Waves of COVID-19 pandemic. Detection and SIR simulations

Nesteruk, I.

Background. Unfortunately, the COVID-19 pandemic is still far from stabilizing. Of particular concern is the sharp increase in the number of diseases in June-July 2020. The causes and consequences of this sharp increase in the number of cases are still waiting for their researchers, but there is already an urgent need to assess the possible duration of the pandemic, the expected number of patients and deaths. The resumption of international passenger traffic needs the information for deciding which countries' citizens are welcome guests. Correct simulation of the infectious disease dynamics needs complicated mathematical models and many efforts for unknown parameters identification. Constant changes in the pandemic conditions (in particular, the peculiarities of quarantine and its violation, situations with testing and isolation of patients) cause various epidemic waves, lead to changes in the parameter values of the mathematical models. Objective. In this article, pandemic waves in Ukraine and in the world will be detected, calculated and discussed. The estimations for hidden periods, epidemic durations and final numbers of cases will be presented. The probabilities of meeting a person spreading the infection and reproduction numbers will be calculated for different countries and regions. Methods. We propose a simple method for the epidemic waves detection based on the differentiation of the smoothed number of cases. We use the known SIR (susceptible-infected-removed) model for the dynamics of the epidemic waves. The known exact solution of the SIR differential equations and statistical approach were modified and used. Results. The optimal values of the SIR model parameters were identified for four waves of pandemic dynamics in Ukraine and five waves in the world. The number of cases and the number of patients spreading the infection versus time were calculated. In particular, the pandemic probably began in August 2019. If current trends continue, the end of the pandemic should be expected no earlier than in March 2021 both in Ukraine and in the world, the global number of cases will exceed 20 million. The probabilities of meeting a person spreading the infection and reproduction numbers were calculated for different countries and regions. Conclusions. The SIR model and statistical approach to the parameter identification are helpful to make some reliable estimations of the epidemic waves. The number of persons spreading the infection versus time was calculated during all the epidemic waves. The obtained information will be useful to regulate the quarantine activities, to predict the medical and economic consequences of the pandemic and to decide which countries' citizens are welcome guests.