Objective. To develop methods for a rapid distance computer diagnosis of COVID-19 based on the analysis of breath sounds. It is known that changes in breath sounds can be the indicators of respiratory organs diseases. Computer analysis of these sounds can indicate their typical changes caused by COVID-19, and can be used for a rapid preliminary diagnosis of this disease. Materials and methods. The method of fast Fourier transform (FFT) was used for computer analysis of breath sounds, recorded near the mouth of 14 COVID-19 patients (aged 1880 years) and 17 healthy volunteers (aged 548 years). The frequency of breath sound records ranged from 44 to 96 kHz. Unlike the conventional methods of computer analysis for diagnosis of diseases based on respiratory sound studying, we offer to test a high-frequency part of FFT (20006000 kHz). Results. While comparing the breath sound FFT in patients and healthy volunteers, we developed the methods for COVID-19 computer diagnosis and determined the numerical criteria in patients and healthy persons. These criteria do not depend on sex and age of the examined persons. Conclusions. The offered computer methods based on the analysis of breath sound FFT in patients and volunteers permit to diagnose COVID -19 with relatively high diagnostic parameters. These methods can be used in development of noninvasive means for preliminary self-express diagnosis of COVID-19.

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven distribution of population, changes in population mobility, and changes in frequency of contacts between susceptible and infected people due to quarantine. We applied obtained analytical and numerical solutions to analyze different stages in the epidemic as well as its wave-like development influenced by imposing and canceling quarantine limitations. To take into account ultimate rate at which the disease spreads and its incubation period (when an infected person is not a source of contagion), we suggest using equations similar to the Cattaneo-Vernotte one. The suggested model allows predicting where the front of morbidity spread is going to occur, that is, a moving frontier between areas where there are infected people and areas where they are absent. Use of such models provides an opportunity to introduce differential quarantine measures basing on more objective grounds. At the end of 2020 mass vaccination started in some countries. We estimated a necessary number of people that had to be vaccinated so that new waves of COVID-19 epidemic would be prevented; in our estimates, not less than 80% of the country population should be vaccinated. Correct prediction of epidemic development is becoming more and more vital at the moment due to new and more contagious COVID-19 virus strains occurring in England, South Africa, and some other countries. Our research results can be used for predicting spread of COVID-19 and other communicable diseases; they can make for taking the most efficient measures for successful control over epidemics.

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven distribution of population, changes in population mobility, and changes in frequency of contacts between susceptible and infected people due to quarantine. We applied obtained analytical and numerical solutions to analyze different stages in the epidemic as well as its wave-like development influenced by imposing and canceling quarantine limitations. To take into account ultimate rate at which the disease spreads and its incubation period (when an infected person is not a source of contagion), we suggest using equations similar to the Cattaneo-Vernotte one. The suggested model allows predicting where the front of morbidity spread is going to occur, that is, a moving frontier between areas where there are infected people and areas where they are absent. Use of such models provides an opportunity to introduce differential quarantine measures basing on more objective grounds. At the end of 2020 mass vaccination started in some countries. We estimated a necessary number of people that had to be vaccinated so that new waves of COVID-19 epidemic would be prevented; in our estimates, not less than 80% of the country population should be vaccinated. Correct prediction of epidemic development is becoming more and more vital at the moment due to new and more contagious COVID-19 virus strains occurring in England, South Africa, and some other countries. Our research results can be used for predicting spread of COVID-19 and other communicable diseases; they can make for taking the most efficient measures for successful control over epidemics.