In view of the problem that the existing researches do not consider the refinement of the factors affecting the network negative energy propagation and construct a propagation dynamics model for analysis, a Weak-Strong-Received-Infected-Evil (WSRIE) model of network negative energy propagation was proposed. Firstly, considering the difference of negative energy immunity and propagation ability of network users, the vulnerable states were divided into weak immunity and strong immunity, and the infectious states were divided into weak infection, strong infection and malicious propagation with unchanged scale. Secondly, according to the negative energy infection mechanism of the network, the state transition law was proposed. Finally, a dynamics model of network negative energy propagation for complex networks was constructed. The simulation comparison experiments on NW small world network and BA scale-free network were carried out. The simulation results show that under the same parameters, the weak immune node density of the NW network is 9 percentage points lower than that of the BA network, indicating that the network with small world characteristics is more susceptible to negative energy. In the BA network, the density of infected nodes with the malicious node degree of 200 is 5 percentage points higher than that with the node degree of 0, indicating that the greater the node degree of the network red opinion leader, the more network users affected by the network negative energy.

For the problem that qualitative analysis methods are mostly adopted for the study of spam information propagation and it is difficult to reveal intrinsic propagation rules of spam information propagation, an ILDR (Ignorant-Lurker-Disseminator-Removed) model of spam information was proposed based on the idea of virus propagation modeling by considering the actual factors such as different input rates and removal rates. Firstly, the equilibrium point and the propagation threshold were calculated, and the stability conditions of the equilibrium point were given. Secondly, the local stability of non-spam information and spam information was proved by the Routh-Hurwitz criterion, then the global stability of non-spam information was certified via the invariance principle of LaSlle, which was proved based on the Bendixson criterion. Theoretical research shows that the non-spam information equilibrium is global asymptotically stable when propagation threshold is less than 1; the spam information equilibrium is global asymptotically stable when propagation threshold is greater than 1. The numerical simulation validates that the value of the propagation threshold can be decreased when decreasing the transfer rate from the lurker to the disseminator, increasing the transfer rate from the ignorant to the remover and the transfer rate from the lurker to the remover; the value of the disseminator can be decreased via increasing the proportionality coefficient from the ignorant to the lurker, or increasing the transfer rate of the disseminator to the remover and the system removal rate.

The impact of individual interest and refutation mechanism on rumor spread was investigated, and a new IWSR (Ignorant-Weak spreader-Strong spreader-Removal) rumor spread model was proposed. The basic reproduction number and equilibrium points of the model were calculated. Using Lyapunov stability theorem, Hurwitz criterion and LaSalle invariance principle, the local stability and global stability of some equilibrium points were proved. Through numerical simulations, it is concluded that increasing the effectivity of the governments' refutation actions or improving people' ability of rumor judgement can effectively suppress rumor spread. Finally, numerical simulations were conducted in WS (Watts-Strogatz) small-world network and BA (Barabási-Albert) scale-free network, showing that the network topology exerts significant influence on rumor spread.