Rumours spreading in nowadays highly connected society is an interesting and important topic in studying human behaviour and communication networks dynamics. As rumours propagation or evolution with respect to time is highly submitted to networks users’ dynamics, rumours propagation in a targeted community may inherit self-purification mechanism due to human ability to judge and clarify allegations and assumptions not based on truth. In this article, we analysed rumours spreading through social media taking into account self-purification mechanism using epidemic control approach. Rumours spreading threshold value was obtained. Results of numerical simulation validated theoretical analysis and suggested controlling social media influence on potential rumours purifiers and disseminators.

Social Networks Ecosystem is evolving faster and Social Networks users’ intensive activities are affecting significantly the network traffic. Generated data from different sending and receiving hosts have to be handled by network active nodes and links. In this paper, we propose to study the interaction between two types of network active hosts by using a Lotka‐Volterra competitive system that considers the subnet limiting supply. We applied our proposed model to two kinds of Online Social Networks’ (OSNs’) users characterized by the intensity of their activities from the generated data perspective. We assumed and proved that the impact of competition is flexible and subject to forwarding protocol and subnet allocated resources. By taking the competition case in the analysis of the differential equations, we show that when competition exists, one stable equilibrium point can be found if certain conditions are respected. Numerical results confirm our theoretical analysis and show that instead of treating equally at the subnet level all data from active hosts, adopting a routing protocol that takes into account the nature of data and the forwarding time is necessary for improving the overall performance of the network.

In most situations where entities interact by sharing limited resources, controlling populations’ density is crucial to maintain ecosystem sustainability. This is the case in a predator-prey type interaction when predator survival relies on its ability to harvest and consume resources. In this article, we analyzed a modified predator-prey model based on Rosenzweig-MacArthur characterized by a delayed conversion of prey into resources and applied the proposed model to network users’ data forwarding at a bottleneck node. We discuss system fixed points behaviour and prove that delaying the handling time has a significant impact on the dynamic of interaction and system bifurcates, exhibits chaotic behaviour and is highly responsive to small perturbations.

Controlling information diffusion or propagation through social networks can be challenging when dealing with information related to a subject of highest interest for the public. The complexity level of control depends on subject importance, users’ dynamic, and network structure. When two published messages or pieces of information share the same interest for targeted readers, analyzing their propagation dynamic for control and prediction is of great interest. This article proposes to model, based on a modified interactive system with Holling type functional response, the dynamic of underlying relationship between two broadcasted messages traveling through social networks media. We showed in the qualitative analysis of the proposed model that system could be stable at certain conditions, and the model-system exhibited very rich dynamical behavior. Numerical simulation results validated theoretical analyses and suggested adapting resources harvesting and assimilation efficiency for an authoritative message to stabilize the system and control the dissemination of information in a closed environment.

Reducing fake news and rumor propagation through social media may be challenging to achieve when dealing with sensible contents and communities with free access to online shared resources. Controlling rumor dissemination and promoting true news are the main techniques used to strangle false information that may result in dramatic effect on human wellbeing in an open or closed environment. In this article, we studied a predator-prey model with constant delay in both predator and prey equations and applied the proposed model to the underlying relationship between the existing rumor propagating through social media and the related authoritative information containing the truth broadcast to reduce the respective rumor negative effect on the targeted community. We showed that the proposed system was very responsive to small perturbations and exhibited complex dynamical behavior around the steady-state equilibrium when interaction occurs and delay is applied, considering the controlled situations. Numerical results suggested applying relatively small delay, which represents the ideal time to publish the related propagating rumor curative content to reduce its diffusion speed and promote the truth.