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.

Dedicating oneself to a greater good is one of the secret ingredients to business success in an evolving and highly interconnected markets environment. For wood companies, this is even more needed to face the overwhelming ongoing environmental crisis affecting business practices and customers' behavior in general. To build solid reputation and increase one's presence on competing markets, wood companies should not only care about products competitiveness, but also customers' perception, environmental awareness and ethical marketing. In this article, we simulated the effect of ethical commerce on wood companies' reputation using a modified competitive and cooperative model based on differential equations considering wood type, products categories and companies brand score or reputation as function of their commitment to social and environmental causes. The qualitative analysis and results of numerical experiment show that, focusing on sharing values, and building strong relationship with customers are highly important for long-term development. Moreover, reducing environmental impact by shifting production strategy towards man-made materials could meet today customers' demands for ethically and environmentally aware manufactured wood products.

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.

While there has been much work analyzing the effects of urban exodus on rural areas' development, particularly in improving these localities' access to better services and decent quality of life, models to date lacked important features such as adaptation time effect on ongoing agricultural projects of new settlers reflecting real difficulties related to individuals abilities. In this article, we show that newcomers individual abilities, educational backgrounds, motivation, and so forth are crucial to promote the development of rural areas and facilitate the relocation or return of a certain group of people in their region of interest. Using a systemic approach, we present a model of urban exodus based on constant delay differential equations considering the local authority and population support and the time needed before the successful settlement of newcomers in the region. Furthermore, we estimate that adaptation time was responsible both for successful settlement increase and failure decrease. To reflect this, we incorporate delay terms in both the successful settlement and failure differential equations. We performed a qualitative analysis of the proposed system and show in numerical simulation that newcomers should be selected in function of their skills and experiences to accelerate their successful settlement, achieve overall socioeconomic development and improve the quality of life and well-being of the inhabitants.