 Research Article
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Risk estimation and prediction of the transmission of coronavirus disease2019 (COVID19) in the mainland of China excluding Hubei province
Infectious Diseases of Poverty volume 9, Article number: 116 (2020)
Abstract
Background
In December 2019, an outbreak of coronavirus disease (later named as COVID19) was identified in Wuhan, China and, later on, detected in other parts of China. Our aim is to evaluate the effectiveness of the evolution of interventions and selfprotection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model.
Methods
A novel COVID19 transmission dynamic model incorporating the intervention measures implemented in China is proposed. COVID19 daily data of the mainland of China excluding Hubei province, including the cumulative confirmed cases, the cumulative deaths, newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020, were archived from the National Health Commission of China (NHCC). We parameterize the model by using the Markov Chain Monte Carlo (MCMC) method and estimate the control reproduction number (R_{c}), as well as the effective daily reproduction ratio R_{e}(t), of the disease transmission in the mainland of China excluding Hubei province.
Results
The estimation outcomes indicate that R_{c} is 3.36 (95% CI: 3.20–3.64) and R_{e}(t) has dropped below 1 since 31 January 2020, which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID19 transmission. Moreover, our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected, and may even cause a second wave of epidemic or outbreaks. By calculating the effective reproduction ratio, we prove that the contact rate should be kept at least less than 30% of the normal level by April, 2020.
Conclusions
To ensure the pandemic ending rapidly, it is necessary to maintain the current integrated restrict interventions and selfprotection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the realtime epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.
Background
Coronaviruses are a group of enveloped viruses with a positivesense, singlestranded RNA and viral particles resembling a crown, from which the name derives. They belong to the order of Nidovirales, family of Coronaviridae, and subfamily of Orthocoronavirinae [1].
In December 2019, an outbreak of coronavirus disease (later named as COVID19 by WHO) was identified in Wuhan, China and, later on, detected in other parts of China. By 27 February, the new virus had infected 78 824 people and killed 2788 people in China [2]. Besides China, more than 4440 people had been infected and 67 died in at least 48 countries and regions [3]. Currently, there are no vaccines or antiviral treatments officially approved for the prevention or management of the diseases. The outbreaks are still ongoing [3].
The basic reproduction number R_{0} is the average number of secondary infections due to an infective case during the infectious period when everyone else in the population is susceptible [4]. While the basic reproduction number with control measures is defined as the control reproduction number R_{c}. At the early stage of the outbreak, estimation of R_{0}/ R_{c} is crucial for determining the potential and severity of an outbreak, and providing precise information for designing and implementing disease outbreak responses, namely the identification of the most appropriate, evidencebased interventions, mitigation measures and the determination of the intensity of such programs in order to achieve the maximal protection of the population with the minimal interruption of socialeconomic activities [5, 6].
Recently, some papers have been released as preprints or undergone peerreview and published to estimate R_{0} and the risk of outbreak. Li et al. [7] analyzed data on the first 425 confirmed cases in Wuhan and determined the epidemiologic characteristics of COVID19. Based on their estimates, the mean incubation period was 5.2 days, and R_{0} was 2.2, which is in line with the result estimated by Riou et al. [8]. Zhao et al. [9] assessed the unreported number of COVID19 cases in China in the first half of January with the estimation of R_{0} 2.56. Considering the impact of the variations in disease reporting rate, Zhao et al. [10] modelled the epidemic curve of COVID19 cases, in the mainland of China from 10 January to 24 January 2020, through the exponential growth and concluded that the mean R_{0} ranged from 2.24 to 3.58 associated with 2fold to 8fold increase in the reporting rate. Li et al. [11] conducted a mathematical modeling study using five independent methods to assess R_{0} of COVID19. Their results illustrated that R_{0} dropped from 4.38 to 3.41 right after the lockdown of Wuhan city. Over the epidemic period of the study COVID19 had an average R_{0} of 3.39. Moreover, Tang et al. formulated a deterministic compartmental model. Their estimations based on likelihood and dynamical model analysis showed that R_{0} with control measures might be as high as 6.47 [6]. Most recently, Chen et al. [12] developed a BatsHostsReservoirPeople transmission network model to simulate the potential transmission from the infectious sources to human. The estimated values of R_{0} were 2.30 from reservoir to person and 3.58 from person to person. We noticed that the estimations of R_{0} in varied studies are different. As mentioned in references of [6, 13], variability in the estimation of the basic reproduction number is a general recognized methodological issue, and standardized methods both for calculating and reporting R_{0} are still missing. Furthermore, the value of R_{0} may vary with key clinical parameters inferred from data which depend on the time period, quality, accuracy, and reliability. To better quantify the evolution of the interventions, Tang et al. fitted the previously proposed model in reference [6] to the data available until 29 January 2020 and reestimated the effective daily reproduction [14]. There are also some literatures focusing on the prediction of COVID19 development trend. Wang et al. formulated a complex network model and analyzed the possible time node and the risk impact of resumption on secondary outbreak in Wuhan and surrounding areas [15]. Roosa et al. [16] utilized several dynamic models to forecast the cumulative number of confirmed cases in the coming 5, 10, and 15 days in Hubei province, and the overall trajectory of the epidemic in China excluding Hubei.
With the gradual alleviation of the epidemic situation in the mainland of China excluding Hubei province, considering the pressure of economic operation and the needs of people’s normal production and life, some places have adjusted the primary response of epidemic prevention and control to the secondary response [17]. In this situation, some critical questions need to be answered promptly. Does the reduction of the emergency response level mean that people can fully or partially relieve from selfproduction? When can people return back to normal life?
The aim of this study is to evaluate the effectiveness of varied interventions and selfprotection measures, estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province by establishing a COVID19 transmission model incorporating the intervention measures implemented and fitting the data obtained from the National Health Commission of China (NHCC).
Methods
Establishment of COVID19 transmission dynamic model
Based on the clinical progression of the disease, epidemiological status of the individuals and intervention measures (including travel restriction, body temperature measurement, close contact tracing, selfisolation and protection, etc.), we propose a novel deterministic COVID19 transmission model. We parameterize the model using data of the mainland of China excluding Hubei province obtained from NHCC, and estimate the control reproduction number as well as the effective daily reproduction ratio of the disease transmission.
The population was grouped into various compartments, namely susceptible (S), exposed (E), infectious with symptoms (I), infectious but asymptomatic (A), isolated susceptible (Si), quarantined infected pending for confirmation (Q), hospitalized (H), and recovered (R). We assume that recovered individuals have immunity during the rest epidemic period. Let N(t)=S(t)+E(t)+I(t)+A(t)+R(t) be the total number of individuals in the free community. In order to fit the data, we explicitly generated additional two groups, i.e. the cumulative number of recovered R_{h}(t) and dead cases D(t) from hospital. The total number of cumulative reported cases is set to be T(t). All the state variables are summarized in Table 1.
Due to the travel restriction, migrations from/to Hubei province and other regions are ignored. Birth and natural death are also neglected. With the increase of the cumulative number of confirmed cases, the probability of contact transmission among the informed susceptible populations would certainly reduce ([18–20], etc.). To better quantify the varied interventions and selfprotection measures, we assume the contact rate to be timedependent c(t)=q_{1}(t)c_{0}, where c_{0} is the initial contact rate and q_{1}(t) is the intervention coefficient with respect to contact. Here we assume that q_{1}(t)=e^{−δT(t)}, which is dependent on the total number of cumulative confirmed cases T(t) and is monotone decreasing with T(t), so as to well reflect the impact of media coverage on people’s psychology and behaviors. c(t)=c_{0} for T=0 and \(\lim \limits _{t \rightarrow \infty } c(T)=0.\) It should be mentioned that the contact function c(t) in [14] is also assumed to be timedependent, but it is not dependent on state variables. Let the transmission probability be β. Thus, the incidence rate can be given by \(\beta c(t)\left (I+ \xi A\right)\frac {S}{N},\) where ξ is the correction factor of transmission probability with asymptomatic infectious individuals.
By frequent monitoring of body temperature and diagnoses in hospitals, symptomatic infectious individuals can be detected. The detection rate is assumed to be q_{2}I(t). Infected individuals in Q class can be confirmed at the rate of ηQ(t) by nucleic acid testing. Additionally, close contact tracing followed by quarantine and isolation is a critical control measure. We assume that, once a case is confirmed, q_{3} individuals would be traced. Therefore, q_{3}(q_{2}I(t)+ηQ(t)) individuals would be traced in a unit time, which is dependent on the number of new confirmed cases q_{2}I(t)+ηQ(t). We also assume that, among these traced individuals, \(\frac {S}{N}\) fraction parts are susceptible, \(\frac {E}{N}\) fraction parts are exposed, \(\frac {I}{N}\) fraction parts are infectious with symptoms and \(\frac {A}{N}\) fraction parts are infectious but asymptomatic. \(\frac {R}{N}\) fraction parts are recovered, which are not needed to be isolated due to protective immunity and will remain in the R class until the end of the epidemic.
The disease transmission flow chart is depicted in Fig. 1 and other parameters are summarized in Table 2. Based on the above assumptions, we formulate the following model to describe the transmission dynamics of COVID19.
According to the concept of next generation matrix in reference [21] and the basic reproduction number presented in reference [22], we calculate the basic reproduction number with control measures, i.e. the control reproduction number, R_{c}, of COVID19, which is given by
With the spreading of the COVID19, intensive intervention measures have been implemented increasingly and people gradually enhanced selfprotection. In order to quantity the daily reproduction number, inspired by Tang et al. [14], the initial contact rate c_{0} in the formula of R_{c} is replaced by the aforementioned timedependent contact rate c(t) to reflect the changes of intervention measures and people’s behaviors. Thereby, we define
as the effective daily reproduction ratio, the average number of new infections induced by a single infected individual during the infectious period at time t. The basic reproduction number or the control reproduction number, which is not timedependent, can depict the transmission risk in the early phase of disease transmission. While the timedependent effective daily reproduction ratio can evaluate the transmission risk changing over time.
Data source
COVID19 daily data excluding Hubei province were archived from NHCC from 20 January (the first day of confirmed cases reported) to 3 March 2020 (Fig. 2) [2]. The data include the cumulative confirmed cases, the cumulative number of deaths, newly confirmed cases and the cumulative number of recovered cases. The data from 20 January to 24 February were fitted to parameterize the model and the data from 25 February to 3 March were used for comparison of the predicted curves and real data.
Parameter estimation
We used the Markov Chain Monte Carlo (MCMC) method with an adaptive MetropolisHastings (MH) algorithm to fit the model. The MH algorithm, a powerful Markov chain method to simulate multivariate distributions, was executed by using the MCMC toolbox introduced in reference [23]. This toolbox provides tools to generate and analyze MetropolisHastings MCMC chains using multivariate Gaussian proposal distribution. The covariance matrix of the proposal distribution can be adapted during the simulation according to adaptive schemes described in references of [24–26].
The algorithm is run for 110 000 iterations with a burnin of the first 80 000 iterations, and the Geweke convergence diagnostic method is employed to assess the convergence of chains. At the significance level of 5% (the critical value of z is 1.96), all parameters and initial values estimated do not reject the original hypothesis of convergence to a posterior distribution (Fig. 3).
Simulations
The population of the mainland of China excluding Hubei province is around 1 336 210 000 [27], which can be set to be the value of S(0). 21 confirmed cases were reported on 20 January 2020 for the first time and the numbers of recovered and dead individuals were both 0. It can be assumed that nobody has been traced at the beginning. Therefore, we set S_{i}(0)=Q(0)=R_{h}(0)=D(0)=0, and H(0)=T(0)=21. The quarantined susceptible individuals were isolated for 14 days, thus μ=1/14 [2]. According to reference [7], the incubation period of COVID19 is about 5.2 days, thus ϕ can be set to be 1/5.2.
Results
It can be seen that our model yields a relatively good visual fit to the epidemic curves (see Fig. 4). The MCMC estimation results of each parameters and initial values of some state variables are given in Tables 1 and 2. By fitting the data, we estimated the control reproduction number R_{c} to be 3.36 (95% CI: 3.20–3.64).
Using the estimated parameter values and the number of cumulative cases T(t), the effective daily reproduction ratio R_{e}(t) can be calculated (Fig. 5). The result demonstrates that R_{e}(t) has dropped sharply from 3.34 (R_{e}(1)=3.34) on 20 January to 0.89 (R_{e}(12)=0.89, less than 1) on 31 January 2020, which implies that the integrated control strategies implemented in the mainland of China excluding Hubei has successfully reduced transmission intensity and prevented the epidemic growth in a short time frame.
Under the current rigorous integrated control and selfprotection measures, the time series of T(t) depicted in Fig. 4a shows that the cumulative number of confirmed cases will continue growing slowly for some duration and tend to its predicted maximum, which is 13 155. Besides, although the number of hospitalized individuals has peaked on around 12 February 2020, but it will not shrink to zero in the near future (Fig. 4e). Obviously, once people start relieving selfisolation and protection, new infections would occur given the existence of undetected infectious individuals. It is the number of undetected infectious individuals that determines when people’s lives are able to return back to normal. Hence we should closely follow the total number of I(t) and R(t). Fig. 4f displays that the number of infectious individuals has been decreasing gradually since the end of January. However, it will not descent down to 1 until late March, which infers that people should be fully aware of the realtime epidemic situation and keep personal protect before April.
Using the estimated parameter values and the expression of the effective reproduction ratio R_{e}(t), the threshold value of the intervention coefficient with respect to contact, q_{1}, can be calculated, which is 0.3. This implies that in order to block the continuous spread of the virus, the value of q_{1} must be less than 0.3 to guarantee R_{e}(t) is below 1. In other words, the contact rate should be kept below 30% of the normal level.
To examine the impact of partial lifting control measures and personal protection, we plot the predicted time series of the number of cumulative confirmed cases, T(t), and the number of the infectious individuals, I(t)+A(t), with different contact rates (Fig. 6). Assuming that the adjusting time is from 5 March 2020, Figs. 6a and b illustrate that contact rate with 20% of the initial value c_{0} will not cause the disease rebounce. However, the epidemic period will be extended for about 40 days until early May and the cumulative number of confirmed cases will increase by around 0.5% to 13 227. While if the starting time of the adjusting is postponed to 20 March, the epidemic time of disease will be extended for about one week and the cumulative number of confirmed cases will increase by only around 0.05% to 13 161, compared with the scenario of no changes. Nevertheless, if the contact rate is half of the initial value, i.e. q_{1}=0.5 and R_{e}(t)=1.68, COVID19 will rebounce on a large scale in a short time frame, even if the starting time is postponed to 20 March. The corresponding analysis results are also listed in Table 3 for comparison.
Discussion
In this paper, we proposed a novel COVID19 transmission model incorporating the intervention measures implemented in China. Particularly, we adopted two novel function forms which dynamically captured the realtime endemic situation. The first one is the contact rate, c(t), which was assumed to be dependent on the cumulative number of confirmed cases to better quantify the varied interventions and selfprotection measures. The other one is the contact tracing function, which was dependent on the number of new cases.
We evaluated the impact of partial lifting control measures on COVID19 transmission. Our results show that relaxing selfprotection too early may lead to a prolonged transmission period and more people would be infected, and may even cause the second wave of epidemic or outbreaks. The reduction of the emergency response level does not mean that people can be relaxed thoroughly. At least until the end of March, life will not be able to return to normal.
In the process of recovery of production and life, we should pay attention to take protective measures to minimize the contact between people, such as wearing masks, keeping social distance, and avoiding crowded places to cut the risk of infection. By calculating the effective reproduction ratio, we assert that people’s contact rate should be kept below 30% of the normal level and the lower the better.
Our study outcomes are based on the assumption of no imported cases from Hubei and other regions. However, new endemic foci outside China are formed, such as Republic of Korea, Italy, Iran, Japan, etc. The WHO recently upgraded the global risk of the epidemic to ‘very high’. Although the current endemic situation in China is under control, these newly formed epidemic foci could generate the risk of second outbreak wave due to imported cases via population migration cross border. With the development of the critical epidemic situation in other countries, it is very important to maintain and strengthen the quarantine of entry personnel. The impact of international mobility on the transmission of COVID19 will be studied in our future works.
We concentrated on the epidemic situation in the mainland of China excluding Hubei province is due to the significant differences of transmission dynamics between Wuhan, Hubei, and the rest of the country. In Wuhan, because of the sudden appearance of the disease, it took much longer time to recognize and understand the disease transmission than other regions. It requires certain time from unknown to known. Therefore, the data accuracy in Wuhan, Hubei is a major issue for parameters’ calibration. In addition, the sudden large outbreak in Wuhan, Hubei exhausted all medical resources in a short time. A more targeted model considering medical resource capacity will be anticipated in the future.
Our results manifest that the model yields a good visual fit to the epidemic curve except for the cumulative recovered cases. The number of predicted recovered cases is less than the number of actual recovered individuals in the later period of data fitting. The possible reason is that the recovery rate of hospitalized individuals was increasing with the improvement of treatment level and the increase of medical resources. In addition, due to increased contact tracing efficiency, large quantity of mild symptomatic cases were detected and hospitalised which has higher recover rate than other classified cases. A timedependent recovery rate may be more suitable to fit the real data. Furthermore, age is a key parameter determining the mortality and recover rates. It is ideal to set up agestructured agentbased or meta populationbased deterministic models which can capture this important risk factor. In this work, the initial value of the susceptible class S(0) was set to be the population of the mainland of China excluding Hubei province. Actually, the number of susceptible individuals is not as many as this number considering the very strict control measures implemented and the difference of behaviors between different age groups. A proper method to estimate the accurate number of susceptible individuals should be studied in the future. Besides, the impact of limited medical resources is another important issue that is not incorporated in our model. The transmission dynamics of COVID19 accounting for the potential negative effects of health systems being overwhelmed on mortality will be studied in our future work.
Conclusions
In conclusion, to ensure the COVID19 pandemic ending rapidly, it is necessary to maintain the current integrated control intervention and selfprotection measures, including travel restriction, quarantine of entry, contact tracing followed by quarantine and isolation and reduction of contact, like wearing masks, keeping social distance, etc. People should be fully aware of the realtime epidemic situation and keep sufficient personal protection until April. If all the above conditions are met, the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.
Availability of data and materials
Not applicable.
Abbreviations
 COVID19:

Corona Virus Disease 2019
 NHCC:

National Health Commission of the People’s Republic of China
 MCMC:

Markov Chain Monte Carlo method
 R _{0} :

Basic reproduction number
 R_{c}; Control reproduction number; R_{e}(t):

Effective daily reproduction ratio
 MCMC:

Markov Chain Monte Carlo method.
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Acknowledgements
The authors thank graduate students Yuanyuan Yu and Jingyuan Li for their efforts in collecting data during the study.
Funding
This work is supported by the National Natural Science Foundation of China (No.11971240 and No.11871093) and the NSF of the Jiangsu Higher Education Committee of China (No.17KJA110002).
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HW designed research; HW conceived the experiments, HW, JC and GY conducted the experiments and analyzed the results; HW and GJ wrote the manuscript. All authors read and approved the final manuscript.
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Wan, H., Cui, J. & Yang, G. Risk estimation and prediction of the transmission of coronavirus disease2019 (COVID19) in the mainland of China excluding Hubei province. Infect Dis Poverty 9, 116 (2020). https://doi.org/10.1186/s40249020006836
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Keywords
 COVID19
 Risk estimation and prediction
 Intervention measure
 Contact tracing
 Control reproduction number
 Effective daily reproduction ratio
 Mathematical model