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 dene the specic

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, inuenza 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 conicts 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

denitions 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 quanties 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 specic

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

unofcial 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 conrmed

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 condence 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 condence

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 condence interval

of [3.37,3.54] and for maximum

likelihood estimation the value

of 2.93 with condence 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 conrmed 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 condence

(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 trafc

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 dene Cumulative cases C=I+R+D.

Revista Médica Vozandes

Volumen 31, Número 1, 2020

9

EDITORIAL

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