Id |
Subject |
Object |
Predicate |
Lexical cue |
T39 |
0-18 |
Sentence |
denotes |
A conceptual model |
T40 |
19-345 |
Sentence |
denotes |
We adopt the ‘Susceptible-Exposed-Infectious-Removed’ (SEIR) framework with the total population size N with two extra classes (1) “D” mimicking the public perception of risk regarding the number of severe and critical cases and deaths; and (2) “C” representing the number of cumulative cases (both reported and not reported). |
T41 |
346-489 |
Sentence |
denotes |
Let S, E, and I represent the susceptible, exposed and infectious populations and R represent the removed population (i.e., recovered or dead). |
T42 |
490-792 |
Sentence |
denotes |
In a recent study (Wu and McGoogan, 2020), Wu and McGoogan found that 81% of cases were of mild symptom (without pneumonia or only mild pneumonia), 14% were severe case with difficulty breathing, and 5% were critical with respiratory failure, septic shock, and/or multiple organ dysfunction or failure. |
T43 |
793-864 |
Sentence |
denotes |
We adopt the transmission rate function formulated in He et al. (2013). |
T44 |
865-972 |
Sentence |
denotes |
We rename the school term effect as the governmental action effect, since the former belongs to the latter. |
T45 |
973-1043 |
Sentence |
denotes |
We also assume a period of zoonotic transmission during December 2019. |
T46 |
1044-1192 |
Sentence |
denotes |
We model the zoonotic transmission (denoted as F) as a stepwise function, which takes zero after the shutdown of Huanan seafood market (presumably). |
T47 |
1193-1406 |
Sentence |
denotes |
We then only model the sustained human-to-human transmission of COVID-19 after this date, along with the emigration of 5 million population before Wuhan was officially locked down (South China Morning Post, 2020). |
T48 |
1407-1587 |
Sentence |
denotes |
Thus, a compartmental model is formulated as follows:(1) S'=-β0SFN-β(t)SIN-μS,E'=β0SFN+β(t)SIN-(σ+μ)E,I'=σE-(γ+μ)I,R'=γI-μR,N'=-μN,D'=d γI-λD,andC'=σE,where(2) β(t)=β0(1−α)1−DNκ. |
T49 |
1588-1853 |
Sentence |
denotes |
The transmission rate, β(t) in Eq. (2), incorporates the impact of governmental action (all actions which can be modelled as a step function), and the decreasing contacts among individuals responding to the proportion of deaths (i.e., the severity of the epidemic). |
T50 |
1854-1938 |
Sentence |
denotes |
We also incorporate the individuals leaving Wuhan before the lock-down in the model. |
T51 |
1939-2268 |
Sentence |
denotes |
We assume (i) the zoonotic cases only make impacts during December 2019 (Huang et al., 2020); (ii) the effect of governmental action starts on 23 January 2020 (in particular, α = 0.4249 during 23–29 January 2020 and α = 0.8478 after that); (iii) the emigration from Wuhan starts on 31 December 2019 and ends on 22 January 2020. |
T52 |
2269-2315 |
Sentence |
denotes |
In this outbreak it seems children are spared. |
T53 |
2316-2414 |
Sentence |
denotes |
Only 0.9% cases are from age 15 or less (Guan et al., 2020), while in China, 0–14 years are 17.2%. |
T54 |
2415-2497 |
Sentence |
denotes |
To take this effect into account, we assume 10% of the population are ‘protected’. |
T55 |
2498-2687 |
Sentence |
denotes |
Recent studies showed the serial interval of COVID-19 could be as short as 5 days (Nishiura et al., 2020a), and the median incubation period could be as short as 4 days (Guan et al., 2020). |
T56 |
2688-2758 |
Sentence |
denotes |
These characteristics imply short latent period and infectious period. |
T57 |
2759-2859 |
Sentence |
denotes |
Thus, we adopt a relatively shorter mean latent period (3 days) and mean infectious period (4 days). |
T58 |
2860-2989 |
Sentence |
denotes |
Different from (He et al., 2013), we use the severe cases and deaths in the individual reaction function, instead of deaths only. |
T59 |
2990-3150 |
Sentence |
denotes |
We also increase the intensity of the governmental action such that the model outcomes (increments in cases) largely match the observed, with a reporting ratio. |
T60 |
3151-3233 |
Sentence |
denotes |
Namely only a proportion of the model generated cases will be reported in reality. |
T61 |
3234-3378 |
Sentence |
denotes |
Many evidences and studies, e.g., (Tuite and Fisman, 2020, Zhao et al., 2020a, Zhao et al., 2020b), suggest the reporting ratio is time-varying. |
T62 |
3379-3419 |
Sentence |
denotes |
We summarise our parameters in Table 1 . |
T63 |
3420-3473 |
Sentence |
denotes |
Table 1 Summary table of the parameters in model (1). |
T64 |
3474-3524 |
Sentence |
denotes |
Parameter Notation Value or range Remark Reference |
T65 |
3525-3584 |
Sentence |
denotes |
Number of zoonotic cases F {0, 10} A stepwise function J.T. |
T66 |
3585-3601 |
Sentence |
denotes |
Wu et al. (2020) |
T67 |
3602-3680 |
Sentence |
denotes |
Initial population size N0 14 million Constant South China Morning Post (2020) |
T68 |
3681-3737 |
Sentence |
denotes |
Initial susceptible population S0 0.9N0 Constant Assumed |
T69 |
3738-3810 |
Sentence |
denotes |
Transmission rate β0 {0.5944, 1.68}a (day−1) A stepwise function Assumed |
T70 |
3811-3896 |
Sentence |
denotes |
Governmental action strength α {0,0.4239,0.8478} A stepwise function He et al. (2013) |
T71 |
3897-3953 |
Sentence |
denotes |
Intensity of responds κ 1117.3 Constant He et al. (2013) |
T72 |
3954-4043 |
Sentence |
denotes |
Emigration rate μ {0, 0.0205} (day−1) A stepwise function South China Morning Post (2020) |
T73 |
4044-4089 |
Sentence |
denotes |
Mean latent period σ−1 3 (days) Constant J.T. |
T74 |
4090-4106 |
Sentence |
denotes |
Wu et al. (2020) |
T75 |
4107-4156 |
Sentence |
denotes |
Mean infectious period γ−1 5 (days) Constant J.T. |
T76 |
4157-4173 |
Sentence |
denotes |
Wu et al. (2020) |
T77 |
4174-4236 |
Sentence |
denotes |
Proportion of severe cases d 0.2 Constant Worldometers. (2020) |
T78 |
4237-4311 |
Sentence |
denotes |
Mean duration of public reaction λ−1 11.2 (days) Constant He et al. (2013) |
T79 |
4312-4453 |
Sentence |
denotes |
a It is derived by assuming that the basic reproduction number, R0=β0γ·σσ+μ=2.8 (referring to Imai et al., 2020, Riou and Althaus, 2020, J.T. |
T80 |
4454-4607 |
Sentence |
denotes |
Wu et al., 2020, Zhao et al., 2020a, Zhao et al., 2020b) when α = 0, by using the next generation matrix approach (van den Driessche and Watmough, 2002). |
T81 |
4608-4650 |
Sentence |
denotes |
The time unit is in year if not mentioned. |