A chi es o Clinical Mic obiology
ISSN 1989-8436
2021
Vol. 12 No. 4:159
1
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Vicen e Ma inez*
Depa men o de Ma ema` iques, Uni e si a
Jaume I, Ins i u de Ma ema` iques i Aplicacions
de Cas ello, Cas ello E-12071, Spain
Co esponding au ho : Ma inez V
 [email p o ec ed]
Depa men o de Ma ema` iques, Uni e si a
Jaume I, Ins i u de Ma ema` iques i Aplicacions
de Cas ello, Cas ello E-12071, Spain.
Ci a ion: Ma inez V (2021) B ie O e iew
on he COVID-19 Pandemic in Spain. A ch Clin
Mic obio Vol.12 No.4: 159
B ie O e iew on he COVID-19 Pandemic
in Spain
Recei ed: June 22, 2021; Accep ed: July 06, 2021; Published: July 13, 2021
Abs ac
We analyze he e olu ion o he COVID-19 pandemic in Spain. Se e al nume ical
me hods and models a e s udied o unde s and how he e olu ion o his
pandemic is e e enced. We also jus i y he adjus men s ha we ha e made in
o de o in e p e he public da a supplied by he Spanish Go e nmen . Finally, we
p esen some o he lessons lea ned so ha we way ca y ou ea ly ac ions when
we a e imme sed in simila pandemics.
Keywo ds: Pandemic; Nume ical simula ion; SIRD model; Ma hema ical modeling
Desc ip ion
Since he eme gence o he co ona i us (SARS-CoV-2) in Decembe
2019 in China and i s sp ead wo ldwide, humani y has
su e ed
one o he wo s known pandemics o da e. The disease caused by
his i us was called COVID-19 by he Wo ld Heal h
O ganiza ion
(WHO), and as o May 2021, i has caused he in ec ion o 150
million people and he dea h o app oxima ely 5 million o hese
people. In Spain, he e ha e been 3,678,390 con i med cases and
79,953 dea hs [1].
In his wo k, we analyze he de elopmen o he COVID-19
pandemic in Spain by adjus ing se e al exis ing ma hema ical
models o desc ibe he e olu ion o in ec ions. Fo he mos pa ,
we use he analysis ca ied ou in he pape "A Modi ied SIRD
Model o S udy he E olu ion o he COVID-19 Pandemic in Spain"
[2], which desc ibes he e olu ion o his pandemic du ing he
i s wa e su e ed in Spain du ing he mon hs o Ma ch and Ap il
2020. We conside ha a wa e o he pandemic occu s when he
numbe o in ec ions eaches a maximum in a ini e pe iod o
ime, ollowed by and dec ease.
Models o In ec ious Disease Dynamics
The SIRD model
The SIRD model was p oposed in 1927 [3] by Ke mack and
McKend ick; since hen, i has been widely used [4-9]. This
model conside s ou ypes o people:
(S) Suscep ible: he people who could become
in ec ed.
(I) In ec ed: he people who a e in ec ed a ha momen .
(R) Reco e ed: he people who ha e had he disease and a e
now heal hy.
(D) Deceased: he people who ha e died o he disease.
I is go e ned by he ollowing sys em o di e en ial equa ions
gi en by
S′( )=- β S( )I( )
I′( )
=β S( )I( )-
αI( )-
γ I ( )
R
′
( )
=α I ( )
D
′
( )=γ I( )
Whe e α is he eco e y a e, β is he in ec ed a e and γ is he
dea h a e, all o hem pe uni o ime. I shows ypical beha io ,
as indica ed in Figu e 1.
Typical beha iou o an epidemic’s e olu ion o e imeFigu e 1:
*
.
Depa men o de Ma emà iques, Uni e si a
Jaume I, Ins i u de Ma emà iques i Aplicacions
de Cas elló, Cas elló E-12071, Spain
Depa men o de Ma emà iques, Uni e si a
Jaume I, Ins i u de Ma emà iques i Aplicacions
de Cas elló, Cas elló E-12071, Spain.
2021
A chi es o Clinical Mic obiology
ISSN 1989-8436
Vol. 12 No. 4:159
2This a icle is a ailable in: h ps://www.acmic ob.com/
The pape "A Modi ied SIRD Model o S udy he E olu ion o he
COVID-19 Pandemic in Spain [2], desc ibed he adjus men
o his
model o he i s wa e o he COVID-19 pandemic in Spain. This
wo k led o he ollowing conclusions:
• The SIRD model, like o he s, is s ongly dependen on he
ini ial da a used o adjus he pa ame e s. I also depends on
he
people exposed o he i us, i.e. he a iable S, suscep ible
people.
Depending on he s ic ness o he isola ion measu es,
his a iable may be signi ican ly highe o lowe a each
s age o he pandemic.
• The p ecision o he es ima ed pa ame e s is de e mined
by heo e ical easoning. The pape shows he e olu ion
o he ep oduc ion numbe du ing he la ency pe iod,
which is e y help ul o unde s anding he e olu ion o he
epidemic.
• The model allows us o make sho - e m p edic ions,
which a e use ul o making decisions ha educe ha m ul
e ec s, o example, o educe he numbe o dea hs using
qua an ine [10]. Since he da a is change, i we adjus he
pa ame e s acco ding o he es ic ions imposed in each
case, a mo e app op ia e global beha io can be obse ed.
• The pape shows he i o a piecewise es ima e a each s age,
conside ing changes in condi ions du ing he e olu ion o
he epidemic. The model allows us o adjus he pa ame e s
in eal ime when he disease is la en . Gi en he simplici y
wi h which i s pa ame e s can be calcula ed, he model can
be easily adap ed o simila in ec ions.
In e es ed eade s can ind a g ea deal o de ail on hese indings
in he pape "A Modi ied SIRD Model o S udy he E olu ion o
he COVID-19 Pandemic in Spain” [2].
O he models
The e is a wide a ie y o models o s udy o he COVID-19 pandemic
in he scien i ic li e a u e: using Bayesian and s ochas ic
echniques
[11-13], including mobili y, con inemen and qua an ine,
ac ional models, and logis ic models, among o he s [14-18]. In
pa icula , show simila beha io s in he es ima es [11-12].
Upda e o he Pandemic Da a since
May 2020
A e he i s wa e, which was he mos unexpec ed, ou mo e
wa es a i ed. The da a a e shown in Figu es 2 and 3, in which i
can be seen ha he maximum numbe o dea hs occu ed se e al
days a e he maximum numbe o in ec ions. The su p ising
hing is ha du ing he i s wa e, mo e dea hs occu ed wi h
ewe in ec ions. This could be explained by he low numbe o
es s ca ied ou du ing he i s wa e, which indica es ha he
numbe o in ec ions epo ed was much lowe han he ac ual
numbe ha exis ed du ing hose da es.
Due o he wo sening o he si ua ion du ing he second wa e,
on Oc obe 25, 2020 he Spanish Go e nmen dec eed ano he
s a e o ala m [19] on Oc obe 25, 2020, imposing es ic i e
mobili y measu es. On Sunday, May 9, 2021, his s a e o ala m
ended, p ima ily due o he success ul implemen a ion o
accina ion p og am. The success o accines in comba ing he
COVID-19 pandemic wo ldwide dese es a pa icula men ion.
Since Decembe 2020 and a e a yea o global esea ch,
he e
a e al eady ou accines ha ha e been au ho ized by he Eu opean
Medicines Agency (EMA) o inocula ion in Eu ope:
P ize -BioNTech,
Mode na, As aZeneca and Janssen.
On Sunday, Decembe 27, 2020, he i s dose o he P ize
accine was adminis e ed in Spain. F om hen un il May 12,
2021, he numbe o doses o accines adminis e ed was eached
18,032,517, and 9,221,285 people had ecei ed he ull dose.
These amoun s a e inc easing a a good pace and i is expec ed
o each 70% o he popula ion o Spain will ha e been accina ed
by he end o he summe o 2021. I is wo h men ioning ha in
June 2021 a new accina ion eco d was b oken in Spain: 624,261
doses in 24 hou s.
Con i med daily cases o COVID-19 in Spain (May
30, 2021). Sou ce: Spanish Go e nmen on 31
May 2021.
Figu e 2:
Numbe o daily dea hs om COVID-19 in Spain
(May 30, 2021). Sou ce: Spanish Go e nmen on
31 May 2021.
Figu e 3:
3
© Unde License o C ea i e Commons A ibu ion 3.0 License
A chi es o Clinical Mic obiology
ISSN 1989-8436
Vol. 12 No. 4: 159
2021
As a inal e lec ion, we will compa e he COVID-19 pandemic wi h
he Spanish lu pandemic ha ook place be ween 1918
and 1920
[20-22]. This e ible pandemic le mo e han 40 million ic ims
wo ldwide, and Spain was one o he mos se e ely a ec ed
coun ies, wi h 8 million people in ec ed and 300,000 dead. In
oday’s socie y, wi h he in e connec ions ha exis in a globalized
wo ld, he pandemic could ha e caused mo e damage, bu
heal h and echnological esou ces a e a supe io hose o he
ea ly wen ie h cen u y. Howe e , he only exis ing measu es
ha ha e been e ec i e hen and now a e isola ion measu es
(qua an ine). This is he only measu e ha can educe he numbe
o people suscep ible o in ec ion wi h he disease ( a iable S o
he SIRD model) [15,23-25] and he e o e s op i s expansion
and he consequen dea hs [10]. Pe haps he only hing ha
di e en ia es us now om hen is ha he g ea e esea ch
capaci y and wo ldwide collabo a ion ha e made i possible o
ob ain accines in jus one yea , a miles one ha would ha e
been impossible o achie e in 1918 [26-36].
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