamics in heterogeneous complex social networks (HCSN) is investigated. The epidemic model is also a compartmental SEIR (susceptible-exposed-infected-removed), with an expanded multidimensional state space for the MC by utilizing two discrete time measures for representing both the “disease” states and the age in each state of the nodes in the HCSN. Moreover, characterizations of the MC at both the mean-field and global levels of the HCSN are given. A statistical analysis of the MC is conducted to find a parameter for the basic reproduction number, \( \mathfrak {R}_{0}\) , of the “disease” in the network; and to find an unbiased and precise estimator for \( \mathfrak {R}_{0}\) . The goodness-of-fit of the estimator is investigated by employing the mean squared error.