key: cord-1046407-y7giefdw authors: Jia, Wangping; Han, Ke; Song, Yang; Cao, Wenzhe; Wang, Shengshu; Yang, Shanshan; Wang, Jianwei; Kou, Fuyin; Tai, Penggang; Li, Jing; Liu, Miao; He, Yao title: Extended SIR prediction of the epidemics trend of COVID-19 in Italy and compared with Hunan, China date: 2020-03-20 journal: nan DOI: 10.1101/2020.03.18.20038570 sha: 85dafe8c9e62aa864a47f79f8452cc157f9392e6 doc_id: 1046407 cord_uid: y7giefdw Background: Coronavirus Disease 2019 (COVID19) is currently a global public health threat. Outside of China, Italy is one of the most suffering countries with the COVID19 epidemic. It is important to predict the epidemics trend of COVID19 epidemic in Italy to help develop public health strategies. Methods: We used time series data of COVID 19 from Jan 22,2020 to Mar 16,2020. An infectious disease dynamic extended susceptible infected removed (eSIR) model, which covers the effects of different intervention measures in dissimilar periods, was applied to estimate the epidemic trend in Italy. The basic reproductive number was estimated using Markov Chain Monte Carlo methods and presented using the resulting posterior mean and 95% credible interval (CI). Hunan, with similar total number of populations in Italy, was used as a comparative item. Results: In the eSIR model, we estimated that the basic reproductive number for COVID 19 was respectively 4.10 (95% CI: 2.15 to 6.77) in Italy and 3.15(95% CI: 1.71 to 5.21) in Hunan. There would be totally 30 086 infected cases (95%CI:7920-81 869) under the current country blockade and the endpoint would be Apr 25 (95%CI: Mar 30 to Aug 07) in Italy. If the country blockade is imposed 5 day later, the total number of infected cases would expand the infection scale 1.50 times. Conclusion: Italy's current strict measures can efficaciously prevent the further spread of COVID19 and should be maintained. Necessary strict public health measures be implemented as soon as possible in other European countries with a high number of COVID19 cases. The most effective strategy needs to be confirmed in further studies. Introduction 34 The Corona Virus Disease 2019 started in Wuhan, China in December and quickly 35 spread to China and many countries and regions in the world (1) (2) (3) . The COVID-19 outbreak made 36 assessment as a pandemic by the World Health Organization (WHO) on March 11. It is currently a 37 global public health threat and more than 100 countries including Italy, Iran, the United States, South 38 Korea, and Japan are suffering from COVID-19. Outside of China, Italy is one of the most suffering 39 countries with the COVID-19 epidemic. As of Mar 16, the cumulative number of confirmed cases in 40 Italy reached 27980, ranking second in the world, the total confirmed deaths, 2158, and the fatality 41 rate, as high as 7.71%, which has become one of the highest among the major epidemic countries. 42 However, few studies have assessed the epidemic status in Italy(4, 5). 43 Global public health measures are required to cope with the rapid spread of the epidemic. China has 44 taken precise and differentiated strategies, including self-quarantine of residents in Wuhan and other 45 areas, community-based prevention and control. These measures have played an important role in 46 preventing and controlling the epidemic. Previous studies have shown that due to the isolation of 47 Wuhan, the overall epidemiological progress in mainland China has been delayed by three to five 48 days and the number of internationally transmitted cases has been reduced by nearly 80%(6). Italy 49 detected the first two cases of imported COVID-19 on Jan 31. After that, Italy was the first country to 50 declare a state of emergency. Since then, various measures have been implemented to control the 51 spread of COVID-19. It is vital to evaluate the role of Italian quarantine measures for decision-52 making. 53 Mathematical modeling is helpful to predict the possibility and severity of disease outbreak and 54 provide key information for determining the type and intensity of disease intervention. The SIR 55 model and its modifications such as SEIR model have been widely applied to the current outbreak of 56 COVID-19. Tang et al. estimated the infectivity of COVID-19 based on a classical susceptible-57 exposed-infected-removed (SEIR) epidemiological model (7). Wu et al proposed an extended SEIR 58 model to forecast the spread of 2019-nCoV both within and outside of mainland China(3) . However, 59 these studies assumed that the exposed population were not infectious, which may be not suitable in 60 COVID-19. Yang Z et al. predicted that China's epidemic will peak in late February and end in late 61 April by a combination of SEIR model and a machine-learning artificial intelligence (AI) 62 approach(8). However, this study and the above studies did not consider the phase-adjusted 63 preventive measures and time-varying parameters, which may affect the accuracy of predictions. 64 We adopted extended susceptible-infected-removed (eSIR) model (9), which covers the effects of 65 different epidemic prevention measures in different periods and helps to achieve the following 66 specific objectives: 67 Methods 72 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2020 . . https://doi.org/10.1101 In this study, we used the publicly available dataset of COVID-19 provided by the Johns Hopkins 74 University(10). This dataset includes many countries' daily count of confirmed cases, recovered 75 cases and deaths. As time-series data, it is available from 22 January 2020. Besides, we also gathered 76 and cross-checked data in DXY.cn(11), a website providing real-time data of the COVID-19. 77 These data are collected through public health authorities' announcements and are directly reported 78 public and unidentified patient data, so ethical approval is not required. 79 The reproduction number, R0, reflects the transmissibility of a virus spreading under no control, 81 representing the average number of new infections generated by each infected person(12 The transmission rate modifier π(t) can be specified according to actual interventions in different 102 times and regions. According to Chinese government isolation measures and previous study, we set 103 π(t)=0.9 if t ∈ (Jan 23, Feb 04], city blockade; π(t)=0.5 if t ∈ (Feb 4, Feb 8], enhanced quarantine; 104 π(t) β All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2020. . https://doi.org/10.1101/2020.03.18.20038570 doi: medRxiv preprint π(t)=0.1 if t ＞Feb 8, more enhanced quarantine in Hunan. In the opinion of Italy government 105 isolation measures, we set π(t)=0.9 if t ＜Mar 4, no concrete quarantine protocols; π(t)=0.5 if t ∈ ( 106 Mar 04, Mar 09], some cities blockade and enhanced quarantine; π(t)=0.1 if t ＞Mar 09, country 107 blockade and more enhanced quarantine in Italy. We also assumed that the Italy government took 108 country blockade and intensified quarantine on Mar 05 or Mar 15. 109 We did prediction with an R software package-eSIR which can output the Markov Chain Monte 110 Carlo (MCMC) estimation, inference, and prediction under the extended SIR models with time-111 varying transmission modifier π(t). The model can also yield the turning points of the 112 epidemiological trend of COVID-19. The first turning point was defined as the mean predicted time 113 when the daily proportion of infected cases becomes smaller than the previous ones. The second 114 turning point was defined as the mean the predicted time when the daily proportion of removed cases 115 (i.e. both recovered and dead) becomes larger than that of infected cases. Besides, an end point was 116 defined as the time when the median proportion of current infected cases turn to zero. 117 We did all analyses in R (version 3.6.2). 118 Results 119 Discussion 143 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2020. . https://doi.org/10. 1101 This impact of the COVID-19 response ( overall quarantine regulations , social distancing, and 144 isolation of infections) in China is encouraging for the many other countries(13).We compared the 145 situation in Hunan, China, which has the similar population as Italy to predict. The spread of COVID-146 19 in Hunan Province appeared relatively early and has now entered a phase of no inflections, which 147 helps to observe the entire course of the epidemic. Besides, due to the similarity of population size and 148 geographical location adjacent to Hubei, Hunan's public health measures can provide useful guidance 149 for Italy in preventing the further spread of In our study, the eSIR model with R software package was used to evaluate the impact of intervention 151 measures on Italian COVID-19 epidemic. In previous studies, estimation of the epidemic of an 152 infectious disease is often performed using constant parameter(14-17). been so far much less severe.(9) But they did not perform each province's analyses. The first and 156 second points in our study are respectively Feb 04 and Feb 09，which are the same as these outside 157 Hubei in China. Furthermore, the actual number of infected cases (1018) is included in the predicted 158 number of infected cases (786-9065) and the endpoint(Feb 29) is included in the predicted 159 endpoint(Feb 19 to Mar 23) in our study, which also reflects stability and accuracy of the eSIR model. 160 Combining the above data and methods, these findings show that eSIR model is more suitable for 161 predicting the epidemic trend of Our results showed that R0 was estimated to be respectively 3.12 (95% CI, 1.83-3.01) and 3 This study showed that COVID-19 spread rapidly throughout Italy after Feb 21. Possible reasons for 172 such rapid growth of infections include:(1) more timely caution and preventative measures were not 173 taken, (2) The number of infections during Jan 31-Feb 20 could be under-reported due to 174 underdiagnosis, given subclinical or asymptomatic cases. The incubation period for COVID-19 is 175 thought to be within 14 days following exposure, with most cases occurring approximately four to five 176 days after exposure (18, 22, 23) . So it seems impossible to maintain totally two or three cases during Jan 177 31-Feb 20 in Italy. In addition, the rapid increase in the number of infections after Feb 21 might reflect 178 a belated realization of the spread of Previous studies have shown that more rigorous government control policies were associated with a 180 slower increase in the infected population (6, 16, (24) (25) (26) (27) including the early detection and isolation of individuals with symptoms, traffic restrictions, medical 188 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted March 20, 2020 . . https://doi.org/10.1101 tracking, and entry or exit screening, can well prevent the further spread of COVID-19. These 189 measures are in line with the latest recommendations by the World Health Organization and a 190 previous study in Spain (28) . But the most effective strategy still needs to be confirmed by further 191 studies. Consequently, it is better and necessary to apply strict public health measures in other 192 European countries with a high number of Our study has some limitations. Firstly, it is based on the assumption that rigorous measures like 194 China have been taken in Italy, although this study uses the new model to obtain dynamic results, 195 which is instructive for the prevention and control of the epidemic in Italy. Secondly, the suspected 196 cases and the daily number of hospitalized cases are not available, so they are not considered in the 197 eSIR model. Thirdly, some unforeseeable factors may affect these estimated data in our study such as 198 super-spreaders exist. 199 In conclusion, the current study is the first to provide a prediction for epidemic trend after strict 200 prevention and control measures were implemented in Italy. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The black dots left to the blue vertical line denote the observed proportions of the infected and removed 329 compartments on the last date of available observations or before. The blue vertical marks is the current 330 time up to which we have observed data (t0). The green and purple vertical lines denote the first and 331 second turning points, respectively. The cyan and salmon color area denotes the 95% credible interval 332 of the predicted proportions of current infected cases before and after t0, respectively. The gray and red 333 curves are the posterior mean and median curves. 334 Epidemiological trend of COVID-19 under existing preventions of Hunan, China and Italy in eSIR 335 model 336 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 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