Fig. 1. SCIR public-opinion propagation mode.

Fig. 2. DI-SCIR public-opinion propagation model based on real-time online users.

Fig. 3. Direct immunity probability P_SR changes with the interventional force α, and the real information credibility β. When α = 0.2859 and ʲ = 1, P_SR takes a maximum value of 0.7620.

Fig. 4. BA scale-free network topology. Nodes having higher degrees are darker in color and larger in area, and the relationship between the nodes is indicated by a solid gray line.

Fig. 5. BA scale-free network degree distribution logarithmic coordinate graph. The x-axis, k, represents the degree of nodes in the network, and the y-axis, P(k), represents the distribution of correspondence degrees.

Fig. 6. Effect of basic reproduction numbers on the spread of public opinion: (a) random chosen R₀ = 1.3914 > 1; (b) random chosen R₀ = 0.9635 < 1.

Fig. 7. Impact of interventional force α on the propagation of public opinion. α takes 0,0.1,0.3,0.55,0.7: density changes of (a) S state node, (b) C state node, (c) I state node, and (d) R state node.

Fig. 8. Impact of real information credibility β on the propagation of public opinion β takes 0,0.1,0.3,0.5,0.7, respectively: density changes of (a) S state node, (b) C state node, (c) I state node, and (d) R state node.

Fig. 9. Impact of interventional time T on the propagation of public opinion. T takes 3, 10, 20, 30, 40, respectively: density changes (a) of S state node, (b) C state node, (c) I state node, and (d) R state node.

Fig. 10. Impact of different models on the spread of public opinion. The models are SIR, SCIR, and the DI-SCIR public-opinion propagation models based on real-time online users: (a) density changes of(a) of S state node, (b) C state node, (c) I state node, and (d) R state node.