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In this paper, based on susceptible–infected–susceptible (SIS) scheme, we introduce a framework that allows us to describe the spreading dynamics of two interacting diseases with active nodes. Different from previous studies, the two different diseases, propagating concurrently on the same population, can interact with each other by modifying their transmission rates. Meanwhile, according to certain probabilities, each node on the complex networks rotates between active state and inactive state. Based on heterogeneous mean-field approach, we analyze the epidemic thresholds of the two diseases and compute the temporal evolution characterizing the spreading dynamics. In addition, we validate these theoretical predictions by numerical simulations with phase diagrams. Results show that the secondary thresholds for the two opposite scenarios (mutual enhancement scenario and mutual impairment scenario) are different. We also find that the value of critical threshold and the final size of spreading dynamics are reduced as the node activity rate decreases.

In signed networks, negative edges represent negative relationships; the increase or gathering of negative interpersonal relationships can lead to social turmoil, which will affect the spreading of diseases or information. Therefore, it is significant to study the impact of the proportion and configuration of negative edges on spreading. In this paper, to study the impact of negative relationships on spreading, we propose a heterogeneous spreading model using signed networks. In this model, we use the balance of the local structure to quantify the probability of contact between individuals, making the contacts heterogeneous. We then examine the impact of negative edges on spreading using numerical simulations. We find that the balance of the network and the spreading coverage (i.e. outbreak size) gradually decrease with the proportion of negative edges. Compared with preference configurations (in which negative signs are placed on edges that have an important impact on spreading), a random configuration (in which negative signs are placed on random edges) has a suppressive effect on spreading. This provides information for epidemic prevention. Finally, we find that there are two important factors — contact probability and spreading paths — that could explain the observed spreading phenomena.

In the research of network structure, long ties are considered to be a hidden but valuable interaction. In this paper, we innovatively interpret the long ties structure in traditional research as a higher-order information spreading path. It effectively avoids the homogenization of information level and redundancy of network structure. The spreading bridge model based on high-order long ties structure is established accordingly. Modern online social behavior is modeled by establishing spreading expansion rate and spreading diffusion rate to improve model adaptability. The spread dynamics model based on multivariate interactions is developed by combining direct-linked spread as a binary interaction relationship in traditional research with bridge-linked spread. The validity of the model is verified by comparing the model simulation results with real cases.

This paper focuses on the internal law of online public opinion spreading under the conditions of different types of spreaders by constructing the model of public opinion spreading by subtypes of spreaders. The new $S{I}_S{I}_O{I}_N$ model is constructed by abstracting factors such as netizens’ interests, emotions and views on hot events in the Internet into propensity indices. The simulation results show that the spread of public opinion after categorizing netizens is more in line with the spread of public opinion in reality. Moreover, netizens tend to show different spreading behaviors in different public opinion cases, and the degree of change in netizens’ propensity varies greatly. All the data used in the simulation experiments are real data and analyzed with real events. The research results are helpful for what kind of control strategies are adopted after the occurrence of hotspot events.

The spread of homogenized information on social networks can create certain positive promotional effects. However, if it is excessively spread, it may lead to constraining effects and even cause negative impacts. In this paper, a spreading model called C-SIRI is proposed, which conducts an in-depth study on the constraining mechanism in the process of information spreading, as well as the rules and characteristics affecting its impact. Taking the COVID-19 epidemic information spreading on Sina Weibo social network from March 2020 to May 2022 as an example, the reliability of this model is verified. The results show that content homogeneity, participation degree and false proportion have a significant influence on the constraining mechanism of social network information spreading, and the threshold of information spreading constraining is closely related to the spreading times. This research helps to understand the role of constraining mechanism in information spreading and promote the application of social networks in information spreading prediction and control.