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The authors have declared that no competing interests exist.

This study integrates the daily intercity migration data with the classic Susceptible-Exposed-Infected-Removed (SEIR) model to construct a new model suitable for describing the dynamics of epidemic spreading of Coronavirus Disease 2019 (COVID-19) in China. Daily intercity migration data for 367 cities in China were collected from Baidu Migration, a mobile-app based human migration tracking data system. Early outbreak data of infected, recovered and death cases from official source (from January 24 to February 16, 2020) were used for model fitting. The set of model parameters obtained from best data fitting using a constrained nonlinear optimisation procedure was used for estimation of the dynamics of epidemic spreading in the following months. The work was completed on February 19, 2020. Our results showed that the number of infections in most cities in China would peak between mid February to early March 2020, with about 0.8%, less than 0.1% and less than 0.01% of the population eventually infected in Wuhan, Hubei Province and the rest of China, respectively. Moreover, for most cities outside and within Hubei Province (except Wuhan), the total number of infected individuals is expected to be less than 300 and 4000, respectively.

The Novel Coronavirus Disease 2019 (COVID-19) (known earlier as New Coronavirus Infected Pneumonia) began to spread since December 2019 from Wuhan, which has been widely regarded as the epicenter of the epidemic, to almost all provinces throughout China and 200 other countries. Up to July 23, 2020, a total of 15,416,529 cases of COVID-19 infection have been confirmed in 213 countries, and the death toll has reached 631,177. In the early phase of the outbreak, China was almost the only country affected by the virus, and on February 19, 2020 (when this work was completed), a total of 74,579 cases were confirmed in China, and the death toll was 2,119. Moreover, as human-to-human transmission had been found to occur in some early Wuhan cases in mid December [

In this paper, we utilized the human migration data collected from Baidu Migration [

Inflow traffic of each city from Wuhan is quantified by migration strength from Wuhan extracted from Baidu Migration data.

In the remainder of the paper, we first introduce the official daily infection data and the intercity migration data used in this study. The SEIR model is modified to incorporate the human migration dynamics, giving a realistic model suitable for studying the COVID-19 epidemic spreading dynamics. Historical data of infected, recovered and death cases from official source and data of daily intercity traffic (number of travellers between cities) extracted from Baidu Migration were used to generate the model parameters, which then enabled estimation of the propagation of the epidemic in the following months. We will conclude with a brief discussion of our estimation of the propagation and the reasonableness of our estimation in view of the measures taken by the Chinese authorities in controlling the spreading of this new disease.

The availability of official data of infected cases in China varies from city to city. Wuhan, being the epicenter, had the first officially confirmed case of COVID-19 infection in China on December 8, 2019 [

(a) Wuhan (available from December 8, 2019); (b) Beijing (available from January 20, 2020); (c) Chongqing (available from January 20, 2020); (d) Shenzhen (available from January 19, 2020); (e) Guangzhou (available from January 21, 2020); (f) Tianjin (available from January 21, 2020).

As human-to-human transmission had been confirmed to occur in the spreading of COVID-19, gatherings of people and intercity travel of infected and exposed individuals within China were identified as the main drives that escalated the spreading of the virus. The period (around 20 days) surrounding the Lunar New Year (mid January to early February in 2020) was the most important holiday period in China. Migrant workers and students traveled from major cities to country towns for family reunions, and returned to the cities at the end of the holiday period. Holiday goers also traveled to and from tourist cities. China’s Ministry of Transport estimated around 3 billion trips to be taken during this period. Wuhan, being a major transport hub and having a large number of higher education institutions as well as manufacturing plants, was among the cities with the largest outflow and inflow traffic before and after the Chinese New Year festival. Our study aimed to incorporate these important human migration dynamics in the construction of the spreading model. We collected daily intercity travel data in China from Baidu Migration, which was a mobile-app based big data system recording movements of mobile phone users. Specifically, we collected Baidu Migration data for 367 cities (or administrative regions) in China over the period of January 1, 2020, to February 13, 2020. Moreover, Baidu Migration data were expected to be inexact and only indicative of the relative volume of movement of people from one city to another. Thus, the migration strengths of cities served as indicative measures of the human traffic volume moving in and out of individual cities and administrative regions, as depicted by the inflow and outflow networks shown in _{ij}(

_{ii}(

_{ij}(_{ji}(

Number of outflow migrants of city

Number of inflow migrants of city

Intercity migration strengths are used to form _{ij}.

The right panels in

In the SEIR model, each individual in a population may assume one of four possible states at any time in the dynamic process of epidemic spreading, namely, susceptible (S), exposed (E), infected (I) and recovered/removed (R). The dynamics of the epidemic can be described by the following set of equations:

Suppose, for city _{i}(_{i}(_{i}(_{i}(_{i} and the eventual percentage of infection is _{i}, then _{i} as the difference between the number of exposed individuals who become infected and the number of removed individuals. However, the onset of the COVID-19 epidemic has occurred in a special period of time in China, during which a huge migration traffic is being carried among cities, leading to a highly rapid transmission of the disease throughout the country. In view of this special migration factor, the SEIR model should incorporate the human migration dynamics in order to capture the essential features of the dynamics of the spreading. In particular, for city _{ij}(_{i}(_{j}(_{j}(_{j}(_{j}(_{j}(_{I} ≪ 1 is a constant representing the possibility of an infected individual moving from one city to another.

Likewise, incorporating the migrant dynamics, the increase in exposed individuals on day _{j}(_{j}(_{j}(_{j} is the infection rate of susceptible individuals in city _{j} is the infection rate of exposed individuals in city _{j}(_{j}(_{j}(_{j}(_{j}(_{j}(

the recovered individuals are assumed to stay in city

the recovery rates in different cities are assumed to be different due to varied quality of treatments and availability of medical facilities;

the recovery rates increase as time goes, as treatment methods are expected to improve gradually (i.e., taking _{j}(

the eventual recovery rates in all cities will converge to the same constant Γ ≈ 1.

In addition, due to intercity migration, the population of city _{j}(_{j}(_{j}(

In summary, our modified SEIR model with consideration of human migration dynamics, for city _{j}(_{j} is the set of parameters including _{j}, _{j}, _{j}, _{j} and _{j}. For computational convenience, we write (_{j}(_{j}(_{j}(_{j}(_{j} are constants throughout the period of spreading, and the spreading begins at _{0}, at which

The model represented by (_{j}, i.e.,
_{j,0} = _{j}(_{0}) is the initial number of infections in city _{j}, _{j}, _{j}, _{j}, _{j}} are parameters that determine the rates of spreading and recovery in city _{1}, _{2}, ⋯, _{K}} essentially has 5

all cities share one parameter set

the numbers of initial infected and exposed individuals in city _{I} _{i}(_{0}) and λ_{E} _{i}(_{0}), respectively, where λ_{I} and λ_{E} are constant. Here, _{i}(_{0}) represents the actual infected number at time _{0}, while λ_{I} _{i}(_{0}) represents the initial infection number used in the model;

each city has an independent _{i}.

Then, the size of the unknown set becomes computationally manageable, i.e.,

Finally, the parameter estimation problem can be formulated as the following constrained nonlinear optimisation problem:
_{L} and Θ_{U}. In this work, an inverse approach is taken to find the unknown parameters and states by solving (

The Root Mean Square Percentage Error (RMSPE) is adopted as the criterion, i.e., fitting error, to measure the difference between the number of infected individuals generated by the model and the official daily infection data.

We perform data fitting of the model, described by (

The propagation profiles, in terms of the number of infected individuals and estimated number of exposed individuals, for all 367 cities are estimated. As limited by space, we only show in _{I} = 1.9407, and λ_{E} = 1.5144. From the estimated propagation profiles of the COVID-19 epidemic for all 367 cities, we have the following findings:

For most cities, the infection numbers would peak between mid February to early March 2020, as shown in

The peak number of infected individuals would be between 1,000 to 5,000 for cities in Hubei, and that outside Hubei would be below 500, as shown in

At the end, about 0.8%, less than 0.1% and less than 0.01% of the population would get infected in Wuhan, Hubei Province and the rest of China, respectively, as presented in

For Wuhan, our model showed that the cumulative number of infections was 105,244 (95% CrI [64297, 146191]), which was consistent with a previous estimation of 75,815 cases (95% CrI [37304, 130330]) [

The shaded band is the 95% confidence interval.

Opinions diverged on the estimated extent of the outbreak of the new coronavirus disease (COVID-19). While there were pure speculations, there were also predictions based on rigorous study of the spreading dynamics. Different models used for prediction and different assumptions made regarding the transmission process would lead to different results and quite diverged conclusions. For instance, an AI-powered simulation run had predicted 2.5 billion people to be infected in 45 days [

The Novel Coronavirus Disease 2019 (COVID-19) epidemic has initially hit China hard. While the virus began to spread to other countries from February 2020, the extent of the outbreak in China remained to be severe in comparison to other countries for much of March and April 2020. Prediction of the severity and duration of the epidemic provided essential information for illuminating social and non-pharmaceutical interventions. However, prediction with the needed level of accuracy was a non-trivial task. In this work, we employed human migration data to provide information on intercity travel that was crucial to the transmission of the novel coronavirus disease from its epicenter Wuhan to other parts of China. The model described in this paper was essentially the classic SEIR model, with intercity travel data supplying the essential information about the number of infected, exposed and recovered individuals moving between different cities. All parameters of the model, including infection rates, recovery rates, and eventual percentage of infected population for 367 cities in China, were identified by fitting the official data collected up to mid-February with the model using a constrained nonlinear programming procedure. Using these parameters, predictions of the number of exposed individuals in 367 cities as well as projections into the next 200 days were made. Our model, however, did not consider the contact network topology that would be necessary if details of the transmission process, such as superspreading events, were to be captured. Nonetheless, our model provided a highly consistent estimation of the propagation of average numbers of exposed, infected and recovered individuals, despite missing details of fluctuation (e.g., sudden surge due to a superspreading event).

Our prediction in mid February 2020 was that provided stringent control measures including travel restriction continue to be in place, the COVID-19 epidemic spreading would peak between mid February to early March 2020, with about 0.8%, less than 0.1% and less than 0.01% of the population eventually infected in Wuhan, Hubei Province and the rest of China, respectively. Moreover, as the effectiveness of treatment improved, the COVID-19 epidemic was expected to end by June 2020. However, possibilities of a second or third wave of outbreaks may exist as intercity travel is still permitted, e.g., homebound travel from regions which are still at different stages of the pandemic progression. It is thus advisable to maintain a high level of vigilance by the public as well as a high level of preparedness for reactivating stringent control measures by government authorities.

PONE-D-20-05906

Modelling and Prediction of the 2019 Coronavirus Disease Spreading in China Incorporating Human Migration Data

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Reviewer #1: This study used SEIR compartments to simulate the dynamics of COVID-19. It is an important issue now but there are some concerns as follows.

1. Many studies incorporated migration data into SEIR model for simulating epidemic dynamics. Authors need to highlight the significant findings of the study.

2. Recent related studies on modeling COVID-19 which simulating the dynamics Wuhan and Hubei for estimated infected persons were published. Authors need to add more comparisons with these studies.

3. Some notations need to be further clarify. For example, the notation of denominators in Equation 6 and Equation 7 should be P_i (t) and P_j (t), respectively.

4. If N_i^s (t) means the susceptible population in city i at time t, isn’t it similar to S_i (t)? please explain their difference more clearly.

5. Which is your notation of initial infection number? I_i (t_0) in line 228 or λ_I I_i (t_0) in line 236?

6. What is the fitting result of the following parameters: δ_i, λ_I, and λ_E?

7. Figure 5 displays the result of forecasting; it should add 95% confidence intervals or error bars to show the variations of estimated values.

8. What is the spatial variation of the prediction? For example, whether the cities strongly interacting with Wuhan have more precise prediction results than the other cities? Or, whether high-population-density cities have more accurate predictions? These comparisons may reflect the value of incorporating human migration data into a SEIR model so that model results can benefit real epidemic prevention tasks.

Reviewer #2: This is a sound analysis of two publicly available data set focusing on intercity migration in China.

The authors may benefit from aa recent paper on migration and covid-19 spread published in April issue of Migration Letters journal. That can be useful to better frame the context of this paper indicating wider link between human mobility and disease diffusion.

Authors may revisit the sentence in second page: "The COVID-19 outbreak, however, began

to occur and escalate in a special holiday period in China (about days surrounding the Lunar New Year), during which a huge volume of intercity travel took place, resulting in outbreaks in multiple regions connected by an active transportation network." Because now we know the virus was out and about in as early as early November.

The data needs to be critically presented; Authors indicate the possibility of incompleteness or inaccuracy of official covid data but it seems they assume Baidu data is free of problems. It is important to note the selectivity bias here. This data is collected by an app, which means there are a lot of questions about its representability. This should be clearly noted so readers can interpret it accordingly.

In the conclusion, authors state "The Coronavirus Disease 2019 (COVID-19) epidemic has hit China hard, 331 and as of February 20, 2020, a total of 74,579 infection cases have been 332 confirmed in China, with death toll reaching 2,119." It is a live incidence but it can be useful if they can include the latest statistics regarding the pandemic while making sure the data and analysis refer to an earlier period.

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Reviewer: 1

Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This study used SEIR compartments to simulate the dynamics of COVID-19. It is an important issue now but there are some concerns as follows.

1. Many studies incorporated migration data into SEIR model for simulating epidemic dynamics. Authors need to highlight the significant findings of the study.

Authors’ Response: This work was completed on February 19, 2020 (medRxiv 10.1101/2020.02.18.20024570). We used a short historical epidemic spreading data and migration data to develop the model and the corresponding system identification algorithm. At the time of performing this work, there was no attempt in combining SEIR model, migration data and system identification techniques to analyze and predict the spread of COVID-19. The results thus have important indicative values on the effectiveness of using limited initial outbreak data in predicting pandemic progression. Remarks have been added to the Discussions section to highlight this. The main findings were listed in the Results section.

2. Recent related studies on modeling COVID-19 which simulating the dynamics Wuhan and Hubei for estimated infected persons were published. Authors need to add more comparisons with these studies.

Authors’ Response: The following information has been added to the Results section.

“For Wuhan, our model shows that the cumulative number of infections was 105,244 (95% CrI [64297,146191]), which was consistent with previous estimation of 75,815 infected cases (95% CrI [37304,130330]) [15]”.

[16] Wu JT, Leung K, Leung GM. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet. 2020 Feb 29; 395(10225):689-97.

3. Some notations need to be further clarify. For example, the notation of denominators in Equation 6 and Equation 7 should be P_i (t) and P_j (t), respectively.

Authors’ Response: The notations have been revised.

4. If N_i^s (t) means the susceptible population in city i at time t, isn’t it similar to S_i (t)? please explain their difference more clearly.

Authors’ Response: Thank you for pointing this out. N_i^s represents the size of the group of susceptible, infected, exposed and removed individuals. Thus, we have N_is(t_0) = S(t_0)+E(t_0)+I(t_0)+R(t_0). This has been included in the Method section of revised paper.

5. Which is your notation of initial infection number? I_i (t_0) in line 228 or λ_I I_i (t_0) in line 236?

Authors’ Response: I_i (t_0) represents the actual infected number at time t_0, while λ_I I_i (t_0) represents the initial infection number used in the model. We have clarified this in the paper.

6. What is the fitting result of the following parameters: δ_i, λ_I, and λ_E?

Authors’ Response: The fitting result of δ_i, λ_I, and λ_E have been added, while Figure 6 (c) shows the distribution of \\delta_i.

7. Figure 5 displays the result of forecasting; it should add 95% confidence intervals or error bars to show the variations of estimated values.

Authors’ Response: The 95% confidence intervals (CrI) have been added to Figures 4 and 5, and in the text.

8. What is the spatial variation of the prediction? For example, whether the cities strongly interacting with Wuhan have more precise prediction results than the other cities? Or, whether high-population-density cities have more accurate predictions? These comparisons may reflect the value of incorporating human migration data into a SEIR model so that model results can benefit real epidemic prevention tasks.

Authors’ Response: The experimental results show that several factors, such as strong interaction with Wuhan and high population density, influence the prediction results to some extent. Actually, the spread of COVID-19 in a city is highly influenced by the control measures, which vary from city to city. If a city adopted strict control measures, the spread of COVID-19 may be much slower and less severe than the predicted results.

Reviewer: 2

Comments to the Author

This is a sound analysis of two publicly available data set focusing on intercity migration in China.

The authors may benefit from a recent paper on migration and covid-19 spread published in April issue of Migration Letters journal. That can be useful to better frame the context of this paper indicating wider link between human mobility and disease diffusion.

Authors’ Response: This work was completed on February 19, 2020 (medRxiv 10.1101/2020.02.18.20024570). We used a short historical epidemic spreading data and migration data to develop the model and the corresponding system identification algorithm. At the time of performing this work, there was no attempt in combining SEIR model, migration data and system identification techniques to analyze and predict the spread of COVID-19. The results thus have important indicative values on the effectiveness of using limited initial outbreak data in predicting pandemic progression. Remarks have been added to the Discussions section to highlight this.

Authors may revisit the sentence in second page: "The COVID-19 outbreak, however, began to occur and escalate in a special holiday period in China (about days surrounding the Lunar New Year), during which a huge volume of intercity travel took place, resulting in outbreaks in multiple regions connected by an active transportation network." Because now we know the virus was out and about in as early as early November.

Authors’ Response: We have checked the literature and available data carefully, and found that the “official” data (up to today from the Chinese National Health Committee) indicated the earliest confirmed case in China being December 8, 2019. Indeed, the spread could have started earlier, but our data analysis could only work according to the official data which showed surges in infected numbers in many Chinese cities beginning mid January, which was the period of “spring rush” in China. We have also edited the text so as to emphasize that we referred to the rapid spread in China which was in the period before the Lunar New Year when huge volume of intercity travel took place.

The data needs to be critically presented; Authors indicate the possibility of incompleteness or inaccuracy of official covid data but it seems they assume Baidu data is free of problems. It is important to note the selectivity bias here. This data is collected by an app, which means there are a lot of questions about its representability. This should be clearly noted so readers can interpret it accordingly.

Authors’ Response: Several works adopted Baidu data to investigate the spread of COVID, which have been cited in the paper. Also, we clarified that the Baidu data were expected to be inexact and served to provide indicative travel volumes which were sufficient for the model fitting. This would serve to alert our readers about this issue.

[14] Chinazzi M, Davis JT, Ajelli M, Gioannini C, Litvinova M, Merler S, y Piontti AP, Mu K, Rossi L, Sun K, Viboud C. The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science. 2020 Apr 24; 368(6489): 395-400.

[15] Lai S, Ruktanonchai NW, Zhou L et al. Effect of non-pharmaceutical interventions to contain COVID-19 in China [published online May 4, 2020]. Nature. 2020;10.1038/s41586-020-2293-x. doi:10.1038/s41586-020-2293-x

In the conclusion, authors state "The Coronavirus Disease 2019 (COVID-19) epidemic has hit China hard, 331 and as of February 20, 2020, a total of 74,579 infection cases have been 332 confirmed in China, with death toll reaching 2,119." It is a live incidence but it can be useful if they can include the latest statistics regarding the pandemic while making sure the data and analysis refer to an earlier period.

Authors’ Response: We have revised the Introduction to include the latest worldwide figures while emphasizing that this work was completed on February 20, 2020.

Submitted filename:

Modeling and Prediction of the 2019 Coronavirus Disease Spreading in China Incorporating Human Migration Data

PONE-D-20-05906R1

Dear Dr. Tse,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The

Reviewer #2: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

Reviewer #3: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: Authors addressed the key concerns raised by myself and other reviewer. This revised version is of acceptable quality for publication.

Reviewer #3: In this work, the authors attempt to modify the classic SEIR model of disease propagation to include data on human mobility. Specifically, the new model seeks to incorporate fluctuations in the total population into the SEIR, something that was previously taken to be fixed. This work is clearly timely and important and the approach seems reasonable. The authors have addressed the comments of previous reviewers.

My major complaint is that it would be nice to see some verification of the numbers. Clearly, when this paper was originally written that would not be possible as they were predicting the future, but that is no longer the case. Looking at official case numbers and timelines, it seems the authors have done a reasonable job making predictions, but some quantitative measure of correctness at this point would be both possible, and a nice addition. Otherwise, it is not clear the to the reader whether this model is viable for future outbreaks.

More minor comments follow:

1. Page 2, around line 29 states that that cities far from Wuhan have a linear relationship between # of infections and distance, but on a log plot, that is not particularly clear.

2. Page 4, lines 119-123, the authors have, a the reviewers suggestion, attempted to acknowledge the problems with Baidu data by stating that the m_ij need only be accurate relative to one another, but it is not exactly clear why this is the case, since the absolute numbers are used to make predictions of individuals and there is no immediately obvious scaling factor.

3. Page 4, line 129, "as seen in Figure 3" is floating here and should be deleted

4. Page 5, equation 4. The alpha factor does not exist in this set of equations for S and E, though it does show up in later equations. It is not clear to my why this was omitted.

**********

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Reviewer #2: No

Reviewer #3: No

PONE-D-20-05906R1

Modeling and Prediction of the 2019 Coronavirus Disease Spreading in China Incorporating Human Migration Data

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