key: cord-0263573-bv16xpuq authors: Nesteruk, I. title: Final sizes and durations of new COVID-19 pandemic waves in Ukraine and around the world predicted by generalized SIR model date: 2021-11-24 journal: nan DOI: 10.1101/2021.11.22.21266683 sha: 2e8a1d5608f9d131b2be7346acaf578997e52a33 doc_id: 263573 cord_uid: bv16xpuq New waves of the COVID-19 pandemic in Ukraine, which began in the summer of 2021, and after holidays in the middle of October 2021, were characterized by almost exponential growth of smoothed daily numbers of new cases. This is a matter of great concern and the need to immediately predict the epidemic dynamics in order to assess the possible maximum values of new cases, the risk of infection and the number of deaths. The generalized SIR-model and corresponding parameter identification procedure was used to simulate and predict the dynamics of two new epidemic waves in Ukraine and one in the whole world. Results of calculations show that new cases in Ukraine will not stop to appear before November 2022. If the global situation with vaccination, testing and treatment will not change, the pandemic could continue for another ten years. the method allows us to hope for a fairly accurate forecast for next pandemic waves in Ukraine (12th and 13th) and in the whole world (6th), to which this study is devoted. Some results concerning the 12th epidemic wave in Ukraine are already available in [13] . Table 1 . Cumulative numbers of laboratory-confirmed Covid-19 cases and deaths in Ukraine in the summer and autumn of 2021 according to the national statistics, [22, 23] . We will use the data set regarding the accumulated numbers of laboratory-confirmed COVID-19 cases and deaths in Ukraine from national sources [22, 23] . 2300504 2497643 3075433 57840 72084 7 2239591 2259151 2303276 2514005 3088501 58081 72557 8 2240246 2259451 2306939 2529913 3107489 58331 73390 9 2240753 2260232 2310554 2541257 3130772 58463 74206 10 2241043 2261354 2314423 2550089 3155519 58700 74857 11 2241217 2262601 2316619 2562085 3179577 59052 75601 12 2241698 2263864 2317824 2578394 3203149 59523 76302 13 2242245 2265217 2321156 2597275 3217639 59935 76705 14 2242868 2265912 2325796 2610899 3228441 60137 77147 15 2243605 2266329 2331540 2623882 3244749 60414 78085 16 2244196 2267219 2338164 2635170 3263417 60633 78754 17 2244495 2268666 2344398 2644694 3284008 60810 79506 18 2244677 2270226 2348381 2660273 -61348 -19 2245275 2271826 2350646 2679185 -61843 -20 2245930 2273558 2355805 2701600 -62389 -21 2246656 2274561 2362559 2725385 -63003 -22 2247419 2275171 2370425 2748614 -63486 -23 2248164 2275863 2379483 2769405 -63872 -24 2248450 2276590 2387750 2784039 -64202 -25 2248663 2278171 2392397 2803159 -64936 -26 2249344 2280203 2395404 2825733 -65628 -27 2250061 2282285 2401956 2851804 -66204 -28 2250907 2284191 2411622 2878674 -66852 -29 2251869 2284940 2423379 2904872 -67393 -30 2252785 2286296 2435413 2922302 -67729 -31 2253269 2288371 -2936238 -68027 -moments of time t j (measured in days) are shown in Table 1 for the period of July to November 2021. The values V j , corresponding to the previous moments of time, can be found in [4, [8] [9] [10] . The period to simulate the 12th wave and the period T c13 : October 28 -November 10, 2021 for the 13th wave. Other V j and t j values will be used to control the accuracy of predictions. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in October 2021 is only 0.47). We will use the average value m= 23.36 to predict the number of deaths in Ukraine during the new 12th and 13th pandemic waves. We will use the data set regarding the accumulated numbers of laboratory-confirmed COVID-19 cases in the whole world from the COVID-19 Data Repository by the Center for Systems Science and Table 2 for the period of May to November 2021. The period T c6 : September 29 -October 12, 2021 will be used for SIR simulations of the sixth pandemic wave in the whole world. Other V j and t j values will be used to control the accuracy of predictions. The generalized SIR-model relates the number of susceptible S, infectious I and removed persons R for a particular epidemic wave i, [8, 20] . The exact solution of the set of non-linear differential equations uses the function corresponding to the number of victims or the cumulative laboratory-confirmed number of cases [8, 20] . Its derivative: yields the estimation of the average daily number of new cases. When the registered number of victims V j is a random realization of its theoretical dependence (1), the exact solution presented in [8, 20] depends on five parameters ( i  is one of them). The details of the optimization procedure for their identification can be found in [21] . Since daily numbers of new cases are random and characterized by some weekly periodicity, we will use the smoothed daily number of accumulated cases: All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 24, 2021. ; https://doi.org/10.1101/2021.11.22.21266683 doi: medRxiv preprint and its numerical derivative: to estimate the smoothed number of new daily cases [3, 4, 9, 19 ]. The optimal values of the general SIR model and other characteristics of the 12th and 13th pandemic waves in Ukraine and the 6th wave in the whole world are calculated and listed in Table 3 . Table 1 ) has already exceeded the Table 3 ) and the expected accumulated perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 24, 2021. ; https://doi.org/10.1101/2021.11.22.21266683 doi: medRxiv preprint really achieved a local maximum on October 10, 2021, but started to increase very rapid after October 17, 2022 (see the red "crosses" in Figs. 1 and 2) . perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 24, 2021. ; https://doi.org/10.1101/2021.11.22.21266683 doi: medRxiv preprint significant increase in contacts during the New Year and Christmas holidays or/and the appearance of a new coronavirus strain could disrupt these positive trends. Unfortunately, the general SIR model cannot predict the emergence of new epidemic waves. It simulates the dynamics for only the period with constant epidemic conditions. Therefore, permanent monitoring of the number of new cases is needed to determine changes in the epidemic dynamics. After that it is possible to do new simulations by means of the generalized SIR model with calculation and use of new values of its parameters. , 12th, and 13th waves in Ukraine are shown by black, blue, and brown lines, respectively. Green lines represent the 6th pandemic wave in the whole world. Numbers of victims V(t)=I(t)+R(t) -solid lines (for the world divided by 60); numbers of infected and spreading I(t) multiplied by 5 -dashed; derivatives dV/dt (eq. (2), multiplied by 100 for Ukraine and by 2 for the world) -dotted. "Circles" correspond to the accumulated numbers of cases registered during the periods of time taken for SIR simulations (for the world divided by 60). "Stars" corresponds to V j values beyond these time periods (for the world divided by 60). "Crosses" show the first derivative (4) multiplied by 100 for Ukraine and by 2 for the world. We can only point out the three possible reasons for the new 13th wave in Ukraine: 1. The long weekend of October 14-17, 2021 without significant quarantine restrictions led to a significant increase in travels and contacts. This period accounted for the maximum number of infected (see the blue dashed curve in Fig. 2) . We observed a similar situation in Ukraine in May 2020, when the lockdown was lifted during the period of the maximum number of infectious people, which led to the emergence of the second epidemic wave before the end of the first one, [4, 9] . An increase in contacts during the holidays in early May 2021 also led to an increase in the number of infectious persons (see the black dashed line in Fig. 1 ). But during this period there was a tendency to reduce the All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 24, 2021. ; daily number of new cases, so the increase in contacts only slowed down this trend (see red "crosses" in Fig. 1 ). 2. Due to a large number of asymptomatic patients, many COVID-19 cases are not detected and registered [26] [27] [28] [29] [30] [31] . The ratio of real to detected cases in Ukraine was estimated to be between 4 and 20 for different periods of time [8, 10] . Such large numbers of undetected cases may suddenly change the number of reported cases, if the population frightened by the increase in mortality begins to seek medical care more often. 3. Appearance of new coronavirus strains. The results of SIR simulations of the 12th and 13th waves in Ukraine are shown by blue and brown lines, respectively. Green lines represent the 6th pandemic wave in the whole world. Numbers of victims V(t)=I(t)+R(t) -solid lines (for the world divided by 60); numbers of infected and spreading I(t) (multiplied by 5 for Ukraine) -dashed; derivatives dV/dt (eq. (2), multiplied by 100 for Ukraine and by 2 for the world) -dotted. The magenta lines represent the estimation of the accumulated number of deaths during the 12th (solid) and 13th (dashed) epidemic waves in Ukraine multiplied by 10. Magenta "triangles" represent the accumulated numbers of death in Ukraine form Table 1 multiplied by 10. "Circles" correspond to the accumulated numbers of cases registered during the periods of time taken for SIR simulations (for the world divided by 60). "Stars" corresponds to V j values beyond these time periods (for the world divided by 60). "Crosses" show the first derivative (4) multiplied by 100 for Ukraine and by 2 for the world. The global number of new cases is also characterized by wave-like behavior (see green "crosses" in Fig. 1 ). But unlike Ukraine and many other countries, the difference between the minimum and maximum values of the derivative (4) is much smaller for the world dynamics. The minima of new global cases also do not go to zero (compare green and red "crosses" in Figs. 1 and 2) . All this limits the use of the SIR model for the long-term predictions. In particular, the increase in daily number of new cases (see green "crosses" in Figs. 1 and 2) indicate the beginning of a new global wave after All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 24, 2021. ; https://doi.org/10.1101/2021.11.22.21266683 doi: medRxiv preprint October 15, 2021 (this fact makes the predictions for the 6 th wave no more relevant). It should be noted that the COVID-19 pandemic is characterized by a very slow decline in the number of infectious I(t). In particular, according to the results of modeling of the 6th world wave (shown in Table 3 ), the number of infectious persons worldwide may be less than 100 in May 2021. This small number is enough to continue the pandemic for almost 10 years. The generalized SIR-model and corresponding parameter identification procedure was used to simulate and predict the dynamics of two new epidemic waves in Ukraine and one in the whole world. 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