Revista Médica Vozandes
Volumen 31, Número 1, 2020
7
outcomes about the behavior of
pandemic in their countries
(4)
.
The initial case of application of data
analytics tools during the current
COVID-19 pandemic, was tested in
China, where statistical models were
used in order to forecast the number
of cases in days after the beginning
of the disease, as well as, the basic
reproduction number R0
(5,6)
. Zhang
et al. [2020] and Zhao et al. [2020],
who modeled the expansion of
COVID19 in their country using
mathematical models based on
Poisson and gamma distributions
to replicate the evolution of daily
cases. As a result, they computed
reproduction factors and levels of
new cases
(5,6)
.
Mathematical Stochastic models
and probabilistic distributions to
explain epidemiology phenomena
have been improved since the
origin of SARS diseases in Hong
Kong and China in early 2000’s,
when new formulations to the SIR
model appeared
(7)
. This classic
method is based in differential
equations in order to obtain
parameters that dene the specic
situation of a pandemic related
to susceptible (S), infectious (I)
and recovered (R), nevertheless,
more variables can be added to
the population analysis. Despite
showing solid estimations about
the evolution of pandemics, such
as, AH1N1, the quality of this kind
of model depends on the volume
of the data. Many variables are
necessary to explain the four
components that derive in a series
of estimated parameters. These
values can be highly sensible
to changes and can present
correlation between them,
sometimes conducting to wrong
conclusions if something was not
considered in the data sources.
Since the very beginning of
modern epidemiology, disease
estimates and understanding
of transmission dynamics have
been an important pillar* in
understanding future outbreaks
and predicting possible disease
outbreaks. Ronald Ross, a medical
doctor in 1902 won his rst Nobel
Prize for his studies in the origins of
the transmission of malaria, years
later, his SIR Model (Susceptible,
Infected and Recovered) was
perfected by William Kermack and
Anderson Mckendrik and since
then it has been used to calculate
the progression of multiple diseases
in which we can include, malaria,
Chagas, inuenza or Zika
(1)
.
With the arrival of multiple
outbreaks, epidemics and
pandemics scenarios, the usefulness
of mathematical models has been
challenged. During 2002 with the
arrival of the recently discovered
SARS-CoV virus, the microorganism
responsible for the Severe Acute
Respiratory Syndrome (SARS),
in 2009 the H1N1 (swine u), the
MERS-CoV (Middle East Respiratory
Syndrome) in 2012 and the most
recently discovered SARS-CoV2
(COVID-19) in 2020 have put the use
of mathematical calculations and
Bayesian estimates to the limit
(2)
.
During the current situation,
the COVID-19 pandemic has
constituted an enormous challenge
for governments and societies to
handle one of the biggest public
health challenges, especially in
those countries with weaker health
systems
(3)
.
In order to counteract the global
challenges of a pandemic, scientists
all over the world have relied on
data in order to use advanced
modelling for disease transmission
estimation and to sketch possible
EDITORIAL
THE IMPORTANCE OF MATHEMATICAL MODELING IN THE
BATTLE AGAINST COVID-19.
1. Universidad de Las Americas, Faculty of Health
Science, One Health Research Group. Quito Ecuador
2. Universidad Nacional de la Plata, Instituto de Física
La Plata, La Plata, Argentina
ORCID ID:
Fernández Naranjo Raúl
https://orcid.org/0000-0002-4875-9652
Feijoo Javier
https://orcid.org/0000-0002-0917-909X
Ortiz Prado Esteban
https://orcid.org/0000-0002-1895-7498
*Corresponding author: Ortiz-Prado Esteban
E-mail: e.ortizprado@gmail.com
Fernández Naranjo Raúl
1
, Feijoo Javier
2
, Ortiz Prado Esteban*
1
Este artículo está bajo una
licencia de Creative Com-
mons de tipo Reconocimien-
to – No comercial – Sin obras
derivadas 4.0 International.
Forma de citar este artículo:
Fernández-Naranjo R, Feijoo J, Ortiz-Pra-
do E. THE IMPORTANCE OF MATHE-
MATICAL MODELING IN THE BATTLE
AGAINST COVID-19. Rev Med Vozandes.
2020; 31 (1): 7-9
Keys Words: SARS-Cov2, Models, Statistical, Burden of Disease
Received: 17 – May - 2020
Accepted: 28 – May - 2020
Publish: 1 – Jul – 2020
Article history
Conflict of interest: All authors declared that
there are no conicts of interest
Financial disclosure: The authors have no nan-
cial relationships relevant to this article to disclose
Authors’ contribution: All the authors contri-
buted in the search, selection of articles and writing.
All the authors reviewed and approved the nal
manuscript.
8
Naranjo-Fernández R, et al.
Revista Médica Vozandes
Volumen 31, Número 1, 2020
with predictive models, it must be
aligned data, methodological
denitions and technical criteria
from medical experts to understand
the insights from models and make
policies quickly. Based on Yuan
et al R naught estimates derived
from any analytical method explain
how the spreading of a disease will
be if no public health policies are
adopted. On the contrary, R
t
is a
pure measure that quanties in real
time how the level of contagious
is evolving in pandemic having
public health actions. According to
this, COVID-19 in Ecuador is being
controlled in function of R
t
estimates
but if no measures were present the
scenery would be complex as large
R
0
values shown
(10)
.
Light strategy system in Ecuador
Many countries are struggling with the
effects of the pandemic, and politics
need to take appropriate decisions
to balance the economy and public
health. The rst step is to know specic
details and parameters of the virus
spread in a population, statistical
models used the data available and
give accurate parameters that rule
the behavior of the pandemic.
One of the countries the pandemic
has affected the most is Ecuador,
a dramatically high number of
unofcial death toll has put this
country to the limit
(3)
. This burden has
already stretched not only the health
system but the economic engine in
As an example, a method is
presented for estimation of
reproduction factors in Ecuador,
using information from conrmed
COVID-19 cases in the country, as
well as, frequentist and Bayesian
statistical frameworks to compute
these quantities. The frequentist
method is used to compute the
basic reproduction number R
0
and
the bayesian method considers a
statistical distribution to compute R
t
the effective reproduction number in
a continuous way by using previous
daily information as input for a joint
estimation of the future distribution
for COVID19 cases based on
previous experience. It is ideal that
both quantities are below 1 to have
signals about the slowing of COVID19
in a country (Figure 1).
It can be seen in Figure 1 the R
t
estimates for Ecuador between
2020-02-28 and 2020-05-05 with its
highest value of 3.77 at 2020-03-
14 and a condence interval of
[2.95,4.42]. Since that day R
t
started
to fall reaching values below 1 at
2020-03-30 with 0.95 and condence
interval of [0.82,1.05]. In the case
of R
0
as static quantity its estimate
with exponential growth method
is 3.45 with condence interval
of [3.37,3.54] and for maximum
likelihood estimation the value
of 2.93 with condence interval
of [2.83,3.04]. R
t
quantities get a
peak and decrease below 1 but
R
0
is always over 1. This could be
contradictory but in order to succeed
Recently, important progress in
the eld of data science and
machine learning, allowed
forecasters and big data analysts
to compute key indicators about
the evolution of COVID-19
(8)
. These
techniques, with large streams
of information being produced
everyday about conrmed cases or
tracing apps interaction, permit the
estimation of probability densities
for epidemiological parameters,
as disease transmissibility, and the
prediction of future observations
with a degree of condence
(9).
Some
models from the machine learning
corpus contemplate trajectory
matching via least square tting
for cases prediction, probabilistic
methods to quantify reproduction
factors, and data assimilation
methods to infer distributional
properties for contagious cases.
The advantage of machine learning
methods against classic methods like
SIR or SIRS models lies on its capacity
of using past information to infer
present or future situations
(9)
.
The key to success in the use of
predictive models for COVID19
management is composed of
two elements: 1) the quality and
availability of data being used about
the situation of virus spreading cases
in the countries and 2) Being able
to consider and use all previous
evidence to make estimations about
a situation in a dynamic way. These
two elements even can shape the
way how results are understood.
Figure 1. R
t
estimated via Bayesian method.
THE IMPORTANCE OF MATHEMATICAL MODELING IN THE BATTLE AGAINST COVID-19.
Acquiring rigorous deductions is often
challenging among life sciences and
medicine due to the highly variability
among species, nevertheless, the
dynamic of infections is well known,
and the use of several mathematical
models will allow us to predict from
several perspectives, opening our
view for plenty of possible scenarios.
In this sense, we conclude that
although the variability in the quantity
and quality of the data varies from
region to region, multiple modeling
will improve the forecast and
therefore have safer estimates for
policy makers to confront epidemics.
We present the estimation for the
light system strategy based on a
mathematical model to show the
probable scenario when passing
from red to yellow to green. When
plotted, this strategy seems to impose
unnecessary risks when changing
from red light (80% lockdown) to
yellow light (60% lockdown). Figure
2 We depict the curve that shows
when changing drastically to green
light, the health system collapses.
The use of mathematics to study
quantitative relationships and
biological variables has allowed
scientists and epidemiologists to offer
new conjectures around disease
transmission and populations.
this middle-income country. Ecuador
is now facing the challenge to reopen
its economy in a controlled manner,
so a second wave is prevented.
For that purpose, ne-tuned
mathematical models can forecast
the consequences of a certain
decision. The proposed system to
reopen the economy in Ecuador is
based on a color code as a trafc
light (Red: Complete lockdown,
Yellow: Reduced lockdown, and
Green: Back to the “new normality”).
We have used the SIRD (Susceptible,
Infected, Recovered, Deaths) model
to analyze the light strategy, including
parameters such as social distancing,
improved hygiene, close borders and
collapse of health system policies.
Figure 2. A SIRD model using 4 Dynamic variables, Susceptibles (S), Active infected (I),
Recovered (R) and Death (D). with the constraint N=S+I+R+D. with N the population.
We also have to dene Cumulative cases C=I+R+D.
Revista Médica Vozandes
Volumen 31, Número 1, 2020
9
EDITORIAL
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