In this paper, the small-scale spatially distributed influences on the infectious disease development are proposed to be modeled by means of diffuse disturbance of the corresponding degenerate model problems. We represent the asymptotic expansions of the solutions of the corresponding singularly-disturbed problems with a time-delay that are reduced to a sequence of problems without a time-delay. The results of numerical experiments that characterize the spatially distributed diffuse influences on the infectious disease development are presented. The decrease in the maximum concentration level of pathogenic antigens due to their diffuse "redistribution" from the locus of infection into less infected areas of the target organ is illustrated.
The approach of modification the infectious disease models that allow to investigate small-scale spatially distributed influences on the process development by diffusion perturbation of the corresponding degenerate problems of the model is proposed. The singularly perturbed model problem with time-delay is reduced to a sequence of problems without time-delay and the corresponding representations of asymptotic expansions the solutions are constructed. The results of numerical experiments that characterize the influence of spatially distributed diffusion "redistributions" of infectious disease factors on the development of the process are given. The decrease in the maximum level of pathogenic antigens concentration in the infection locus due to their diffusion "redistribution" is illustrated.
For a long time, the problem of deterioration of the bed and floodplain (young river landscape) of the Prut River has attracted attention in practical, environmental and scientific terms. This applies to all components of the landscape, ecosystems. But the central, main problem is hydromorphological transformation, associated primarily with the extraction of river alluvium. In recent decades the relevant research has been conducted.At the same time, negative processes continue to develop and require appropriate development of monitoring, database formation, understanding of the causes and patterns. In particular, the database should necessarily include data on the territorial structure of the river valley, the young river landscape. Thus, there is an urgent task to identify and assess the current state of the young river landscape of the Prut and systematize data on the patterns of processes of its hydromorphological transformation. The purpose of the study is to systematize information on the main processes of anthropogenic impact and the corresponding processes of transformation of the hydromorphological basis of the young river landscape of the Prut within Chernivtsi region to identify their patterns, consequences and assess and, on this basis, their current state. The object of research is the young river landscape of the Prut (within the Chernivtsi region), which develops on the basis of the riverbed and floodplain. The subject of research - manifestations, patterns of consequences of anthropogenic transformation of the hydromorphological basis of the young landscape of the Prut River. Methods, research procedure - hydromorphological analysis of the territorial structure of the river valley with the formation of a database of territorial landscape features in the form of homogeneous areas; systematic analysis of factors of anthropogenic transformation of the young river landscape; analysis of changes in the morphology of the riverbed and floodplain using GIS and GPS technologies. The state of research in the context of the research. A number of scientific works had been devoted to the study of anthropogenic changes in the bed and floodplain of the Prut River. In particular, regarding changes in morphology, these are the works of Yu. Yushchenko, A. Kyrylyuk, M. Pasichnyk, M. Nastyuk [3,4,7,9,11]. An important issue of the study is to identify the territorial structure of the river hydromorphological landscape.This is one of the important tasks of riverbed science [10] and landscape studies. Relevant studies are conducted in relation to rivers and river valleys of the Uppon Prut system [5, 9, 11,12]. Conclusions.Threats from catastrophic floods are an important factor in shaping the relations between society and the Carpathian rivers. Flood protection programs have long been developed. An important element are the embankment dams. Currently, most dams perform their function quite well. Last but not least, this is due to the entrenchment of riverbed. But this positive has a "bitter taste". In addition, an objective assessment of the effectiveness of flood protection and shore protection requires a thorough study of their entire history, which is the subject of a significant separate study. The risk factor for floods has influenced not only the objective formation of the system of protection by society, but also the "not very correct" use of the concepts of "harmful effects of water" and the regulation of riverbeds. It is known that due to the entrenchment of riverbeds, engineering structures in their channels are destroyed. But the entrenchment of riverbeds, as we found out, is anthropogenically caused. What is the "harmful effect of water"? Processes in society are probably harmful… The main factor in the anthropogenic transformation of the hydromorphological basis of the young landscape of the Prut River was the selection of alluvium from the riverbed. This led to a significant entrenchment of the river, especially in places of picking of river sediments (over 4 meters), and an increase in the relative height of floodplains with a corresponding transformation of their hydrological regime and other consequences. When the river entrenchment happened, the riverbed and the flow move to a lower hypsometric level and the objective laws of the flow-channel system begin to appear on it. These are the laws of formation and development of certain forms, the laws of hydromorphology. This includes the development of so-called intra-riverbed forms, and the development of riverbed forms (branches, meanders). It can also lead to conflicts with human interests: erosion of shores, coastal areas, buildings, etc. In such conditions, protective control work is really needed. But they can and should be carried out without the selection of river alluvium, which is not always in the case. By selecting alluvium again, we are only exacerbating the problem. Thus, it would seem that fair ideas of protection against dangerous phenomena and regulation of the flow-channel system are actually used incorrectly and lead to a worsening of the situation. A dangerous anthropogenic geomorphological process is developing. According to all methods of assessing the state of the hydromorphological basis of the landscape for the Prut River, estimates of "very bad" or "pre-crisis state" were obtained.
The purpose of the research was to study the pedagogical aspects of students’ digital competence development and the degree of teachers’ encouragement to develop their own professional digital competence. The study is based on quantitative and qualitative methodology and contains an online structured interview of 132 teachers of Ukraine who took an online course on the development of digital competencies. Results. University teachers demonstrated different beliefs and effectiveness in the use of ICT for pedagogical purposes. Although a few teachers seamlessly integrated ICT into the learning process, most were more tool-oriented and supported a teacher-rather than student-centered approach when designing online courses. In a pandemic, teachers are massively interested in the development of digital competence as part of professional development. At the same time, the strategy of the university and the practice of functioning of the university testify to the lack of a course for the implementation of absolute digital pedagogy.
Research of precipitation, water balance of river basins, and the impact of precipitation on river runoff remain relevant in the context of global and regional climate change. Nowadays, many scientific research all over the world are devoted to the research of the problem of river runoff change under the influence of climatic factors. This kind of research has been developing strongly in Ukraine in recent decades. In particular, they concern the rivers of the Ukrainian Carpathians. The basin of the river Putyla to the line of the village of Putyla has an area of 181 km2. It is located in the south-eastern part of the Carpathian and characterized by a significant influence of warm rains on the formation of water runoff. The average annual runoff is characterized by rather complex patterns of change both in time and space. There are periodic, cyclical and unidirectional changes that occur under the influence of a complex system of factors. Climate is a major factor of the water change. Thus, the research of the average runoff of the Putila River has different aspects.To determine the effect of precipitation on river runoff, the method of comparing difference-integral curves of annual runoff and precipitation, as well as water-balance methods are used. Long-term changes and intra-annual distribution of precipitation, in particular rainfall, according to the observations of the meteorological station Selyatyn were analyzed. We constructed a differential integrated curve of modular coefficients of the average annual precipitation in the Putil district. It clearly reflects the cyclical changes in precipitation. Long-term changes and intra-annual distribution of water runoff in the Putyla River also were analyzed. During the observation period, periods of long-term fluctuations of the average annual precipitation were revealed. The average annual rainfall is 842.9 mm. The annual course is stable, ie the greatest amount of precipitation falls in the summer, when there are intense thunderstorms and showers, the least – in winter. Based on the data of hydrological observations, the average long-term value of water consumption according to GP Putila is 2.47 m3/s. We calculated the coefficient of variability (variation). The coefficient of variation for average costs is 0.21 (21%), and for precipitation – 0.7 (7%). The connection between precipitation and runoff was established. We have built a comprehensive schedule of annual distribution of precipitation and costs of the Putyla River for 2010. You can see that in the spring due to snowmelt there is an influx of water and there is a spring flood. It is known that 2010 in Putilsky district was full of water. The reduction of water consumption in the Putyla River in the cold period of the year with a decrease in precipitation is also observed. Graph of the dependence of the runoff of the Putyla River on precipitation in the village of Selyatyn showed a fairly clear relationship between the variable values of runoff and precipitation (the coefficient of variation is 0,66). The feeding structure of the Putyla River is mixed. The main share is occupied by rain, less - snow and groundwater. Key words: climate change, precipitation, runoff, rivers, long-term changes in runoff, intra-annual distribution of precipitation and runoff, Putyla river.
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