| Id |
Subject |
Object |
Predicate |
Lexical cue |
| T33 |
0-7 |
Sentence |
denotes |
Methods |
| T34 |
9-37 |
Sentence |
denotes |
Time-dependent dynamic model |
| T35 |
38-212 |
Sentence |
denotes |
On January 23rd, 2020, Wuhan, the epicenter of the current coronavirus outbreak, announced the implementation of travel restriction as strategy for controlling the infection. |
| T36 |
213-319 |
Sentence |
denotes |
Following this announcement, many other cities and provinces of China decided to enforce similar measures. |
| T37 |
320-473 |
Sentence |
denotes |
In the meantime, many other control measures have been adopted, like convincing all the residents to stay at home and avoid contacts as much as possible. |
| T38 |
474-596 |
Sentence |
denotes |
From the mathematical point of view, this can significantly contribute to decreasing the contact rate c among the persons. |
| T39 |
597-833 |
Sentence |
denotes |
On the other hand, also from January 23rd, 2020, gradually increasing numbers of 2019-nCoV testing kits were sent to Wuhan from other provinces, gradually shortening the time period of diagnosis (i.e. the value of δI increases greatly). |
| T40 |
834-1192 |
Sentence |
denotes |
Considering these control strategies, we adapted our previous model (Tang et al., 2020) as time-dependent dynamic system, by taking January 23rd, 2020 as the newly initial time:S’=−(βc(t)+c(t)q(1−β))S(I+θA)+λSq,E’=βc(t)(1−q)S(I+θA)−σE,I’=σϱE−(δI(t)+α+γI)I,A’=σ(1−ϱ)E−γAA,Sq’=(1−β)c(t)qS(I+θA)−λSq,Eq’=βc(t)qS(I+θA)−δqEq,H’=δI(t)I+δqEq−(α+γH)H,R’=γII+γAA+γHH, |
| T41 |
1193-1530 |
Sentence |
denotes |
Here, we assume that the contact rate c(t) is a decreasing function with respect to time t, which is given byc(t)=(c0−cb)e−r1t+cb,where c0 is the contact rate at the initial time (i.e. January 23rd, 2020), cb is the minimum contact rate under the current control strategies, and r1 is the exponential decreasing rate of the contact rate. |
| T42 |
1531-1590 |
Sentence |
denotes |
Definitely, there are c(0)=c0 and limt→∞c(t)=cb with cb<c0. |
| T43 |
1591-1685 |
Sentence |
denotes |
This is basically to assume the contacts are decreasing and the change rate per contact is r1. |
| T44 |
1686-1843 |
Sentence |
denotes |
This constant provides a measure of public health intervention improvement in terms of self-isolation of all including susceptible individuals in the period. |
| T45 |
1844-2214 |
Sentence |
denotes |
Similarly, we set δI(t) to be an increasing function with respect to time t, equivalently, the period of diagnosis 1/δI(t) is a decreasing function of t with the following form:1δI(t)=(1δI0−1δIf)e−r2t+1δIf.here, δI0 is the diagnose rate at the initial time with δI(0)=δI0, δIf is the fastest diagnose rate with limt→∞δI(0)=δIf, and r2 is the exponential decreasing rate. |
| T46 |
2215-2288 |
Sentence |
denotes |
This rate is highly relevant to the resources available in the epicenter. |
| T47 |
2289-2777 |
Sentence |
denotes |
Using the formula we derived in (Tang et al., 2020) but replacing the constant contact rate c and δI with the aforementioned time-dependent coefficients to reflect the evolving public health interventions and resources available, we definedRd(t)=[βϱc(t)(1−q)δI(t)+α+γI+βc(t)θ(1−ϱ)(1−q)γA]S0.as the effective daily reproduction ratio, to measure the ‘daily reproduction number’, the number of new infections induced by a single infected individual during his/her infectious period per day. |
| T48 |
2779-2787 |
Sentence |
denotes |
The data |
| T49 |
2788-3021 |
Sentence |
denotes |
We obtained the updated data of the cumulative number of laboratory-confirmed 2019-nCov cases from the National Health Commission of the People’s Republic of China (National Health Commission of the People’s Republic of China, 2020). |
| T50 |
3022-3274 |
Sentence |
denotes |
The data information includes the cumulative confirmed cases, the cumulative number of deaths, newly confirmed cases and the cumulative number of cured cases, which are reported daily by the National Health Commission of the People’s Republic of China. |
| T51 |
3276-3304 |
Sentence |
denotes |
Parameter estimation process |
| T52 |
3305-3496 |
Sentence |
denotes |
Under the gradually enhanced control strategies since January 23rd, 2020, the parameter values with substantial changes include the contact rate, the diagnose rate and the quarantined rate q. |
| T53 |
3497-3623 |
Sentence |
denotes |
Therefore, we fixed the parameter values except these three as the estimated values in our previous study (Tang et al., 2020). |
| T54 |
3624-3761 |
Sentence |
denotes |
The initial contact rate c0 is assumed to be the average contact rate between January 10th, 2020 and January 22nd, 2020, hence c0=14.781. |
| T55 |
3762-3805 |
Sentence |
denotes |
With the same assumption, we set δI0=0.133. |
| T56 |
3806-3952 |
Sentence |
denotes |
Note that, the initial conditions can be obtained by solving our previous model (Tang et al., 2020) from January 10th, 2020 to January 23rd, 2020. |
| T57 |
3953-4024 |
Sentence |
denotes |
Thus, the main task is to estimate the parameter values q,cb,r1,δIf,r2. |
| T58 |
4025-4195 |
Sentence |
denotes |
We use the Markov Chain Monte Carlo (MCMC) method to fit the model to the data, and adopt an adaptive Metropolis-Hastings (M-H) algorithm to carry out the MCMC procedure. |
| T59 |
4196-4375 |
Sentence |
denotes |
The algorithm is run for 70,000 iterations with a burn-in of the first 50,000 iterations, and the Geweke convergence diagnostic method is employed to assess convergence of chains. |
| T60 |
4376-4421 |
Sentence |
denotes |
The estimation results are given in Table 1 . |
| T61 |
4422-4447 |
Sentence |
denotes |
Table 1 Parameter values. |
| T62 |
4448-4521 |
Sentence |
denotes |
Parameter Definitions Estimated mean value Standard deviation Data source |
| T63 |
4522-4572 |
Sentence |
denotes |
c0 Contact rate at the initial time 14.781 0.904 1 |
| T64 |
4573-4652 |
Sentence |
denotes |
cb Minimum contact rate under the current control strategies 2.9253 0.5235 MCMC |
| T65 |
4653-4717 |
Sentence |
denotes |
r1 Exponential decreasing rate of contact rate 1.3768 0.283 MCMC |
| T66 |
4718-4785 |
Sentence |
denotes |
β Probability of transmission per contact 2.1011×10−8 1.1886×10−9 1 |
| T67 |
4786-4856 |
Sentence |
denotes |
q Quarantined rate of exposed individuals 1.2858×10−5 3.1488×10−6 MCMC |
| T68 |
4857-4927 |
Sentence |
denotes |
σ Transition rate of exposed individuals to the infected class 1/7 – 2 |
| T69 |
4928-5029 |
Sentence |
denotes |
λ Rate at which the quarantined uninfected contacts were released into the wider community 1/14 – 3,4 |
| T70 |
5030-5108 |
Sentence |
denotes |
ϱ Probability of having symptoms among infected individuals 0.86834 0.049227 1 |
| T71 |
5109-5225 |
Sentence |
denotes |
δI0 Initial transition rate of symptomatic infected individuals to the quarantined infected class 0.13266 0.021315 1 |
| T72 |
5226-5283 |
Sentence |
denotes |
1/δIf The shortest period of diagnosis 0.3654 0.1431 MCMC |
| T73 |
5284-5350 |
Sentence |
denotes |
r2 Exponential decreasing rate of diagnose rate 0.3283 0.0225 MCMC |
| T74 |
5351-5456 |
Sentence |
denotes |
δq Transition rate of quarantined exposed individuals to the quarantined infected class 0.1259 0.052032 1 |
| T75 |
5457-5528 |
Sentence |
denotes |
γI Recovery rate of symptomatic infected individuals 0.33029 0.052135 1 |
| T76 |
5529-5601 |
Sentence |
denotes |
γA Recovery rate of asymptomatic infected individuals 0.13978 0.034821 1 |
| T77 |
5602-5673 |
Sentence |
denotes |
γH Recovery rate of quarantined infected individuals 0.11624 0.038725 1 |
| T78 |
5674-5728 |
Sentence |
denotes |
α Disease-induced death rate 1.7826×10−5 6.8331×10−6 1 |
