No abstract

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.

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.