The mathematical model reported here describes the dynamics of the ongoing coronavirus disease 2019 (COVID-19) epidemic, which is different in many aspects from the previous severe acute respiratory syndrome (SARS) epidemic. We developed this model when the COVID-19 epidemic was at its early phase. We reasoned that, with our model, the effects of different measures could be assessed for infection control. Unlike the homogeneous models, our model accounts for human population heterogeneity, where subpopulations (e.g., age groups) have different infection risks. The heterogeneous model estimates several characteristics of the epidemic more accurately compared to the homogeneous models. According to our analysis, the total number of infections and their peak number are lower compared to the assessment with the homogeneous models. Furthermore, the early-stage infection increase is little changed when population heterogeneity is considered, whereas the late-stage infection decrease slows. The model predicts that the anti-epidemic measures, like the ones undertaken in China and the rest of the world, decrease the basic reproductive number but do not result in the development of a sufficient collective immunity, which poses a risk of a second wave. More recent developments confirmed our conclusion that the epidemic has a high likelihood to restart after the quarantine measures are lifted.

Background. At the current stage of COVID-19 pandemic, forecasts become particularly important regarding the possibility that the total incidence could reach the level where the disease stops spreading because a considerable portion of the population has become immune and collective immunity could be reached. Such forecasts are valuable because the currently undertaken restrictive measures prevent mass morbidity but do not result in the development of a robust collective immunity. Thus, in the absence of efficient vaccines and medical treatments, lifting restrictive measures carries the risk that a second wave of the epidemic could occur. Methods. We developed a heterogeneous model of COVID-19 dynamics. The model accounted for the differences in the infection risk across subpopulations, particularly the age-depended susceptibility to the disease. Based on this model, an equation for the minimal number of infections was calculated as a condition for the epidemic to start declining. The basic reproductive number of 2.5 was used for the disease spread without restrictions. The model was applied to COVID-19 data from Italy. Findings. We found that the heterogeneous model of epidemic dynamics yielded a lower proportion, compared to a homogeneous model, for the minimal incidence needed for the epidemic to stop. When applied to the data for Italy, the model yielded a more optimistic assessment of the minimum total incidence needed to reach collective immunity: 43% versus 60% estimated with a homogeneous model. Interpretation. Because of the high heterogeneity of COVID-19 infection risk across the different age groups, with a higher susceptibility for the elderly, homogeneous models overestimate the level of collective immunity needed for the disease to stop spreading. This inaccuracy can be corrected by the homogeneous model introduced here. To improve the estimate even further additional factors should be considered that contribute to heterogeneity, including social and professional activity, gender and individual resistance to the pathogen.

This work is aimed at analyzing demand dynamics for hydrocarbon fuels from March 2020 and developing a forecast model for the near future. Based on the method of artificial neural network with feedforward and backpropagation learning, a model is proposed for forecasting oil demand and passenger mobility during a pandemic for the United States, Russia, and India. The results of the calculations showed that road and air transport dynamics strongly depend on the application of measures to limit and ban and the level of COVID‐19 incidence in a country. The proposed method can be used to make forecasts during pandemics and unforeseen situations to regulate the price policy for hydrocarbon fuels and the safety of passenger traffic in the future.

The ongoing Coronavirus disease 2019 (COVID-19) epidemic is different from the previous epidemic of severe acute respiratory syndrome (SARS), which demands a rigorous analysis for the selection of anti-epidemic measures and their lifting when the epidemic subsides. Here we estimate the basic reproductive number for COVID-19 and propose a dynamical model for the time course of infection number. With this model, we assessed the effects of different measures for infection risk control. The model is different from the previous ones as it models the population as heterogeneous, with subpopulations having different infection risks. Our analyses showed that after this heterogeneity is incorporated in the model, several characteristics of the epidemic are estimated more accurately: the total number of cases and peak number of cases are lower compared to the homogeneous case, the early-stage growth rate in the number of infection cases is little affected, and the decrease in the number of infections slows down during the epidemic late stage. The comparison of our model results with the available data for COVID-19 indicates that the anti-epidemic measures undertaken in China and the rest of the world managed to decrease the basic reproductive number but did not assure an accumulation of sufficient collective immunity. Thus, the epidemic has a high likelihood to restart, which necessitates a careful approach to lifting the quarantine measures.

This study investigates demutational changes in plant communities of phosphorite mines between 2005 and 2021. A total of 23 plant species were initially found in the surveyed areas in 2005, while 68 species were identified in spring 2021. The plant communities were categorized into five different groups, with the older communities (No. I and II) exhibiting richer vegetation and greater diversity. Community No. III comprised various cereals, legumes, orchid plants, and mosses. Dominant species in community No. I included Betula pubescens, Carpinus betulus, Quercus robur, and Picea obovata, while community No. II featured Juniperus communis, Larix sibirica, Pinus sylvestris, and Abies sibirica. Erosion was observed in community No. V on slopes of different ages. The study also found changes in physicochemical indices, such as increased organic matter concentration and decreased pH value (4.9). The basal respiration rate of the pit soil was low (around 0.4 mg CO2/m2/h), and carbonate content ranged from 0.06 to 0.9%. This study presents novel data on the dynamics of species composition, plant community structure, and physicochemical soil parameters in human-altered habitats, thereby contributing to the expansion of our knowledge of vegetation recovery and evolution in such environments.