Approximation methods for analyzing multiscale stochastic vector-borne epidemic models

Estimation of the probability of daily fluctuations of incidence of COVID-19 according to official data

When studying the dynamics of morbidity and mortality, one should not limit ourselves to analyzing general trends. Interesting information can be obtained from the analysis of deviations in morbidity and mortality from the general dynamics. Comparison of the cases of morbidity or death for adjacent time intervals allows us to find out whether the changes in conditions were for short periods of time and whether the cases of morbidity or death were independent. The article consists of two parts: Study of the probability distribution (CDF) of the difference between two independent observations of the Poisson distribution; Application of the results to analyze the morbidity and mortality trends by day for the new coronavirus infection. For the distribution function of the module of difference between two independent observations of the Poisson distribution, an analytical expression has been obtained that allows to get an exact solution. A program has been created, whose software can be downloaded at http://1mgmu.com/nau/DeltaPoisson/DeltaPoisson.zip. An approximate solution that does not require complex calculations has also been obtained, which can be used for an average of more than 20. If real difference is greater than expected, it may be in the following cases: morbidity or mortality varies considerably during the day. That could happen, for example, if the registered number of morbidity on Saturday and Sunday is less than on weekdays due to the management model of the health system, or if the cases are not independent; for example, due to the active identification of infected people among those who have come into contact with the patient. If the difference is less than expected, it may be due to external limiting factors, such as a shortage of test systems for making a diagnosis, a limited number of pathologists to determine the cause of death, and so on. In the analysis of the actual data for COVID-19 it was found that for Poland and Russia, excluding Moscow, the difference in the number of cases and deaths is greater than expected, while for Moscow-less than expected. This may be due to the information policy-the effort to somehow reassure Moscow's population, which in the spring of 2020 had a high incidence rate of the new coronavirus infection.