The article examines the problems of the emergence and development of the flow of refugees from Ukraine during the first half of 2022 as a complex phenomenon that depends on rational (economic) and irrational (social-psychological) factors. The phenomenological model, created on the basis of the Burgers’ equation, which reproduces the process of the involvement of the new refugees to the flow and the resistance of the environment to the formation of this flow, made it possible to analyze such subtle effects as the existence of a hub country, where the initial accumulation of refugees takes place, followed by redistribution, and the influence of infrastructure problems in the exit country. Transitional regimes from the infrastructural problems prevailing in the country of exit to the predominant influence of the hub-country effects are also considered. It is concluded that the entry to new levels of the refugee flow could be achieved due to the effects of emotional and economic (rational) behavior of refugees replenishing the hub, i.e., a stepwise development of the refugee flow is possible if new hubs would be created, or the existing hub will be freed up from overloading. On the basis of mathematical modeling, it is shown that in the case when the refugee flow is restrained by infrastructural problems in the exodus country, the exit to the stationary regime is delayed. Identification of the proposed model was carried out based on the empirical data on the refugee flow development using the apparatus of incorrect problems of the mathematical physics. A comparison of the dynamic effects of the refugee flow development from Ukraine with similar processes in Syria and Iraq was carried out, which allowed for identification of the zones of influence of infrastructure problems and the hub effect in the refugee flow development. The use of the concept of refugees’ economic independence (self-sufficiency), which was developed in 2018 by the Office of the United Nations High Commissioner for Refugees, was proposed as a basis for policy formation in the field of refugee assistance. The consequences of the discrete use of this concept in the case of refugees from Syria are analyzed, and the dynamics of employment opportunities for these refugees in countries with similar and different socio-cultural conditions were compared. A conclusion was made about the fundamental difference in the employment trends in those types of countries. The authors formulated proposals regarding the utilization of the Monte Carlo methods and the learning model for researching the peculiarities of the process of Ukrainian refugees achieving a certain level of economic independence (self-sufficiency), determining the typical time of reaching such a level, obtaining the distribution of probabilities of getting the first job depending on the initial competencies and skills of refuges, their education, experience, and foreign languages mastery.
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