key: cord-0854508-irh1cwvz authors: Pan, Hanshuang; Shao, Nian; Yan, Yue; Luo, Xinyue; Ahmadi, Ali; Fadaei, Yasin; Cheng, Jin; Chen, Wenbin title: Multi-chain Fudan-CCDC model for COVID-19 in Iran date: 2020-04-28 journal: nan DOI: 10.1101/2020.04.22.20075630 sha: f363e6ab869c80cde54e2749b6f3fb5d169fd128 doc_id: 854508 cord_uid: irh1cwvz Background: COVID-19 has been deeply affecting people's lives all over the world. It is significant for prevention and control to model the evolution effectively and efficiently . Methods: We first propose the multi-chain Fudan-CCDC model which is based on the original single-chain model to describe the revival of COVID-19 in some countries. Multi-chains are considered as the superposition of distinctive single chains. Parameter identification is carried out by minimizing the penalty function. Results: From results of numerical simulations, the multi-chain model performs well on data fitting and reasonably interprets the revival phenomena. The band of 25% fluctuation of simulation results could contain most seemly unsteady increments. Conclusion: The multi-chain model has better performance on data fitting in revival situations compared with the single-chain model. It is predicted by the three-chain model with data by Apr 21 that the epidemic curve of Iran would level off on round May 10, and the final cumulative confirmed cases would be around 88820. The upper bound of the 95% confidence interval would be around 96000. COVID-19 is a new pandemic disease and precise data on its epidemic spread are not available in Iran and in the world. Important questions in peoples mind are as follow: How many people have COVID-19 in Iran? What is the status of COVID-19 epidemic curve in Iran? When will the epidemic will develop and how it ends? Those questions have been preliminarily investigated in terms of modeling and use the daily reports of definitive COVID-19 patients released by Iran Ministry of Health and Medical Education in [2] . In this paper, we apply the multi-chain Fudan-CCDC model to analyze COVID-19 situations in Iran and present our predictions. The Fudan-CCDC model has been proposed in [10, 9, 13] based on the TDD-NCP model [14, 4, 3, 6, 7, 12] , where the time delay process was taken into account. It also introduced a series of new convolution kernels for the time delay terms by applying several time distributions acquired from an important paper [5] by CCDC (China Center for Disease Control and Prevention). Both the TDD-NCP model and the Fudan-CCDC model are single-chain models, and have been performed well in 2 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 April 28, 2020. . https://doi.org /10.1101 /10. /2020 analyzing the evolution of COVID-19 in China, and its early stage of global transmission [11, 15] . When tracking with our models, we proposed a multi-chain model in [8] to model the epidemic trend and predict cases in Singapore and found that the multi-chain model had better performance on data fitting in revival situations of countries like Singapore. We introduce two models in this part, the single-chain Fudan-CCDC model and the multi-chain Fudan-CCDC model, which are similar to [8] . The single-chain Fudan-CCDC model describes one chain of transmission. And the multi-chain Fudan-CCDC model assumes that there may more than one transmission chain in the country, due to new imported cases, the spread of the epidemic in different regions or other reasons. As is mentioned in [11, 9, 10, 13, 15] , our single-chain Fudan-CCDC model is as follows: where β and are the infection rate and the isolation rate respectively, which can be changed in time. I(k) and J(k) represent the cumulative infected people and the cumulative confirmed cases at day k, respectively, and G(k) is the instant (not cumulative) 3 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 April 28, 2020. . https://doi.org/10.1101/2020.04.22.20075630 doi: medRxiv preprint number of infected isolated not yet confirmed by the hospital. I 0 (k) is the number of people who are infected but not in quarantine or hospitalization. f 2 (k) and f 4 (k) are the transition probabilities from infection to illness onset, and from infection to hospitalization, respectively, which are extracted from [5] by CCDC. The kernels like f 2 (k) and f 4 (k) may be different in country. Note that the expression (3) is a little bit different from the one in [8] mainly considering the real situation. The model can be used to fit the reported numbers of the cumulative confirmed cases and predict the evolution of epidemic, and the details can be found in [11, 9, 10, 13, 15 ]. As is mentioned in [8] , the multi-chain Fudan-CCDC model is the superposition of several single chains: and we obtain the sum forms: where t m is the start time of the m-th source. For both the multi-chain model, infection rate β and isolation rate of the fisrt chain are obtained by fitting data before a specific time node. Considering that the isolation rate should be stable in a certain region, we suppose that it stay the same. 4 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 April 28, 2020. The optimization process is similar with the method used in [8] , however we changed the objective function as follows: . where f (β, ; t) = ||J − data|| 2 , and data means the public data of cumulative confirmed cases. The unknown parameters were estimated by running the fminsearch, a MATLAB function. And we get the 95% confidence interval (CI) of our prediction by nlpredci. While tracking the Iran's epidemic trend in every day [2, 1] , single chain model performed well at first. However, around March 17, we found that single chain model failed for the daily increment did not drop down as model expected, then we first successfully identify the parameters of two-chain model on March 19. As we mentioned in [8] , when a sudden turn appears in the curve of reported confirmed cases, we have reason to suppose that there is a new chain. Around March 24 we can observe that in Iran's epidemic trend. Similarly, on April 10, there is a sudden increase in daily increment ,which was twice the predicted value of the previous two-chain model. At the same time, we observed that the public data of total confirmed cases exceeds the maximum of the previous twochain model, shown in Fig 1. That all aroused the suspicion whether the third chain is generated. We did reverse a new chain. 5 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 April 28, 2020. 6 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 April 28, 2020. In Figure 2 (b), we show the 95% CI with blue lines, the scattered are still public data, the black line represents our predicted result. (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 April 28, 2020. (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 April 28, 2020. Table In Table 1 , the notations t j , i j , r j , j represents jth chain's parameters, the notation max is the predicted final infected number, and t end represents the predicted end date. As so far, through simulations, we find that the evolution of the epidemic so far can be well explained by three-chain Fudan-CCDC model, although in real-life transmissions, the number of chains may be far more than three. It is very happy to see that the trend 9 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 April 28, 2020. Observing the parameter table (see Table 1 ), we can see that each parameter is relatively stable. The final number of people predicted was not fluctuating too much, and the prediction of the end of the epidemic is stable after April 11. Since April 10 when we observed the new chain, the second chain has been performing more stable than the third chain. The change of results between April 10th and 11th was the largest during these days, mainly due to the large gap between the increments in the two consecutive days and the model prediction results, then the model was revised accordingly. It can be seen from Figure 5 that the prediction results of the model on April 12 have been able to accurately characterize the third chain, so that in the following week, the trend of the epidemic is in line with model prediction. In the experiment, we can see that the newest chain is unstable at first, generally increasing. Compared with the results of April 10 and April 11, the third chain had a jump. After April 11, the third chain tends to stabilize. There are two possible reasons. One is that as time goes by, the information exposed by the new chain increases, and after going out of the independent trend, the model is revised during optimization. Second, the propagation of the third chain itself is still unstable, and the intensity of the third chain itself is gradually increasing with the passage of time. If there are two reasons, it is of great significance to discover and block the transmission in time. Its hard to verify the new chain at the very early stage. Only when the number of infections caused by the new chain reaches a certain relative size will it be discovered. 10 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 April 28, 2020. . This can be seen from the third chain of propagation from March 12, but it was not discovered until April 10. After all, the model only analyzes and interprets the data, and cannot determine the propagation in reality. All a good model can do is to discover the new chain of transmission as early as possible and evaluate its impact as accurately as possible, which will ultimately help in the judgment of epidemic decisions. Model accuracy also depends on public data. For poor quality data, what the model can do is to propose better optimization methods and data processing methods. But the ultimate influence is ultimately limited. Good data will undoubtedly bring more accurate results. These may be improved in future work. In our multi-chain model assumption, multiple propagation chains are independent and do not affect each other. But when multiple chains appear within a short period of time, do we need more delicate models to characterize? These questions will be improved in the next stage of work. According to the data results as of April 21, the end for the Iran epidemic is about May 10, and the final number is about 88820. At the same time, we need to pay close attention to the daily increment at this stage. When the daily increment does not drop down or even has a Numerical rebound, it may indicate anthor chain, then the duration of the epidemic will be extended and the total number will also increase. This article illustrates that it is of great significance to prevent the spread of new chains. To achieve this, people need to practice social distancing, detect and isolate the confected early. 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 April 28, 2020. . https://doi.org/10.1101/2020.04.22.20075630 doi: medRxiv preprint 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 April 28, 2020. . https://doi.org/10.1101/2020.04.22.20075630 doi: medRxiv preprint The national committee on covid-19 epidemiology in ministry of health and medical education Modeling and forecasting trend of covid-19 epidemic in iran until may 13, 2020 A time delay dynamic system with external source for the local outbreak of 2019-nCoV A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia A time delay dynamic model with external source and the basic reproductive number estimation for the outbreak of Novel Coronavirus Pneumonia Modeling the trend of outbreak of COVID-19 in the Diamond Princess cruise ship based on a time-delay dynamic system Multi-chain fudanccdc model for covid-19 -a revisit to singapore's case Some novel statistical time delay dynamic model by statistics data from CCDC on Novel Coronavirus Pneumonia The reproductive number r 0 of COVID-19 based on estimate of a statistical time delay dynamical system COVID-19 in Japan: what could happen in the future? Modeling for COVID-19 and the prediction of the number of the infected based on fudan-ccdc Dynamic models for CoVID-19 and data analysis Modeling and prediction for the trend of outbreak of NCP based on a time-delay dynamic system COVID-19 in Singapore: another story of success We are very grateful to the efforts of Cheng's group members and the supports by