key: cord-0817475-gdsh8wmv
authors: Tang, Biao; Xia, Fan; Tang, Sanyi; Bragazzi, Nicola Luigi; Li, Qian; Sun, Xiaodan; Liang, Juhua; Xiao, Yanni; Wu, Jianhong
title: The effectiveness of quarantine and isolation determine the trend of the COVID-19 epidemics in the final phase of the current outbreak in China
date: 2020-04-17
journal: International journal of infectious diseases : IJID : official publication of the International Society for Infectious Diseases
DOI: 10.1016/j.ijid.2020.03.018
sha: a95685ea275d774647cdcbfdc16241b53aab1c73
doc_id: 817475
cord_uid: gdsh8wmv

Abstract Objectives Since January 23rd 2020, stringent measures for controlling the novel coronavirus epidemics have been gradually enforced and strengthened in mainland China. The detection and diagnosis have been improved as well. However, the daily reported cases staying in a high level make the epidemics trend prediction difficult. Methods Since the traditional SEIR model does not evaluate the effectiveness of control strategies, a novel model in line with the current epidemics process and control measures was proposed, utilizing multisource datasets including cumulative number of reported, death, quarantined and suspected cases. Results Results show that the trend of the epidemics mainly depends on quarantined and suspected cases. The predicted cumulative numbers of quarantined and suspected cases nearly reached static states and their inflection points have already been achieved, with the epidemics peak coming soon. The estimated effective reproduction numbers using model-free and model-based methods are decreasing, as well as new infections, while new reported cases are increasing. Most infected cases have been quarantined or put in suspected class, which has been ignored in existing models. Conclusions The uncertainty analyses reveal that the epidemics is still uncertain and it is important to continue enhancing the quarantine and isolation strategy and improving the detection rate in mainland China.

 Most infected cases have been quarantined or put in suspected class, which has been ignored in existing models.

 Results of our model show that the trend of the epidemics mainly depends on quarantined and suspected cases. 

Early identifying signature features of an outbreak can provide policy-and decision-makers with timely information to implement effective interventions. 1,2 Recently, a novel coronavirus outbreak has occurred in Wuhan, Hubei, China, and has spread out to neighboring countries. [3] [4] [5] During the early stages, the prediction of the COVID-19 epidemics by means of transmission dynamics models relies on the cumulative number of reported cases or the number of newly reported ones. The dynamical impact of the increasingly strong measures of the Chinese government has not been fully captured. Unprecedented interventions, including strict contact tracing, quarantine of entire towns/cities and travel restrictions, have added and will add further uncertainty to the analysis of the epidemics.

When enforcing such measures to a sample of 100 people, at least 9 of these may be found infected. Nearly 50% of infected people are confirmed from suspected cases. 6 It is unfeasible to predict the impact of the COVID-19 epidemics without taking into account the effects of the J o u r n a l P r e -p r o o f recently implemented measures. Estimates based on transmission dynamics models not including quarantined/suspected cases, as well as the cumulative reported cases from these compartments, cannot be used for informing public health policies. 7 Since January 23 rd 2020, after the implementation of the lock-down strategy in Wuhan, all other Chinese provinces have adopted similar measures. Nevertheless, the number of recently reported cases has increased faster than before, because of the incubation period of the virus, or the introduction of new screening/testing measures. Moreover, the diagnosis and treatment procedures have been simplified, and the detection effort has been strengthened. 8

As such, the classical SEIR model cannot be used to depict and fit the data. The evolutionary trend of the epidemics depends on the strength of interventions, especially on the scale of quarantined and suspected populations. 7 It is necessary to devise a dynamic model with suspected compartment incorporating prevention and control strategies to predict the trend of the COVID-19 epidemics based on multiple data sources and assess the efficacy of control strategies. We also incorporate the model-free method to estimate the effective number and to verify the declining trend of new infections.

We obtained data of laboratory-confirmed COVID-19 cases in China from the "National Health Commission" of the People's Republic of China and the Hubei's "Health Commission". [9] [10] [11] Data information includes the newly reported cases, the cumulative number of reported confirmed cases, J o u r n a l P r e -p r o o f the cumulative number of cured cases, the number of death cases, and the cumulative numbers of quarantined/suspected cases (Figure 1 ). The number of quarantined cases does not include the number of suspected cases although the suspected cases have been isolated. Except for Hubei, the mean duration of hospital stays was around 9 days, with the shortest hospitalization duration of 5 days (in Hainan) and the longest hospitalization duration of 12.75 days (in Guangdong). The duration of hospital stays in Hubei was around 20 days, because, on the one hand, more severe patients were found in Hubei, and on the other hand, Wuhan has set stricter discharge standards. In addition to the usual standards of two nucleic acid tests being negative within an interval of 24 hours, Wuhan requires 10-12 days more of observation in the hospital. [10] [11] [12] [13] Since the number of daily cases in hospital is not suitable to identify the model/estimate the parameters, we use cumulative data.

Data used in the present study is reported in Appendix 1.

A deterministic SEIR model based on the clinical progression of the disease, epidemiological status of the individuals, and intervention measures was proposed ( Figure 2) . We stratify the populations as susceptible ( ), exposed ( ), infected ( ), hospitalized ( ) and recovered ( ) compartments, and we further stratify the population to quarantined susceptible ( ), and quarantined suspected individuals ( ). We extend our model structure, 9 including the quarantined suspected compartment, which consists of exposed infectious individuals resulting from contact tracing and individuals with common fever needing clinical medication.

J o u r n a l P r e -p r o o f By enforcing contact tracing, a proportion, , of individuals exposed to the virus is quarantined, and can either move to the compartment or , depending on whether they are effectively infected or not, 14, 15 while the other proportion, 1q, consists of individuals exposed to the virus who are missed from contact tracing and move to the exposed compartment once effectively infected or stay in compartment otherwise.

Let the transmission probability be β and the contact rate be c. Then, the quarantined individuals, if infected (or uninfected), move to the compartment (or S q ) at a rate of (or (1 -) )).

Those who are not quarantined, if infected, will move to the compartment at a rate of βc(1 − q).

Let constant m be the transition rate from susceptible class to the suspected compartment via general clinical medication due to fever or illness-like symptoms.

Data on suspected individuals and also most of confirmed cases come from this compartment.

The suspected individuals leave this compartment at a rate of , with a proportion, f , if has been confirmed to be infected by the COVID-19, going to the hospitalized compartment, whilst the other proportion, 1-f , has been proven to be not infected by the COVID-19 and goes back to the susceptible class once recovery (Table 1) . denotes the contact rate modeled as exponential decreasing rate, assuming that the contacts are decreasing gradually considering the implementation of interventions.

( ) is an increasing function with respect to time t:

where 0 is the initial quarantined rate of exposed individuals with (0) = 0 , is the maximum quarantined rate under the current control strategies with lim →∞ ( ) = and > 0 , and 2 is the quarantined rate modeled as exponential increasing rate. This function reflects the gradually enhanced contact tracing.

The transition rate ( ) is an increasing function with respect to time t, the period of diagnosis 1/ ( ) is a decreasing function of t:

where δ I0 is the initial diagnose rate, is the fastest diagnose rate, and 3 is the exponential decreasing rate of the detection period. ) be the probability that a patient was confirmed at time and ℎ days after illness onset, which is the probability that a patient was confirmed at time and with illness onset being the interval

Let ( ≤ ℎ| 0 = ) be the probability that a patient was confirmed ℎ days after the illness onset on time . Then

We use equations (4) and (5) 

We estimate 0 and based on the illness onset data per day 0 (which is used to replace ).

To estimate the onset-to-confirmation distribution , we have collected detailed information of some patients confirmed before January 30 th 2020 from the Health Commissions of different cities, including dates of illness onset and dates of confirmation. We use the data of these patients with illness onset before January 20 th (ten days prior to the latest onset date of the patients in the data) to avoid underestimating .

By fitting a Weibull distribution on the illness onset data before January 30 th , we estimate to be Weibull distributed (mean 7.67, standard deviation 2.88). By fitting a Weibull distribution on the data of cases confirmed on day s we estimate ( ≤ ℎ| = ) to be Weibull distributed with from the literature, 21 we chose = 22 in formula (4) . We obtain = for ≤ 19, (Figure 3 ), and hence we only need to estimate the distribution ( ≤ ℎ| = ) for = 20,21,22. Therefore, then { 0 } ≤3 can be estimated by formula (4) and formula (5).

We estimate the daily number of cases with illness onset on the day from December 8 th , 2019 to , to estimate the effective reproduction number (Figure 4(A) ). It has a peak around January 20 th and begins to decrease after January 20 th . It is worth noting that started to be stable from late January and was still above 1. By repeating the above process, we also estimated the data on cases with illness onset in the Hubei Province between December 8 th -February 2 nd and based on that we further estimated the effective reproduction number for Hubei (Figure 4(B) ). It follows from Figure 3 (B) that the data on cases with illness onset for Hubei is quite similar to that for China before mid-January. From Figure 4 (B) the effective reproduction number for Hubei shows a declining trend, which decreases quicker than that for mainland China, compared with Figure 4 (A).

The number of cases with illness onset in Hubei may peak earlier than in mainland China. From 

By simultaneously fitting the proposed model to the four columns of data of cumulative reported, death, quarantined and suspected cases, we obtain the estimations for the unknown parameters and initial conditions. The best fitting result is shown in Figure 5 (black curves). From Figure 5 the inflection points of cumulative quarantined and suspected population have been basically reached, while the cumulative number of reported cases nearly reaches its inflection point, which implies that the COVID-19 epidemic will nearly peak. Comparing the results in Figure 5 Interventions including intensive contact tracing followed by quarantine and isolation are indicated. The gray compartment means suspected case compartment consisting of contact tracing Eq and fever clinics.

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Waived, since all data utilized are publicly available.

None.J o u r n a l P r e -p r o o f