key: cord-1003858-vqke48ur authors: Nesteruk, Igor title: Stabilization of the coronavirus pandemic in Italy and global prospects date: 2020-03-30 journal: nan DOI: 10.1101/2020.03.28.20045898 sha: c11bf5973ac0226c766a5bbe8024d0d993a55dd4 doc_id: 1003858 cord_uid: vqke48ur The pandemic caused by coronavirus COVID-19 are of great concern. A detailed scientific analysis of this phenomenon is still to come, but now it is urgently needed to evaluate the parameters of the disease dynamics in order to make some preliminary estimations of the number of cases and possible duration of the pandemic. The corresponding mathematical models must be simple enough, since their parameters are unknown and have to be estimated using limited statistical data sets. The SIR model, statistical approach to the parameter identification and the official WHO daily data about the confirmed cumulative number of cases were used to calculate the SIR curves and make some estimations and predictions. New cases in Italy could stop to appear after May 12, 2020, and the final number of such accumulated cases could be around 112 thousand. Some prospects for the global pandemic dynamics are discussed. Here, we consider the development of epidemic outbreak in Italy caused by coronavirus COVID-19 (2019-nCoV) (see e.g., [1] ). Some investigations of the epidemic spreading in mainland China [2] [3] [4] [5] [6] [7] could be useful to understand the epidemic outbreak in other countries, since we deal with the same pathogen. A preliminary comparison of the epidemic dynamics in Italy and in mainland China has been done in [8, 9] . In [10] the global coronavirus epidemic dynamics was analyzed. In this paper we will use the official WHO daily data [1] for the confirmed accumulated number of patients (victims) V(t) (number of persons who caught the infection and got sick; t is time measured in days), the SIR model [11] [12] [13] [14] and the statistics-based method of parameter identification [14] in order to calculate the pandemic characteristics and to make some estimations and predictions. 2 9 2036 2732 64 5753 3 10 2502 3367 108 7341 4 11 3089 4307 129 8993 5 12 3858 5820 148 11197 6 13 4636 7491 213 14347 7 14 5883 9453 213 17593 8 15 7375 12242 213 21291 9 16 9172 15130 472 25265 10 17 10149 18124 696 29609 11 18 12462 23112 987 36410 12 19 15113 28892 1264 43788 13 20 17660 36263 1678 53427 14 21 21157 45060 1678 64304 15 22 24747 55623 1678 The official data about the accumulated number of confirmed cases in Italy V j ; European region V Ej , USA V Uj and global numbers V Gj (without cases inmainland China and the Republic of Korea) from the WHO daily situation reports ( numbers 33-65, [1] ) will be used. The corresponding moments of time t j (in days) are also shown in Table 1 . The SIR model for an infectious disease [6, [11] [12] [13] [14] relates the number of susceptible persons S (persons who are sensitive to the pathogen and not protected); the number of infected is I (persons who are sick and spread the infection; please don't confuse with the number of still ill persons, so known active cases) and the number of removed R (persons who no longer spread the infection; this number is the sum of isolated, recovered, dead, and infected people who left the region);  and  are constants. To determine the initial conditions for the set of equations (1-3), let us suppose that at the moment of the epidemic outbreak 0 t , [6, 14] : The analytical solution for the set of equations (1-3) was obtained by introducing the function , corresponding to the number of victims or cumulative confirmed number of cases, [14] : The solution for the SIR set of differential equations depends on four parameters N,  , which can be identified with the use of the statistical approach developed in [14] . This method and V j data set for Italy were used to define the optimal (the most reliable) values of four parameters and calculate numbers of infected I , susceptible S, removed R persons and the number of victims V=I+R . Corresponding dependences versus time are shown in Fig. 1 . Usually the number of cases during the initial period of an epidemic outbreak is not reliable. To avoid their influence on the results, only V j values for the period February 5-22, 2020 (12 29 j t   ) were used for calculations (see blue "circles" in Fig. 1 ). Other points were used only for comparison 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 March 30, 2020. . https://doi.org/10.1101/2020.03.28.20045898 doi: medRxiv preprint (blue "triangles") and verification of predictions (blue "stars"). The use of data corresponding the initial stage of the epidemic ("circles" and "triangles" together) did not yield a stable reliable prediction. The calculated optimal values of parameters are: in [9] (on March 24 the accumulated number of cases confirmed in mainland China is 81848, see [1] , situation report No 65). On March 9, 2020 it was calculated that the epidemic in Italy develops more rapid than it was in China, [15] . Unfortunately, this conclusion seems to be true. For Italy: numbers of infected I (green line), removed R (black line) and the number of victims V=I+R (blue line); "circles" correspond to the confirmed accumulated number of cases taken for calculations; "triangles" correspond to the cases during initial stage of the epidemic; "stars" -last two data points used only for a verification of the prediction. Brawn, red and magenta markers represent respectively the numbers of cases in European region, USA and in the World (without cases in mainland China and South Korea); corresponding dashed lines fit the points. 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 March 30, 2020. . To estimate the duration of the coronavirus epidemic outbreak in Italy, we can use the hours. By comparison, in South Korea was approximately 4.3 hours [16] and in mainland China -2.5 days [9] . By mid-April 2020, there will still be more than thousand people spreading the infection in Italy (see green line in Fig. 1 ). The calculated value 0 t and blue line in Fig. 1 March 24) is much smaller than in Italy. All the parameters in SIR model are supposed to be constant. If the quarantine measures and speed of isolation change or new infected persons are coming in the country, the accuracy of the prediction reduces. Since the recent situation in mainland China and the Republic of Korea is stable, The estimations of global pandemic prospects have been done without cases in this two regions. The corresponding numbers V Gj are shown in the last column of Table 1 and in the Fig. 1 (magenta "circles"). The number of cases V Ej and V Uj are also shown in Fig. 1 (brown and red "circles" respectively). It can be seen that V Ej , V Uj and V Gj numbers follow straight lines in the logarithmic scale. It means that the epidemic dynamics in these regions is still exponential and is far from stabilization. To estimate the slopes of these lines the linear regression for the values log( ), , , was used (see, e.g., [14, 17] ). The corresponding best fitting dashed lines are shown in Fig.1 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 March 30, 2020. . https://doi.org/10.1101/2020.03.28.20045898 doi: medRxiv preprint globally. Let us hope that quarantine measures and fast isolation of infected persons will reduce these sad figures. 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