Modelling-based evaluation of the effect of quarantine control by the Chinese government in the coronavirus disease 2019 outbreak
preprint
OA: gold
CC-BY-NC-ND-4.0
Abstract
The novel coronavirus disease 2019 (COVID-19) epidemic, which was first identified in Wuhan, China in December 2019, has rapidly spread all over China and across the world. By the end of February 2020, the epidemic outside Hubei province in China has been well controlled, yet the next wave of transmission in other countries may have just begun. A retrospective modeling of the transmission dynamics would provide insights into the epidemiological characteristics of the disease and evaluation of the effectiveness of the strict measures that have been taken by central and local governments of China. Using a refined susceptible-exposed-infectious-removed (SEIR) transmission model and a new strategy of model fitting, we were able to estimate model parameters in a dynamic manner. The resulting parameter estimation can well reflect the prevention policy scenarios. Our simulation results with different degrees of government control suggest that the strictly enforced quarantine and travel ban have significantly decreased the otherwise uncontrollable spread of the disease. Our results suggest similar measures should be considered by other countries that are of high risk of COVID-19 outbreak. Summary Background The novel coronavirus disease 2019 (COVID-19) epidemic, which was first reported in Wuhan and rapidly spread across the world, has been well controlled in China but is only starting to take off in other countries. Here we provide a retrospective modelling analysis of the transmission dynamics in China and evaluated the effectiveness of the strict government control strategies. Methods We considerably refined the original susceptible-exposed-infectious-removed (SEIR) transmission model, and used the publicly available data from Jan 13 rd to Feb 29 th for model fitting and parameter estimation in a dynamic manner considering effect of prevention policies. We then used the estimated model parameters to simulate the epidemic trend and transmission risk of the disease with various degrees of government control. Findings The severity rate and the fatality rate remain unchanged during the whole epidemic. While government intervention had a moderate effect on the incubation rate (σ), the recovered rate (γ) endured several fold increase. Strikingly, a significant decrease in the infectious rate (β) was observed. Without government control, peak infected cases in Wuhan would reach 7.78 million (70% of the whole population) and total deaths could reach 319000 based on the current mortality rate (4.1%). Interpretation Our simulation results with different degrees of government control suggest that the strictly enforced quarantine and travel ban have significantly decreased the otherwise uncontrollable spread of the disease. Our results suggest similar measures should be considered by other countries that are of high risk of COVID-19 outbreak. Funding The National Natural Science Foundation of China (21877060). Research in context Evidence before the study A global outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been posing significant threats to public health worldwide. By the end of February 2020, 87645 confirmed cases are reported around the world, including 7330 severe cases and 2994 fatalities. We searched PubMed and preprint archive for papers published up to Feb 29 th , 2020, using keywords “COVID-19”, “SARS-CoV-2”, “2019-nCoV”, and “novel coronavirus.” We found several researches on the transmission dynamics of COVID-19; however, only one preprint predicted the effect of government intervention in China with incomplete epidemiological data. Added value of this study Since the epidemic is already close to its end in China except Wuhan city, we have the opportunity to carry out a relatively complete retrospective analysis. We optimized the SEIR model using a dynamic fitting approach, taking into account the government measures and reached a much more precise fitting of the data comparing to other studies published. We showed that the severity rate and the fatality rate remain unchanged during the whole epidemic, suggesting the only effective way to control the disease is to control the number of infections. While government intervention had a moderate effect on the incubation rate (σ), it is essential for increasing the recovered rate (γ), and for decreasing and stabilizing the infectious rate (β). We also simulated the scenarios with various degrees of government control which could be a useful tool to predict the necessity of government intervention. An interactive online application was made available to the public on Feb 24 th , 2020. Implications of all the available evidence The COVID-19 outbreak has already been effectively controlled in China; however, the risk of rapid global explosion is extremely high due to the high transmissive rate of the SARS-CoV-2 virus. The quarantine measures adopted by the Chinese government are essential for the control of the COVID-19 epidemic.
Full text
50,509 characters
· extracted from
oa-pdf
· 8 sections
· click to expand
Keywords
C O VID- 19; r et r ospe ct ive modeling; simula tion; epidemic s pr ea d i n g; tr a nsmis s ion
model
Abstract
The nov el cor o na v ir us dis ea se 201 9 (C OVID -19) epidemic , whi c h w as fir st iden ti fie d
in W uhan, China in D ecem ber 201 9, has r apidly spr ead all ov er Ch i n a a n d acr o s s the
w orld. B y the end of F ebrua r y 2020, th e epide mic out s ide Hube i p r ovince in China
h a s b e e n w e l l co n t r o l l e d , y e t t h e n e x t w a v e o f t r a n s m i s s i o n i n o t h e r co u n t r i e s m a y
ha v e just begun. A r et rospectiv e modeling of the t r ansmis sion dyna mics w ould
pr ovide insigh ts in t o the ep idemio logi c al char a ct erist ics of th e disease and ev alua tion
of t h e e ff ectiveness of the s trict m ea s ur es t ha t ha v e been t ak en by cen tr al a n d loc a l
gov ernmen t s of China. Using a r e fine d su s cep tible-e xpos ed- inf ect ious - r em ov ed (SEIR)
tr ans mis si o n model and a n e w st r a t egy of model f itting , we w er e able t o es tima t e
model par a m eter s in a dynamic m an ner . The r esulting par amet er est ima t i on c an w el l
r e f lect t he pr e v ent i o n po licy s cenarios. Our simula tion r esults with di f f er e n t degr ees
of gover nment con tr ol s ug g e s t t ha t t he s trictly enf or ced quar a n t ine and tr a v el ban
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.
ha v e s ignific an tly decr eased the ot he rwise unco n tr ol lable spr ead of the di sea s e. Our
r esults s u g g e s t similar measur es s h ould be cons ider ed b y other coun tries tha t ar e of
high risk of C O V ID-19 ou tbr eak.
Summary
Background
The n ovel c or ona vi r us disease 201 9 (C O VID -19) ep i d emic, whi ch w as f ir s t r epo r t ed
in W uhan and r apidl y spr ead acr o s s t he w orld, has been w ell c on tr o l led in China but
i s o n l y s t a r t i n g t o t a k e o f f i n o t h e r co u n t r i e s . H e r e w e p r o v i d e a r e t r o s p e c t i v e
modelling a n al y sis of the tr ansmis s ion dynamics in China and e v alua t ed the
e ff ectiveness of t he str ict gover nmen t c on t r o l st r a t egies.
Methods
W e co n s ider ab l y r e fined the or iginal su sceptible-e xposed-inf ectious-r em o v ed (SEIR)
tr ans mis si o n model, and used the publicly av ailable da t a fr om Jan 13
rd t o Fe b 2 9 th f o r
model f it t ing and par a m et er estimation in a dynamic mann e r c onsidering e f f ec t of
pr ev ent i o n polici es. W e then us ed th e es timat ed mode l par ameter s t o s im ulat e t he
epidemic t r end and tr ans missi o n risk of the dis ea se with var ious degr ees of
gov ernmen t con tr ol.
Findings
The sever ity r a t e and the f a t ality r a t e r emain un chang ed d uring the who l e ep i d emic.
Whil e gov er nmen t int erv e n tion had a moder a t e e ff ect on t he i n c uba t ion r at e (
σ ), the
r ecov er ed r a t e ( γ) endur ed s ev er al fo l d incr eas e. S t rikingly , a s ignific an t d ec r eas e in
the inf ectious r at e ( β ) w a s ob ser v ed. W it hout gov ernment con t rol, pe ak inf ec t ed
cas e s in W uhan wou l d r eac h 7 .78 million ( 70% of the w h ole popul a tion) and t ot a l
dea ths could r eac h 319000 ba s ed on t he c ur r en t m or t ality r at e (4.1%).
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Interpretat ion
O u r s i m u l a t i o n r e s u l t s w i t h d i f f e r e n t d e g r e e s o f g o v e r n m e n t co n t r o l s u g g e s t t h a t t h e
s trictly enf or ced quar an t i n e and t r a v e l ban ha v e signific an t ly dec r eas ed the
other wis e uncon t r ol lable s p r ead of th e dis ea se. O ur r esult s s u g g e s t si m il ar meas u r es
should be co ns ider ed by o ther c oun tries t ha t ar e o f high risk of C O VID- 19 o utbr e ak.
Funding : The Na tional N a t ur al Scienc e F ounda tion o f China (21877060).
Research in context
E vidence before the study
A global o u tbr eak of cor ona virus di s ea se 2019 (C OV ID -19), cau s ed by t he s ev er e
acut e r es pir a t ory s yndr ome cor ona vi r us 2 (SAR S- CoV-2) , ha s been po sing signif i c an t
thr eats t o public health w or ldwi d e. B y t he end o f F ebruar y 2020, 8764 5 con firmed
cas e s ar e r epor t ed ar oun d the world, inc luding 733 0 s e v e r e ca s e s a n d 2 9 9 4 f a t alit ies .
W e sear ched PubM ed and pr epr i n t archiv e f or paper s publ ished up t o F eb 29
th , 2020,
using k e yw or ds “C O V ID- 19” , “SAR S - CoV-2” , “ 2019-n Co V ” , and “novel cor ona virus. ”
W e f ound s ev er al r es ear ch es on th e tr a n s mis s ion dynamic s of C O VID -19; how ever ,
only one pr epri n t p r edict ed the e ff ect of gov ernm en t int er ven ti o n in China with
incomplet e e pidem iological dat a.
Added value of this study
Since the epidemic is al r eady clo s e t o its end in China e xcept W uhan c it y , we ha ve
the oppor tun ity t o carr y out a r el a t i vely comp l et e r etr ospec tiv e analy s i s. W e
optim i z ed t he SEIR mod el us ing a dynamic fitting a p pr oac h, t aking int o a cc oun t the
gov ernmen t measur es and r eache d a much m or e p r ecise fit ting of t he da t a
comparing t o othe r s tudies publis h ed. W e show ed t ha t the s ev erit y r a t e and th e
f a t ali ty r a t e r emain unchang ed dur ing the whole ep idemic, s u g g es ting the on l y
e ff ec tive w a y t o con t r ol t he dis ease is t o con tr ol th e nu m ber of inf ec t i ons . Whil e
gov ernmen t i n t er ven t ion had a mo der a t e e ff ect on the incuba ti on r a te (
σ ), it is
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
es s en tial f o r incr easing the r ecover e d r a t e ( γ), and f or decr eas ing and st a b i lizing the
inf ectious r at e ( β ). W e also simula t ed t he scenarios with var ious d egr ees of
gov ernmen t contr ol whic h could b e a us e fu l t oo l t o p r edic t the ne c e ssity of
gov ernmen t int er v e n tion . An i n t er acti v e online applic ation w as made a v ail able t o the
public on F eb 24 th , 2020.
Implications of all the available evidence
The C OV I D-19 outbr eak ha s alr eady b een e ff ectively c on tr oll ed in China; how ever ,
the ris k o f r apid global e xplosion is e xt r eme ly high due t o the h i gh tr ans miss iv e r a t e
of the SAR S-Co V-2 vi rus. The quar an t ine m e asur es adopt ed by t he Chines e
gov ernmen t ar e es sen tial f or t he co nt r ol of the C O VID- 19 e p i d emic .
In troduction
The r ecen t o utbr eak of nov e l c or o na v ir us d i sea se 2 019 (C O VID- 19) h as a lr ead y
become a n epidemic o f global s cale . T w o m on ths a go , o n D e c 30
th 2 01 9, t he fir st
c onfirm e d c as e w as of ficia lly r eport ed by local author ities of W uhan ci t y , China 1,2 .
The pa th og en w as soon iden t ified as a new co r ona virus on Jan 7 th 2020 and
t ent ative ly nam ed 2019-nC O V 2,3 and la t e r r ena med SA R S-CoV-2 by the Int erna ti onal
Comm i t tee on T a x o nom y of V ir us es 4 . H ow eve r , str ic t co ntr ol m ea sur es, including the
lock d own of W uhan city did not t a k e e f f e ct un t i l Jan 23 rd , by w h i ch time sever a l
milli on peop le ha ve al r eady t r a v el l ed outside W uh a n f or t h e upcoming Ch inese Ne w
Y ear , spr eading t he disea s e all ov er China. B y the e n d of Januar y , conf ir med case s
w er e r ep or t ed by sev er al oth er c oun t r ies , leading t o the declar a tion o f Pu blic Health
Emer g ency of In t ern a tion a l Concern (PH EIC) by WH O
5 on Jan 30 th . F or t he whol e
mon t h of F ebr uary , r ig o r ous p r ev en tion and con t r ol meas ur es w er e t ak en b y the
Chinese g o ver nmen t and the whole coun tr y is li t er ally i n a loc k down st a t e. The
necessit y of t hes e str ic t measur es has been quest ioned bot h dom es tic al ly and
in t e r na t ionally c o ncer ning the d evas ta ting ef f ect s on the global ec onom y; and ther e
is al s o s ev er e deba t e ov er when t he s e co n tr ol meas ur es , in c luding tr a v el bans and
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
public g a th ering b a n s, s ho uld be lifted. Ho wev er , the ef f ecti v enes s of these s trict
con tr o l mea sur e s ha s n ot been s y s t ema tically ev aluat ed using epidemiol o gical d at a.
Her e w e pr ov ided a r etr ospectiv e mo delling-based ev a lua t ion o f t he eff ectiv enes s of
gov ernmen t con tr o l measur es on C O VID- 19 in China. U s ing a w ell-recogni zed
su sceptible-e xposed-inf ectious-r ecover ed (SEIR) m ode l, w e f it t ed th e pub lic da t a b y
t aking t he e ff ec t of pr even t ion pol icies in t o con s ider a t ion and ac h i ev ed an almos t
perf e ct fi t f or the r eal dat a. K ey epide miologic al p a r amet er s including inc u b at ion r at e
(
σ ) , i n f e ct i o u s r a t e ( β ) and r ecov ered r a t e ( γ) and w er e es timat ed in a dynamic
manner . Thes e est i m at es w er e t hen used t o par am et e riz e our mod el an d diff e r en t
out come s c enarios w er e s imula t ed with v arious degr ees of gov ernmen t con tr ol. An
in t er acti v e w eb-based Shin y applic at ion bas ed on our mo dell ing is no w a v ail able
online (ht t p://compbio.nju.edu .c n/n cov2019 / ). Our find i n g s ma y pr ovide a u s e fu l
t ool f o r analy z ing the i m pact of c ontr ol measur es and pr edic ting the tr a nsmis s ion
dynamics in ot her coun tr i es.
Methods
Data c ol lecti on
Daily cumula tiv e num ber of co nfirm ed ca ses, dead ca ses and r ec ov er ed c ase s ( fr om
Jan 13
rd , 2020 t o F eb 29 th , 2020) inf ect ed by C OV ID-19 w er e c oll ect e d f r om the
T encen t s o c ial netw or k s (h t t ps : / /n e ws.qq. com/z t 202 0/ pag e/f eiy a n .h tm ); t he daily
number o f sev er e cases w er e ob t a in ed fr o m o f f ic ial w ebsit es of the N a ti o nal H ealth
Comm i ssion of C hina and of health c ommiss ion s of pr ovince s , municip alities and
major ci t ies . O v er sea s da t a w ere obt ained f r om the o f f icial w ebs it e of W H O
(h t t ps : / /ww w . who.in t/ emer g encies /d isea se s/ n ov el-c or ona virus-2019/ si t ua tion- r epor
ts/ ) . All co l lect ed dat a w e r e doubl e check ed. B y finali zing this manus cript, t he perio d
of da t a cover ag e st a r ts fr om m i d-Janu ar y t o the end of F ebr ua ry 2020.
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Model, paramet er estimation and simulation
The su scept i b l e- e x posed-inf ectiou s -r eco ver ed (SEIR) c ompar tme n t a l mod el is one of
the best m o dels t o d es cribe the ep i demic of d is ease s with a lat en t pha se lik e the
SAR S-Co V-2. W e ado pt ed the f o l lowi ng or dinary diff er en t ial equ a tion (OD E) model t o
si m ula t e th e epide mic of C O VID -19 f or each in v estig a t ed pop ul at ion:
/g1749
/g1750
/g1750
/g1748
/g1750
/g1750
/g1747
/g1856/g1845
/g1856/g1872/g3404 /g3398/g2010/g1845/g1835
/g1840
/g1856/g1831
/g1856/g1872/g3404 /g2010/g1845/g1835
/g1840 /g3398/g2026 /g1831
/g1856/g1835
/g1856/g1872/g3404/g2026 /g1831/g3398/g2011 /g1835
/g1856/g1844
/g1856/g1872/g3404/g2011 /g1835
/g1
wher e S, E, I, and R w er e the nu m be r of s usceptible, la t ent (o r e x posed), i n f ec t ious ,
and r emov ed ind ividuals (includ i n g r ec ov er ed ind ividuals and dea th) a t t ime t
and N /g3404 S /g3397 E /g3397 I /g3397 R is the s iz e of popula ti on. W e as s um e tha t N is cons t an t
in a in ves tig a t ed p opula t ion. In th e SEIR m odel, the inf ectious r a t e, β , con t r ols the
r a t e of s pr ead which r epr esen ts the pr ob a b i l it y of tr ansmit t ing d iseas e betw een a
su sceptible and an inf ectious individ ual. The incuba tion r at e, σ , is the r ate of lat ent
individuals becoming inf ec t ious (a v e r ag e dur a t i o n of inc uba t i o n is 1/ σ ). R ecov ery
rate , γ, is the r a te o f inf ectious indiv iduals r em oved fr om t he tr ans m i s sion s y s t em,
which i s det er mined by the a v er ag e dur a tion o f i n f ec t ion.
W e suppo se th at the epide m i c spr eading t r end of C OV ID-19 suf f er ed the fi r st period
of fr ee propag a tion ( b e f or e Jan 2 3
rd , 2020) and t hen under t he heal th policies
in t er vent ion. There f or e, the r e is no o ne- fi t-all set of par am et er s t o f it t h e model with
t h e a g g regate d ata . I n ste a d , we a s s u m e t h at th e m o d e l p a ra m e te r s d y n a m i ca l l y
chang ed during the epidem i c c our se and w as depend e n t on th e degr ee of pr ev ention.
Based on s uch an a ssumption , w e inf er red the mode l par am eter s i n a s t epwis e
manner a t each time poi n t, using t he la t est o f ficially c onf i r med i n f ect e d da t a . W e
then in v es tig a t ed the pa tt ern of pa r amet er d y nam i cs and cor r ela t ed t hes e with
v arious pr even t i on m eas ur es in dif f er en t popu la t ions. As e xpe ct ed, the p at t e rn of
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
es tima t ed par amet e r (es p ecially the inf ect ious r a t e β ) dynami cs c an w ell r e f lec t the
out come o f con t r ol po lic i es. W e f urt her f o r ecast ed the epidemi c sp r eading b y
es tima ting t he m odel par amet er s usin g polynom i al r egr es s ion -bas ed
machine-learning app r oach, whic h h as b een us ed t o des cribe nonlinear p henomena
su ch as the p r ogr es s ion of di seas e epide mic s
6 . Finally , we s imu l a t e d possi b l e
spr eading cour s e of C OV ID-19 in W uhan s ub j e c t ed t o di f f e r ent quar an ti ne r a t e as
r e f lect ed by t he d y n a m ics of the pr ed ic t ed par amet er s .
Statistical analysis
If no t spe cified, al l s t a tis tic al analyse s and da t a visual iz a tion w er e done in R ( ver s ion
3.6.2). W e u sed non- par ametr ic t es ts t o as s e s s dif f er ences a m ong dif f eren t gr oup
(Wilco x on t est t o co mpar e t w o gr oup s and K ru s k al-W allis t es t t o c ompar e thr ee or
mor e gr oups). W e used R pa ck a g es su c h a s g gplot2 and p l o tly f or gr aphic s.
Role of the funding source
The funder s of th i s st ud y had n o r ole i n t he stu dy design, da t a collec tion, da t a
analy s i s, da t a int erpr et ation, or wri ti n g o f the r eport. The cor r es p onding a uthor s had
full access t o all the dat a and had f i nal r e sponsibility f or th e decis ion t o submit f or
publica tion.
Results
Since the impact of an epidem i c depends on b oth t he num ber o f per s o ns inf ect ed
and the spectr um of clinical sev erity , w e fir s t analy z ed th e chang e of s e v erit y r a te
and t he f a t al it y r a t e ove r t i me and found tha t bo th par amet er s r emain u nchang ed
ov er t he in v est i g a t ed phas e f or each pr ovi n c e and ar e not aff ect ed by t he st rictness
of con tr o l measur es ( Fig. 1 ), indica ting tha t t o t al nu mbe r of s ev er e cases a nd d eat hs
ar e lar g e ly det erm ined by t he t ot al number of inf ections, thus sup por ting th e
impor t ance a n d ur g ency of outbr ea k pr event ion and co ntr ol o f t r ansmis sio n.
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
The s u sceptible-e xposed-inf ectious-rec ov er ed (SEIR) t r ansmission model is one of
the bes t m od el s t o describe the epid em ic of di sease s with a lat ent ph a se. Ho wev er , it
is o nly a ccur a t e under con ditions of no i n tervent ion. In the r ea l w orld, var ious
degr ees o f in t erv ention ha ve been adopt ed; as a r es ult , t he S EIR mode l does not
tr uly r eflect t he s p r ead o f t he epide mic. T o solve this discr epancy , w e optimiz ed the
model i n a s t epwise manner a t ea ch time p oi n t, using t he la t es t of fici al con firmed
inf ect ed dat a t o fit the SEIR m odel. W e thu s obt ained dynam i c chang e s of the th r ee
model par amet er s: inf ectious r a t e (
β ) , incuba tion r a t e ( σ ) and r ecover ed r at e ( γ) ( Fig.
2A) . As e x pect ed , incuba tion r a t e ( σ ) s how s lit t le t o no ne chang e over t ime ( Fig.
2B,C). In th i s r egar d, the av er a g e d ura tion of incuba tion is es timat ed t o be 5.9 da y s
based on dat a in W uhan, which is g ener a lly in agr eem en t with e xis ting rep orts 7–10 .
Whil e r ecov er ed r a te ( γ) s ho w s a slo w but s t eady incr ea se ov er time ( Fig. 2D ), t h e
inf ectious r a t e dr ama t i c al ly chan g ed dur ing the whole outb r eak pr oces s ( Fig. 2B,E ).
The na tional inf ectious r a t e c learly peak ed ar oun d Jan 23 rd , t he da y of W uhan
lock d own and ha s c on tinued t o dr op ever si n c e. This t r end i s m or e appa r en t when
analy z ing t he da t a o f W uhan city alone ( Fig. 2E ) . T h e cu r v e f o r o t h e r c i t i e s d i s p l a y e d
a con tinuous des c ending tr end fr o m the beginning of the a v ai la b l e da t a poi n t
(ar o und Jan 20
th , t he cit y o f N anjing w as shown a s an e xample in Fig. 2E ), when s trict
con tr o l measur es ha v e alr eady been i n plac e. In W uhan, the r ecov ery r a t e ( γ) has
c on tinued t o inc r eas e wi t h mor e t h an 2- f old chang e which i s pr obably d ue t o the
dr ama t ic impr ove m ent of me dic a l c onditions, s u c h a s th e imm obil i z a tion of
thou s ands of ph y s i cians fr o m all ov er the coun try and immediat e est a b l i shmen t of
sever al new hospit als in W uhan . T h es e da t a indica t e a s ignifican t c or r ela t io n
betw een t he inf ectious r a t e (
β ) a n d t h e re co v e r y ra te ( γ) with pr ev ent i o n and con tr ol
measur es.
Ne x t , w e simula t ed t he poss ible out come sc enarios with dif f eren t degr ees of
gov ernmen t p r e v ention. Ass u ming t her e is a di r ect c orr el a t i o n wit h t h e value o f
inf ectious r at e and the st rictnes s of p r ev en ti on meas ur es (a s sho wn in Fig. 2 ), we
si m ula t ed t he outb r ea k dynamics in d i f f e r ent pr ev e n t i o n sc enarios u sin g d i f f er e n t
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
es tima t ed par ame t er s in W uhan ( Fig. 3A ). In the ca s e of low t o no pr e v ent ion (with
high inf ectious r a t e at the ear l y st ag e), the peak o f p r ed i ct ed inf ection case s w ould
ev en tual ly r each ca. 7.78 million, c ov ering 70% of the who l e popu la t ion of W uhan
city . The number of pot ential ly inf ect ed individua ls dr ama t ically r edu ce as the
inf ectious r a t e decr eases up on pr ev e n tion int er v e n ti ons ( Fig. 3B ) . T h e s e data s u g ges t
tha t s tr ic t pr even t ion is v it a l ly importan t t o r educe the peak of inf ection c a s e s.
Us ing a similar appr oach , w e ne x t m odeled a ll t he pub lic ly a vailable da t a on se v er a l
diff er e n t coun tries tha t already ha v e consi d er able amoun t s of confir med ca s es and
pr edict their epidem ic cur v e with var ious degr ees of gov ern men t c o n tr ol , as s um i n g
si m il ar tr ansmis s ion p r opert i es of the virus in diff e r ent coun t ies ( Fig. 4 ).In Sing apor e,
wher e only mild gov ernm en t i n terve n t ion e x is t e d, a surpr is in gly co n tinuo us de cr eas e
i n t h e i n f e ct i o u s r a t e (
β ) and in cr eas e in th e r ec ove r y r a t e ( γ) w as ob s erved , i m plyi n g
the pot en t ial inhibi t o r y e f f ect of w ar m c lima te on th e spr eading of the vi r us; wher ea s
the s it ua tion in It aly , K or ea, a n d Ir an ar e qu i ckl y det er ior a ting. Fo r J a p a n , although
the i n f ect ious r a t e ( β ) i s g e t t i n g b e t t e r , t h e r e co v e r y r a t e ( γ) is not , implying either a
la t ency i n h os pit a liz a tion o r lack of dedic a t ed m edic al r es ou r ces .
Discussion
B y the end of F ebruar y 20 20 , tw o mon th s aft er its outbr eak i n W uhan, t he C OV ID-19
epidemic has alr eady spr ead t o m ore t han fifty c oun tr ies . A r eas with a high risk of
e xponen tia l out b r eak incl u de Japan, South K or ea, It aly , Si n gapo r e and Ir an. Since the
si t ua tion in C hina has alr eady b e en well con tr olled, a r et rospec t ive ev alua tion of the
epidemio logical c har ac t er i s tics and tr a n s mis s ion dynami cs w ould pr ovid e valuabl e
insi gh t s t ha t migh t hel p with d i sease con t r ol decis ions w orld- w ide. T o our knowl ed ge,
our w or k is t he fir s t t o evalua t e the e ff ect i v en ess of gov ernm en t c o n t r ol on the
spr ead of C O VID -19 u s ing a modelling appr o ach.
In agr eem en t with o ther s
11–14 , w e f ound t he SEIR-lik e models t o b e the mo st
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
appr o priat e m odel f or ana ly zi n g the tr ansmis s ion dynamics of C O VID -19 . H ow eve r ,
the t r aditi onal app r oach f or f itting t h e SEIR model is ba s ed on the ov er all t r end dat a
of the ep idem ic us ing h y po thesiz ed par amet er s and thus th e model d o not w ell fi t
the r eal -li f e da t a (i.e. th e r eal -li f e d a t a tr end does no t conf o rm t o the ideal SEIR
model cu r v e). The main r eas on is tha t the tr aditi o nal appr oac h does not t ak e in t o
accou n t th e impact of pr ev en t ion an d c on tr ol st r a t egies on t he epidem ic dynamic s .
In th i s s tudy , w e adjust ed th e SEIR mo de l t o objectiv ely re f lect t he impact of
pr ev ent i o n and con tr ol str a tegy on t he i n f ec t ious r a t e. N on etheles s , o ur stud y ha s
sever al m a jo r lim it ations. Fir s tly , w e w er e not able t o de rive a g ener al iz ed model with
finalized par amet er s t o fit the over all ep idemic spr eading. Ins t ead, t he mod el
p a r a m e t e r s w e r e e s t i m a t e d i n a d y n a m i c m a n n e r i n o u r s t u d y . T h i s i s i n l i n e w i t h t h e
obser v a tion of dynamic t r ans m issi on p r opert i es of the virus
15 . Seco ndly , the
si gn i f ican ce of t h e mode l l ar g el y d ep ends on the a ccur ac y of es timat ed p ar amet er s .
Alth ough the r e i s not a golden st a n dar d so f ar t o evaluat e t he acc ur acy of o ur mode l
par amet er s, the est ima t ed dur a t i o n of incuba tion (1/
σ ) f r om our mod el-derived
par amet er incuba t i on r a t e ( σ ) is highly i n agr eemen t wi th pr evious es ti ma tions b y
other st udi es 7–10 , and th e dynamic val ues of th e i n f ec t ious r at e ( β ) is wi t hin the r a n ge
of the r ecen t es ti ma t ion by Y ang et al . 14 . These ob s erva t i o ns s u g g e s t our appr oach
f or mode l par amet e r est im a tion is p l ausible. Thir dly , our ep idem i c f o r ecas t w as
somehow se n s itiv e t o o ur pr edict i o n of par am e t er s which w er e estima t ed fr om the ir
ov er all dynamic pa t t erns. Nonetheles s , s u ch f o r ec a s ting w ou l d st il l be acc ur a t e in a
short period. In this r eg ar d, art i f icial int ell i g enc e (AI)-i n s pir ed methods
14,16 m a y b e
alt ernat i ves t o epidemio logical models f or th e r eal-tim e f or ecas ting of tr ansmis s ion
dynamics of C OV ID -19.
The f a ct tha t the sev erity and the f a t ality r a t e r e main unchang ed dur i n g the who l e
epidemic co ur se s u g g e s t s t ha t the bi ology of t he virus i t s elf d i d not chang e over t ime ;
this is in line with g enetic s equ encing r e sults tha t f e w mu t a t ions ar e iden ti fied
among virus s am ples collec t ed fr om d i f f er e n t g ener ations of pa tients
17,18 . H o w e v e r , it
is har d t o pr edi ct whether this f e a tu r e of t he vi rus will chang e as it spr e ad in other
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
coun tr i es. The s i gnifican tly h i gher r eport ed f at al i t y r a t e in W uhan c ity and Hube i
pr ovince comp a r ing t o ot her r egion s ar e pr obably due t o t he short age of medical
supplies and the under es timat i o n o f t o t al cases of inf ection . The less on s in W uhan
als o t augh t us tha t if t he outbr eak i n a hea vily popula t ed metr opol it an ar ea is not
w ell c on tr oll ed soon enou gh, r apid s a t ur a tion of the ho s pit a l capacity is inevit able
and devas t a ting. Ther e f or e, th e only e f f ec t ive w a y is t o co n tr ol the epid emic is t o
mitig a t e t r ans m ission (inf ectious r a t e) and t his has pr ov ed t o be suc c es sf ul in C hina.
Ther e is no doubt that the capabil ity of manag e men t and contr ol of C OV ID-19
t r a n s m i s s i o n h e a v i l y r e l y o n t h e p r e p a r e d n e s s o f a co u n t r y ’ s h e a l t h s y s t e m . W h i l e i t
r emains deba t ab le whether lar g e econom y bodies in Asia such a s South K or ea and
Japan should adopt si m i lar con t r o l meas u r es a s t he Chine s e gov ernmen t ; i n less
dev eloped c ountr ies w it h insuf ficien t medic al r esour ces and ab sen ce of a pan demic
pr epar ednes s plan, a mild r espons e migh t be inadequat e t o deal wi th su ch an
outb r eak. Extr eme quar antine and tr anspor t con tr ol meas u r es s imilar t o China
should be c o ns ider ed t o mi tig a t e local tr ansmission f ollowing confirmed import at ion.
In con c lus ion, w e ha v e const ru c t ed an SEIR mod el and fit t ed al l th e public ly a v ail able
China C O VID -201 9 da t a i n a dynamic manner , and g et a f air ly ac c ur a t e model o f the
whole pr o ces s of the epide mic in China. W e est ima t ed the o ver all fa t al ity r a t e t o b e
0.68% o utsi d e of Hubei pr ovince. Thr o ugh simula tion, we als o evalua t ed the
impor t ance and e ff ectiveness of st r ic t gover nmen t c ont r ol enf or c ed by Chine s e
autho rit ies. It is clear tha t the c o n t r o l measur es, bo th i n W uhan and n a tionwide,
ha v e significan t ly r ed uc ed tr ans m is s i b i li t y . Con sidering the pot en tia l thr ea t o f f a s t
w orldwide C O VID- 19 outbr ea k t o public health and global ec onom y , mor e s tric t
gov ernmen t con tr ols ar e advi sed bas ed on the China e xper ience.
Contribut ors
DC a n d CY des igned t he st udy . C Y and DC did t he li t er a tu r e s ear ch. XZ, Z W , R Y and SC
c ollect ed and m a n ual ly chec k ed t he da t a. D C analy z ed the da t a and dev elop ed the
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Shin y applicat ion with suppor t fr om X Z, Z W , ZJ and WF . DC de s igned t he figur es. CY
and DC i n t erp r et ed the r es ults and wr ot e t h e manuscr ipt with input f r o m FY .
Declaration of int erests
W e de clar e no c ompet i n g int er est s .
Dat a sharing
The original dat a tha t suppo rt the f i n dings of t h is s tudy ar e a v ai labl e fr om th e
Nat ional Hea lth C omm iss ion of t he P eople’ s R epu bli c of C hina as w ell as the W H O. In
or der t o e ff i cien t ly us e our c ompile d da t a as w ell as mode lling r es ult s by e xt ernal
user s, we developed an in tegr a tiv e web-based applicat ion with t he Shin y fr amew or k
(h t t p://shin y .r stu dio.com /
), whi ch c ombines the c omput ational pow er of R with
fr i en dly and in t er ac t ive w eb int erf ace s. Our c ompiled da t abase is pub l icly a v aila b l e
fr o m t he websit e of N an j ing Univer s it y (h t tp://compbio.nju.ed u. c n/ncov 2019/ ) on
F eb 24
th , 2020 , wher e it w ould be up d at ed in ti me dur ing the out break. D at a us ed in
this analysi s i s fr o z en on F eb 29 th , 20 2 0.
Acknowledgm ents
W e w ould lik e t o th ank C hen y u Zh a n g fr om Nanjing U niv er sity ( NJU ) and Y u X ue fr om
Hu a zhong U n i ver s ity of Science and Technolog y (H US T) f or help f ul discu ssion and
su g ge s tions. W e t hank W an shan N ing fr om HUST , and Y ik ai Zhu and Liang-Y u F u f r o m
NJU f or t echnic al support . The stu d y w as suppor t ed by the Fundamen t al R es ear c h
Funds f or t he Cen t r al Univ er sities a nd the Na tional N a tu r al Science F ounda tion o f
China (2187706 0 ).
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
References
1 L i Q , Guan X, W u P , et al. E arly T r a nsmis s ion Dynamics in W uhan, Chin a, of
N ov el Co r ona virus–Inf ect ed Pne um onia. N Engl J Med 2020.
DOI:1 0.105 6/nejmoa2001 316.
2 Huang C, W a n g Y , L i X, et al. Clinical f e a tur es of p atients inf ec t ed w it h 2 019
nov el cor ona v ir us i n W uhan, Ch i n a. Lancet 2020.
DOI:1 0.101 6/S014 0-673 6(20)301 83- 5 .
3 Chen N , Zhou M, D ong X, et al. Epidemiologic al and clinical c har ac t erist ics of
99 ca se s of 2 019 n ov el c or ona virus p neumo nia i n W uhan, C hina: a de script ive
st ud y . Lancet 20 20. D OI:1 0.101 6/S0 1 40-6736(20)30 21 1-7.
4 W H O. Naming the cor on aviru s diseas e (C OVID -19) and t he vi rus tha t causes it.
2020.
h t tps:// ww w . who .i n t /emer g encies/ d isea ses/nov el - c or ona virus-2019/t ech n ic al
-guidance/ naming-t he-c or ona virus-di sea s e- (co v id- 2019)-and-t he-v irus-th a t -c a
us e s-it.
5 W H O. St a t em ent on the second meeting of t he In terna tional H ealth
R egula tions ( 2005) Emer g ency Com mitt ee r eg a r ding the outb r eak of novel
cor ona virus (2 019-nC oV). 2 0 20.
h t tps:// ww w . who .i n t / new s-r oo m/ det ail /30-01- 2020-st a t ement- on -the - s econd
-meeting-of-the - i n t e rna tional-h ealth - r egula tions-%282005%2 9-emer g ency -c o
mmitt ee-r eg ar ding-t he- outb reak-of-novel- cor ona v i r us-%282019-nc ov %29.
6 G r eenla n d S. Dose-R esponse and t r end analy sis in epidemiology: Al t er nat iv es
t o ca t egor ical analy si s . Epidemiology 1995.
DOI:1 0.109 7/00 00164 8-19950 7000- 0 0005.
7 Back er J A , Klink enber g D , W alling a J . Inc uba tion per iod o f 2019 n ov e l
cor ona virus (2019-n CoV) inf ec t i o ns a m ong tr av e ller s fr o m W uhan, China,
20-28 January 2020. Euro Surveill 2020.
DOI:1 0.280 7/15 60-7917. E S.2 020.2 5.5 .200006 2.
8 Chan J F W , Y uan S , K ok KH , et al. A f amilial clust er of pneumonia ass o c i a t ed
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
wi t h t he 2019 nov el cor ona virus indi ca ting per son-t o- p er son t r ansmissio n: a
st udy o f a f amily clu s t er . Lancet 2020. D O I:1 0 .101 6/ S0 140-673 6 (20)3015 4-9.
9 L iu T , Hu J , K an g M , et al. T r an s m i s s i o n dynamics of 2019 nov el cor ona vir us
(2019-nCo V). bioRxiv 2 020. D OI:10. 11 01/ 20 2 0.01. 25.91 9787.
10 G uan W , Ni Z, Hu Y , et al. C l inic al Charact er istics of Cor on aviru s D i sea se 201 9 in
China. N Engl J Med 2020; : N EJM oa2 002032.
11 Zhou T , Liu Q , Y an g Z, et al. Pr elim in ary pr edic t ion o f the bas ic r epr oduction
number of t he W uhan nov el cor o na virus 2019 -nCoV . J Evid Based Med 2020.
DOI:1 0.111 1/jebm.123 76.
12 W u J T , Leung K, Leun g G M . N ow ca st i n g and f or eca st i n g t he pot en t ia l dom est ic
and in t e rna t ion a l spr ead of t he 2019-nCo V outbr eak origina ting in W uhan,
China: a modelling stu dy . Lancet 2020 . DOI: 10.10 16/S0 140-67 36(20)3 02 60-9.
13 Shao P , Shan Y . Bew ar e o f as ympt oma t i c tr ansmiss ion: Study on 20 19- nCoV
pr ev ention and con tr ol measur es b ased on e xt ended SEIR m odel. bioRxiv 2 020.
DOI:1 0.110 1/20 20.01 .28.9 23169 .
14 Y an g Z, Z en g Z, W an g K, et al. Mod if i ed S EIR and A I pr ed iction o f the ep ide mics
tr end o f C O VID -19 in C hina und e r public health i n t er v entions. 20 20; 2019.
DOI:1 0.210 37/jt d.202 0.02. 64.
15 L iu T , Hu J , K ang M, et al. Ti m e-varying tr ansmi s s ion dynamics of N ovel
Cor ona virus Pneu monia i n China. bioRxiv 2 020.
DOI:1 0.110 1/20 20.01 .25.9 19787 .
16 Hu Z, Ge Q , Li S, Jin L , Xion g M. Ar tificial In telligen c e F or ec as ting of Covid-1 9 in
China. arxiv 2020; : 1– 20.
17 Cer aolo C, G ior gi FM . G eno mic var i an ce of the 2019 -nCoV c or ona v ir us . J Med
Virol 2020. D O I :10.1 002 / jm v .257 00.
18 L u R, Zhao X, Li J , et al. Genomic ch ar act er is a tion and ep idemiol o g y of 2019
nov el co r ona v irus: implic ations f or vi rus or igins a n d r ecept or b inding. Lancet
2020. D OI:1 0.101 6/S01 40-673 6(20)3 0251 -8.
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Figures
Figure 1 . The sever ity r a t e and th e mort ali ty r at e o f C O VID-1 9 in m a inland C hina fr om
Jan 13 rd t o F eb 29 th , 2020. H ea tmaps s h owi n g t he s ev erit y r a tio ( A ) and the mort al it y
rate ( B ) in di f f e r ent pr o v inces or m unicipalities of main land China. The mono t onic
dis tribut ion of da t a ov e r t i me w as as s e s s ed by M ann-K endall t r end t est s . P-v alues
adjus t ed w er e c or r ec t ed with the B enjamini- H ochber g method in o r de r t o con tr ol
the f alse discov ery r a t e. “*” indica tes an adju s t ed p-v alue < 0.001 . Sc a t t e r plot s
showin g the po s it i v e cor r elation o f t h e number of s ev er e c a ses ( C ) or m or ta l i t y ( D )
and inf ect ed c as es on F eb 29
th , 2020 .
Figure 2. P a r amet er es timation o f the SEIR tr ansmis s ion model. ( A ) H e a tm a p
showin g the d ynamic chang e of e stima t ed par amet er s of t he SEIR model over time.
In or d e r to compa r e dat a a m ong di ff e r en t c it ies , only r el a ti v e v alues ar e shown in the
hea tmap. Dat a f or e x a m ple cities (in r ed) ar e s hown i n ( C-E ). ( B ) F old chang es of the
thr ee par amet er s of t he SEIR model. Dynam i cs of e st ima t ed σ ( C ) o r γ ( D ) p a ra m e te r s
ov er ti m e in W uhan. ( E ) Dynamics of esti m at ed β par a m et er ov er t i me in the
popula ti o n of m a inl and China ( left ), W uhan city (m i d dle) and Nanjing city (r ig h t ). In
this f ig u r e, t he m odel ing analy si s w as p erf or med in the p opulat i o ns of the Hub ei
pr ovince, mainland China as w ell as the t op 44 cities of the whol e ma inl and China.
Dash lines indica t e the dat e of loc k down of W uhan.
Figure 3. Simula ti o n of epide mic spr ead i n g in W uhan st a r ting w it h diff erent
pr ev ent i o n scenar ios. ( A ) Si m u la t io n analy si s showin g th e predict ed con firmed
individuals b a sed on est i m at ed v al u e s of the
β par amet er a t dif f e r e n t t i m e poin ts. β
v alues ar e high a t t he early st age and low a t t he lat e s t ag e, as ind i ca t ed i n the color
leg end. Arr ow show s t he change o f epide mic c u r v e under diff eren t pr ev ention
s cenar ios . (B ) R e l a t ions hip between t he estimat ed β par amet er and t h e p e ak of
pr edic t ed confir m ed indiv iduals using the corr esponding β v a l u e .
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Figure 4. An al y sis of t he C O V ID- 19 dat a outside of China, with a f ocus on the
outb r eak i n F ebr ua ry . The r epor t ed inf ect ed c as es ( A ) and m or t ality (B ) in t he t op f i ve
coun tr i es and the Diamo nd Princ es s s hip in F ebruar y 202 0. H ea tmaps s how the
dynamic c hang e of es tima t ed p a r ame t er s β (C ) a nd γ ( D ) of t he S EIR m odel over ti me.
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Mortality rate (%)
15
20
25
30
01
05
10
15
20
25
29
Tianjin
Xinjiang
Anhui
Jiangsu
Shaanxi
Shandong
Beijing
Sichuan
Liaoning
Inner Mongolia
Shanghai
Jilin
Guizhou
Jiangxi
Fujian
Henan *
Hunan
Guangdong
Zhejiang
Hainan
Chongqing
Yunnan
Shanxi
Guangxi
Hebei
Qinghai
Ningxia
Gansu
Heilongjiang
Hubei
China
Jan 2020 Feb 2020
Severity rate (%)
15
20
25
30
01
05
10
15
20
25
29
*
*
*
*
*
Jan 2020 Feb 2020
A B
C D
/uni25CF
/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
1
10
102
103
102 103 104
Infected cases
Mortality
Feb 29, 2020
Huanggang
Wuhan
Xiaogan
Xiantao Henan
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
1
10
102
103
104
10 10 2 103 104
Infected cases
Severe cases
Feb 29, 2020
Wuhan
Xiangyang
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
Chongqing
Fujian
Gansu
Guangdong
Guangxi
Guizhou
Hainan
Hebei
Heilongjiang
Henan
Hubei
Hunan
Jiangxi
Jilin
Liaoning
Shaanxi
Shandong
Shanghai
Sichuan
Tianjin
Xinjiang
Zhejiang
0
10
20
30
40
50
0
1
2
3
4
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
A
DC
E
B
/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF
6.4e−06
p < 2.22e−16
p < 2.22e−16
0
50
100
150
beta sigma gamma
Fold change
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
0
0.25
0.50
0.75
1.00
Jan 15 Feb 01 Feb 15
China (beta)
/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
0
0.25
0.50
0.75
Jan 15 Feb 01 Feb 15
Wuhan (beta)
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
0
0.25
0.50
0.75
Jan 15 Feb 01 Feb 15
Nanjing (beta)
/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF
0.01
0.02
0.03
0.04
0.05
Jan 15 Feb 01 Feb 15
Wuhan (gamma)
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF
0.05
0.10
0.15
0.20
0.25
Jan 15 Feb 01 Feb 15
Wuhan (sigma)
Bengbu
Dongguan
Chengdu
Shaoyang
Guangzhou
Zhengzhou
Xinyang
Harbin
Bozhou
Ningbo
Xi'an
Shangqiu
Shangrao
Changsha
Yichun
Xinyu
Nanjing
Nanchang
Wenzhou
Jiujiang
Shenzhen
Hefei
Y ueyang
Suzhou
Zhuhai
Fuyang
Zhumadian
T aizhou
Hangzhou
Suizhou
Ezhou
Yichang
Xiantao
Jingmen
Xiangyang
Tianmen
Qianjiang
Xianning
Huangshi
Xiaogan
Shiyan
Jingzhou
Huanggang
Wuhan
Hubei
China
sigma σ
20
30
01
10
20
29
gamma γ
20
30
01
10
20
29
beta β
11
20
30
01
10
20
29
Jan 2020 Feb 2020
Low
High
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
B
102
103
104
105
106
107
Jan 15 Feb 01 Feb 15 Mar 01 Mar 15
Predicted infected cases
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
10-9.5 10-9.0 10-8.5 10-8.0 10-7.5
beta
Max infected cases
105
106
107
Early
Late
beta
High
Low
A Wuhan
Wuhan
Early
Late
beta
High
Low
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
1
10
102
103
Feb 03 Feb 10 Feb 17 Feb 24
Infected cases
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF/uni25CF
/uni25CF
0
10
20
30
Feb 03 Feb 10 Feb 17 Feb 24
Mortality
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
/uni25CF
Diamond Princess ship
Iran
Italy
Japan
South Korea
Singapore
A B
C
Low High
Diamond Princess
Japan
Iran
Italy
South Korea
Singapore
gamma
01 10 20 2901 10 20 29
beta
Feb 2020
. CC-BY-NC-ND 4.0 International licenseIt is made available under a
is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 10, 2020. ; https://doi.org/10.1101/2020.03.03.20030445doi: medRxiv preprint
Text is read by the "Ask this paper" AI Q&A widget below. Extraction quality varies by source — PMC NXML preserves structure cleanly, OA-HTML may include some navigation residue, and OA-PDF can have broken hyphenation. The publisher copy (via DOI) is the canonical version.
My notes (saved in your browser only)
Ask this paper
Answers must be backed by verbatim quotes from this paper's full text. Hallucinated quotes are dropped automatically; if no verbatim passage answers the question, we say so. How this works
Citation neighborhood (no data yet)
We don't have any in-corpus citations linked to this paper yet. The paper's references may be in our DB but unresolved to ``paper_id`` (resolution happens at ingest when the cited DOI matches a row we already have). Run the cross-source citation reconcile pass to retry.
Source provenance
- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00
- unpaywall
- last seen: 2026-05-21T05:10:58.409756+00:00
License: CC-BY-NC-ND-4.0