In this paper, a new SEIR (susceptible-exposed-infected-removed) rumor spreading
model with demographics on scale-free networks is proposed and investigated. Then
the basic reproductive number R0 and equilibria are obtained. The theoretical analysis
indicates that the basic reproduction number R0 has no correlation with the
degree-dependent immigration. The globally asymptotical stability of rumor-free
equilibrium and the permanence of the rumor are proved in detail. By using a novel
monotone iterative technique, we strictly prove the global attractivity of the
rumor-prevailing equilibrium.

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• Global stability of a SEIR rumor spreading model with demographics on scale-free networks