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Bioscience Journal  Original Article 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

DEMAND FORECAST IN THE EMERGENCY DEPARTMENT IN MINAS 
GERAIS, BRAZIL 

 
PREVISÃO DE DEMANDA NO DEPARTAMENTO DE EMERGÊNCIA EM 

MINAS GERAIS, BRASIL 
 

Franciele Guimarães de BRITO1; Elmiro Santos RESENDE2;  
Aurélia Aparecida de Araújo RODRIGUES3; Marcelle Aparecida Barros JUNQUEIRA4;  

Vívian Ribeiro BARRETO5; João Batista DESTRO FILHO6 
1. Pos graduated by Federal University of Uberlândia, PhD in biomedical engineering from the Federal University of Uberlândia; 2. 

Professor at the Federal University of Uberlândia in the Medicine School, PhD from the São Paulo Federal University; 3. Professor at 
the Federal University of Uberlândia in the Mathematics School, PhD from the Pontifical Catholic University of Rio de Janeiro; 4. 

Professor at the Federal University of Uberlândia in the Nursing School, PhD from the São Paulo Federal University of Ribeirão Preto; 
5. Graduated in Statistic of the Federal University of Uberlândia; 6. Professor at the Federal University of Uberlândia in the Electrical 

Engineering School, PhD from the Nice-Sophia Antipolis University of France 
 

ABSTRACT: This study presents a mathematical model to carry out the demand forecasts in relation 
to patientes classified as green in the emergency department of a municipality in Minas Gerais, Brazil. In 
addition, another approach will investigate whether the green patients demand remains the same over the 
weekend, as compared to the weekdays, since there is no support from Primary Health Care units over the 
weekend. A retrospective study of the emergency service in the municipality of Monte Carmelo was carried out 
from January 2014 to December 2017.The time series of the patients classified as green during the host by the 
nurse, according to the Manchester Triage Scale, was analyzed in the temporal domain for the construction of a 
parametric model with the purpose of realizing the demand forecast. The Manchester Triage Scale has been 
adopted in most emergency department as a guiding instrument for risk classification, prioritizing the most 
serious cases. The data processing was fulfilled using Software R Version 3.4. The ARIMA model (1,1,1) 
presented a better fit for this forecast. The predictions of this model are values close to those observed for the 
number of patients seen that ranges from 1780.4 to 1796.6 patients per month. In relation to the demand of 
patients classified as green at the weekend, it has shown that it is slightly lower than the weekend, but it is still 
an expressive demand. The application of the models must be seen by the managers as a tool to aid decisions, 
thus it must support processes of planning, management and evaluation of public policies. In this context, 
mathematical models for demand forecasting are an instrument for management care and services. 
 

KEYWORDS: Triage. Health service needs and demands. Public health. 
 
INTRODUCTION 
 

A Integrated Delivery Systems in the scope 
of Unified Health System was established as a 
strategy to overcome the fragmentation of attention 
and management in the Health Regions and improve 
the political and institutional functioning of the 
Unified Health System, with a view to assuring 
users the set of actions and services that they need 
with effectiveness and efficiency (BRASIL, 2010). 

The emergency department is an important 
component of this health care and requires the 
organization of local health systems and the 
articulation between the different levels of attention 
to provide a qualified and decisive service to the 
emergency department. Health care in these 
situations should be articulated with Primary Health 
Care, since in addition to its effective functioning, it 
is necessary to develop health promotion actions 

and prevent diseases and injuries, diagnosis, 
treatment, rehabilitation and palliative care. 

Health actions and services must be 
organized so that they function in a harmonious and 
integrated way, overcoming the hegemonic logic of 
fragmentation of the health service organization 
within isolated programs, which are isolated and 
without connection with the epidemiological needs 
of the population and socio-demographic conditions 
of the region (BRASIL, 2013). 

In an attempt to address the challenges 
related to the organization of emergency services, 
the actions of the Ministry of Health have been 
focused on the need to reorganize the work process 
in order to meet the different levels of specificity 
and resolution in the care giving to patients with 
acute aggravations (BRASIL, 2009). 

In this context of reorganization of the 
processes, the Ministry of Health through the 

Received: 11/12/18 
Accepted: 05/06/19 



1641 
Demand forecast…  BRITO, F. G. et al. 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

National Policy of Humanization of Attention and 
Management of the Unified Health System proposes 
innovations in managerial practices and health 
production practices. Thus, in 2004, the User 
Embracement with Risk Classification was pointed 
out as a device for change in health care, 
management and production in health. 

The User Embracement with Risk 
Classification in the emergency department 
instituted in 2011, forms the basis of the process and 
of care flows, a requirement of all points of attention 
(BRASIL, 2011). Understood as a relational 
technological intervention device, the User 
Embracement with Risk Classification is guided by 
qualified listening, link building, guarantee of 
access with accountability, resolution of health 
services, as well as prioritization of the most serious 
patients for care (BRASIL, 2009). 

Therefore the User Embracement with Risk 
Classification is a guiding guide for attention and 
management of the emergency department, a 
measure of intervention for reorganization of 
urgency and emergency entry and in the 
implementation of networked health production. 
The Ministry of Health recommends that risk 
classification should follow a guiding protocol 
(BRASIL, 2009). 

At the global level, the most used protocols 
are: Australian Triage Scale, Canadian Emergency 
Department Triage and Acuity Scale, Emergency 
Severity Index e Manchester Triage Scale (PINTO 
JUNIOR et al., 2012). 

In this way, classification systems were 
created with the purpose of prioritizing service in an 
objective manner and based on the degree of risk. In 
Brazil, among the existing screening scales, the 
Manchester Triage Scale (MTS) has been adopted in 
most emergency department as a guiding instrument 
for risk classification, prioritizing the most serious 
cases. 

In this scale, the most frequent complaints 
of the patients treated in the emergency department 
are arranged in flow charts. Each flowchart has a set 
of discriminators that represent the signs and 
symptoms related to the main complaint presented 
by the patient. Each level of clinical priority has 
discriminators that define the patient's level of risk. 
Once classified, it is important that the patient is 
monitored and reevaluated, since his clinical 
condition may worsen or decrease (MACKWAY-
JONES et al., 2010). 

The assignment of risk to patients consists 
of a complex decision-making process in which 
nurses have been the most appropriate professionals 
to perform this task (FORSGEREN et al., 2012). 

The MTS includes levels of priority, color to be 
assigned, and an estimate of waiting time for 
medical care. Based on the identification of the 
user's main complaint by the nurse, a specific 
flowchart is selected, guided by the discriminators. 

Thus, the MTS screening scale classifies the 
patient into five priority levels: level 1 red 
(emergent, must receive immediate medical 
attention); level 2 orange (very urgent, medical 
evaluation in up to 10 minutes); level 3 yellow 
(urgent, medical evaluation in up to 60 minutes); 
level 4 green (not very urgent, medical evaluation in 
up to 120 minutes); level 5 blue (not urgent and can 
wait up to 240 minutes for medical attention) 
(MACKWAY-JONES et al., 2010). 

The reality of the emergency department 
around the world is overcrowded. The points of 
attention to acute conditions began to have 
management difficulties due to the increase of 
chronic conditions and consequently the increase of 
the use of these services, becoming the main cause 
of people's dissatisfaction with their health systems. 
The fact is that at the moment when the correlation 
between the presence of chronic conditions poorly 
managed by the health system and the emergency 
department, it is obvious that the vast majority of 
patients who enter today through the urgency 
presents acute exacerbations of chronic conditions 
(CORDEIRO JÚNIOR, 2008). 

These services serve a considerable volume 
of users that could be served in less complex units 
(FRANGO et al., 2018). However, Primary Health 
Care is organized to perform scheduled care, 
causing surplus demand to be informally referred 
informally to the emergency department (GHEN et 
al., 2015). 

The Primary Health Care is the first level of 
care and coordinates care at all points of care, 
presents a great capacity for resolving primary care 
about the health needs of the population. The 
Primary Health Care as a care coordinator must also 
be understood as the communication center of the 
Integrated Delivery Systems, which means being 
able to order the flows and against the flows of 
people, the products and the information between 
the different components of the networks. 

The implementation of the Family Health 
Strategy aimed at reorganizing the Primary Health 
Care in Brazil, according to Unified Health System 
guidelines. The Family Health Strategy should focus 
on the intervention of factors that put health at risk, 
in order to promote the quality of life of the 
Brazilian population. Thus, the health care model, 
recommended by the Unified Health System, has an 



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Demand forecast…  BRITO, F. G. et al. 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

emphasis on Family Health Strategy and the 
principles of Primary Health Care. 

However, the Family Health Strategy is a 
paradigmatic historical, procedural and tense change 
in political conflicts in the conformation of the 
health system. Thus, it still perpetuates the 
traditional model of care, with health cut short by 
public health programs, instability of promotion and 
surveillance actions, focus on spontaneous demand, 
in the illness and in the medical professional 
(FRANGO et al., 2018). It should be noted that 
patients classified as green and blue by MTS do not 
fit as urgent cases, therefore, they could be treated 
in health services of less complexity as in the 
Primary Health Care units through the Family 
Health Strategy. 

In this way, it is necessary to organize the 
Integrated Delivery Systems on a permanent basis, 
especially the emergency department. Proper 
planning is necessary for this to occur. The time 
series can be useful in managing this demand by 
analyzing the actual number of services performed 
over time. 

A time series is any set of observations 
ordered in time (MORRETIN; TOLOI, 2006). The 
observation of the behavior of needs in a given 
population and acquisition of knowledge about the 
likely evolution of the series over the next few years 
is an important tool in planning. 

The basic principle underlying ARIMA 
models considers data correlations studied at 
different times. Data analysis using the time series 
technique, in particular the ARIMA model, is 
essential for planning and management decisions, 
based on the predictions. This model is adopted in 
different research fields, such as epidemiology (Lin, 
2015), economics (Rotela Junior, 2014), earth 
sciences (Shirvani, 2015). When applications to 
health care are considered, one should point out 
recent works as follows. Zhirui He and Hongbing 
Tao published a study using the ARIMA method to 
describe the epidemiology of influenza virus in 
children in Wuhan, China, during the nine influenza 
seasons (2007-2015), in order to to predict the 
different types of influenza in the future (He and 
Tao, 2018). 

However, the analysis of care data in the 
emergency department is of fundamental 
importance to monitor; plan and intervene. Thus, 
this study has as main objective is to present a 
suitable model to carry out the predictions regarding 
the services classified as green in the emergency 
department of the municipality of Monte Carmelo, 
since these represent the greatest demand in the 
service. In addition, another approach will 

investigate whether the green patients' demand 
remains the same over the weekend, as compared to 
the weekdays, since there is no support from 
Primary Health Care units over the weekend. This 
study aimed to present a mathematical model to 
carry out the demand forecasts in relation to 
patientes classified as green in the emergency 
department of a municipality in Minas Gerais, 
Brazil. 
 
MATERIAL AND METHODS 
 

A retrospective study of the emergency 
department of the municipality of Monte Carmelo 
was carried out in January/2014 to December/2017. 
All the patients classified as green in the emergency 
unit of the municipality of Monte Carmelo during 
the study period were included. The research was 
carried out after approval by the Research Ethics 
Committee of the Federal University of Uberlândia - 
Minas Gerais, opinion number 1.990.248 and 
2.360.801. 

The data collected during the period 
considered were organized into tables of Excel 
composing a database. This database contains the 
time series and their filters that correspond to the 
priority levels adopted by the MTS. The filter in a 
database is the designation used for any criteria used 
in the data grouping (PELLEGRINI, 2000). 

One of the approaches used in the analysis 
of time series is made in the time domain and the 
proposed mathematical models are parametric 
models. The goal is to build models for the series 
with certain purposes. 

For the application of the models were used 
all the observations of the patients attended per 
month in the urgency and emergency service in the 
period mentioned that received the green 
classification during the reception by the Nurse of 
the unit. 

The software used for data processing was 
Software R Version 3.4 (R DEVELOPMENT 
CORE TEAM, 2018). The free software R is a 
language and environment for statistical computing 
and graphical techniques, in which among the 
statistical varieties includes analysis of time series. 
Through this data processing, a forecast horizon of 
twelve months was made for the time series. 

The forecasting methods are classified 
according to their approaches, which are: 
quantitative; qualitative or the combination of the 
two. For prediction using quantitative methods, it is 
necessary to construct mathematical models based 
on historical data that describe the variation of 



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Demand forecast…  BRITO, F. G. et al. 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

demand over time, the time series models 
(PELLEGRINI, 2000). 

The methodology for time series proposed 
by Box and Jenkins in 1976 is developed based on 
three steps: identification of the model to be used; 
estimation of the identified parameters and 
verification of the model obtained (BOX; 
JENKINS, 2015). It should be emphasized the 
importance of verifying the stationarity and 
seasonality condition of the series before beginning 
the described steps (WANG, 2011). The steps 
described are repeated several times by testing 
several models, until obtaining a satisfactory model. 
After verification of these conditions, the model can 
be used for forecasting (FAVA, 2000). 

For more than half a century Autoregressive 
Integrated Moving Average (ARIMA) models have 
been used in several areas that forecast through time 
series (HO et al., 2002). There are general and 
specific applications performed in the medical field 
(WERNER; RIBEIRO, 2003). 

A methodology widely used in the analysis 
of parametric models is known as the Box and 
Jenkins approach. This methodology consists in 
adjusting the integrated autoregressive models of 
moving averages, ARIMA (p, d, q), to a set of data, 
where AR (p) is the autoregressive process of order 
p; (d) is the number of differences applied; MA (q) 
the process of moving averages of order q 
(MORRETIN; TOLOI, 2006). 

Thus, the general structure ARIMA (p, d, q) 
is expressed by equation 1 (MORRETIN; TOLOI, 
2006). 

 
                              (1)   

      
The identification of the appropriate model 

is done through the functions of autocorrelation and 
partial autocorrelation by observing the lags of the 
graphs. The Autocorrelation Function (ACF) is 
expressed by equation 2 (MORRETIN; TOLOI, 
2006). 

 
                (2) 

 
The Partial Autocorrelation Function 

(PACF) corresponds to the correlation between two 
serial observations, Zt and Zt-k, removing the effect 
of the observations Zt-1, Zt-2, ..., Zt- (k + 1), and it 
is denoted by equation 3 (MORRETIN; TOLOI, 
2006). 

 
(3) 

 

In summary, it is assumed that the strategy 
for the construction of the model will be based on an 
interactive cycle, in which the structure of the model 
is based on the data itself. The stages of the cycle 
are: a general class of models is considered for 
analysis; there is identification of a model, based on 
autocorrelation, partial autocorrelation and other 
criteria; then it comes to the estimation phase, in 
which the parameters of the identified model are 
estimated and finally, there is the verification or 
diagnosis of the adjusted model, through the residue 
analysis, to know if it is suitable for the purposes in 
view (forecast, for example) (MORRETIN; TOLOI, 
2006). 

It should be emphasized that the most 
important phase of the ARIMA model is the 
identification of the p, d, q values of the ARIMA 
model (p, d, q), as well as preliminary estimates of 
the parameters to be used in the estimation stage 
(MORRETIN; TOLOI, 2006) . 

Statistical tests should also be used 
throughout all stages of the cycle so that the choice 
of model parameters is the most appropriate. Among 
these tests we can mention the Signal Test (Cox-
Stuart) to analyze trend; Friedman's test to verify 
seasonality; Dickey-Fuller test for steady behavior; 
Ljung-Box test and Shapiro-Wilk test for residue 
analysis and diagnosis (MORRETIN; TOLOI, 
2006). 

 
RESULTS AND DISCUSSION 

 
The municipality of Monte Carmelo, located 

in the mesoregion of the Triângulo Mineiro and Alto 
Paranaíba, in the State of Minas Gerais. Compared 
to the previous year, a total population of the 
municipality corresponded to 45772 population, 
with a demographic base of 34.08 population / km2 
(IBGE, 2018). 

The emergency department of the 
municipality reached 120230 patients in the period 
from January 2014 to December 2017, with an 
average of 2470 patients per month. As shown in 
Graph 1, all patients who arrive at the service are 
hosted by the Nurse Practitioner and are classified 
by MTS. It should be noted that 3394 patients, in 
this period, were classified as whites, because they 
sought unity without any clinical complaint. 

The statistical analysis in Table 1 shows that 
patients classified as green correspond to the higher 
demand for care in the service (60.93%), an average 
of 1526.10 visits per month. 

This finding is similar to the study carried 
out on the clinical demand in the Emergency 
department in central western of Minas Gerais, 



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Demand forecast…  BRITO, F. G. et al. 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

health care center, which found that 61% of the 
patients seen were classified as green. The main 
complaints related to these patients were 

"Indisposition in the adult" (40.1%), "limb problem" 
(14.4%), "headache" (10.8%) and "abdominal pain" 
(5.9%) (DINIZ et al., 2014). 

 
 
Graph 1: Time series of the number of patients classified by the Manchester Triage Scale per month. 
 
Table 1. Statistical analysis for patients classified by the Manchester Triage Scale, 2014 to 2017 
 N 

 

Md Q1 Q3 s CV 
Red 480 10 7 3.75 12 11.71 117.07% 
Orange 9339 194.56 194.5 126.25 248 79.43 40.82% 
Yellow 29803 620.89 640 396 790.5 281.65 45.36% 
Green 73253 1526.10 1669.5 1087.25 1883.25 616.66 40.41% 
Blue 3961 82.52 68.5 39.75 92.75 69.83 84.62% 

 
In the present study we analyzed the time 

series of patients classified as green attended per 
month in the mentioned period due to the high 
demand of this type of patients. By studying this 
series will be possible to obtain a suitable model to 
carry out the forecasts in the next 12 months. 

The first step in the analysis of a time series 
is the construction of its graph, which will reveal 
important characteristics such as trend, seasonality, 
variability, outliers, etc. The original time series of 
the number of patients attended per month have 48 
observations for each priority level, from the period 
between 2014 and 2017, graph 1. It is not possible 
to perceive the presence of trend and seasonality in 
the series in the groups of green patients (not very 
urgent) that will be analyzed in the study. 

In addition to the graphical inspection, it is 
possible to use statistical hypothesis tests to verify if 
there are trends and seasonality in the series. Since 
most procedures of statistical analysis of time series 
assume that they are stationary, it is necessary to 
transform the original data if they do not form a 
stationary series. The most common transformation 
is to make successive differences from the original 
series until a stationary series is obtained. In normal 
situations, it will suffice to take one or two 
differences so that the series becomes stationary 
(MORRETIN; TOLOI, 2006). 

Thus, to verify if the data present a biased 
behavior, the Signal Test (Cox-Stuart) was carried 
up and to verify the seasonality the Friedman Test 
was carried up too. At the 5% level of significance, 
there is statistical evidence that can guarantee that 
the series have no trend (p-value = 0.8388), or 
seasonality (p-value = 0.06041). 

 An analysis of the variation in the number 
of visits was also carried up and it was found that it 
has high variability (coefficient of variation = 
380270.3). Thus, the first difference in the data was 
applied and the Dickey-Fuller Test was carried up to 
certify that this transformation was enough to make 
the series stationary. Thus, at the 5% level of 
significance, there is statistical evidence that can 
guarantee that the series has stationary behavior (p-
value = 0.01). 

The next step of this analysis is to identify 
the filters that will compose the model, that is, the 
presence and number of self-correcting components 
and moving averages, respectively. For this, the 
technique commonly used is the analysis of the ACF 
and PACF. The decision is made based on the 
standards identified for each of the functions, ACF 
and PACF (JACOBS et al., 2003). 

Thus, we performed an analysis of the 
correlograms of the Autocorrelation ACF and PACF 
of the original series to investigate the significant 



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Demand forecast…  BRITO, F. G. et al. 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

lags. Among the several models tested, the ARIMA 
model (1,1,1) presents a better prediction. 

To obtain a model that fit the data was used 
the model ARIMA. The ARIMA models were 
described by Box and Jenkins in 1976 and are 
characterized as one of the most widespread 
methodologies for time series analysis 
(MADDALA, 2003; MORRETIN; TOLOI, 2006; 
BOX; JENKINS, 2015). 

The analysis of the prediction errors allows 
to choose, among the applied models, the one that is 
most adequate to make predictions for the series 
under study (AFONSO et al., 2011). Thus, to fit the 
most adequate model to perform predictions of the 
number of green patients attended per month, tests 
were done with the two different models, comparing 
them based on the Mean Absolute Error (MAPE) 
(NOVAES et al., 2010; ROSALES-LÓPEZ et al., 
2018). For the green patients, the ARIMA model 
(1,1,1) obtained a prediction error of 13.98%, since 
it was the lowest value, it uses it to make the 
predictions of the 12 months. 

For the selected ARIMA model, it was 
investigated whether or not it adequately represents 

the data (MORRETIN; TOLOI, 2006). In this case, 
the model residues can not be autocorrelated. If this 
condition is not verified, it is necessary to search for 
another model (MORRETIN; TOLOI, 2006; FAVA, 
2000). For the residue independence test, the Ljung-
Box test was statistically confirmed to be 
independent (p-value = 0.9262). To analyze the 
normality of the residues the Shapiro-Wilk Test was 
carried up, proving that the residues have a normal 
distribution (p-value = 0.5713). When analyzing the 
homogeneity of the variances, it was verified that 
the residues have random behavior, variance is 
constant. 

 According to the validated model, ARIMA 
(1,1,1), the numbers of care provided in the next 12 
months for the green patients are represented by the 
blue line in the graph (Figure 1). In January 2018, 
the number of patients expected is 1780.4, in 
February 2018, the number of patients expected is 
1789, and so on. According to the forecast presented 
for the year 2018 in figure 1, the number of patients 
varies between 1780.4 and 1796.6 patients per 
month. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
Figure 1. Time series with predicted number of patients for the next 12 months 
  

The ARIMA model was used to predict 
monthly visits to an emergency department in the 
southern region of Taiwan, using the time series 
from 2009 to 2016. In this study the ARIMA model 
(0,0,1) was considered appropriate to provide for 
future emergency consultations at that hospital. The 
authors point out that the results can be used to 
assist in decision-making processes and the findings 
provide new insights into the reasons for 
overcrowding in the emergency department 
(JUANG et al., 2017). 

Another study conducted at Illinois Medical 
Hospital, Chicago, which has 897 tertiary care beds, 
evaluated the predictability of patient volume using 
a variety of known prediction techniques 
(exponential smoothing methods, ARIMA, seasonal 
ARIMA, and conditional autoregressive 
generalization). Among these techniques ARIMA 
presented the lowest MAPE, that is, the best 
performance in predicting the volume of patients in 
the hospital. Thus, the technique can accurately 
predict the volume of patients in the near future 
(KIN et al., 2014). 

 Prediction 
Jan/18 1780.4 
Feb/18 1789 

Mar/18 1793.1 
Apr/18 1795 
May/18 1795.9 
Jun/18 1796.4 
Jul/18 1796.6 

Aug/18 1796.6 
Sep/18 1796.7 
Oct/18 1796.7 
Nov/18 1796.7 
Dec/18 1796.7 



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Demand forecast…  BRITO, F. G. et al. 

Biosci. J., Uberlândia, v. 35, n. 5, p. 1640-1650 , Sep./Oct. 2019 
http://dx.doi.org/10.14393/BJ-v35n5a2019-46115 

In Canada, it was also analyzed the time 
series of patients who were admitted to the 
emergency room in the Province of Ontario with 
Chronic Obstructive Pulmonary Disease. The 
ARIMA method was used to predict future rates of 
hospital and emergency room visits. The authors 
emphasize the relevance of the information 
generated in order to alert doctors, hospitals and 
decision makers about the increasing need for 
resources and policies to meet the future needs of 
the population (GERSHON et al., 2017). 

The importance of generating quality 
information for the planning, monitoring and 
evaluation of health services provided to the 
population in scope of the Unified Health System 
should be emphasized in order to have a more 
effective and efficient model, appropriate to the 
characteristics of the population of each region of 
Brazil (TOMASI et al., 2011). Thus, the time series 
can be useful in the management of demand in the 
urgency and emergency services by analyzing the 
actual number of services carried out. In this way it 
allows the observation of the behavior of the needs 
in a certain population and acquisition of knowledge 

about the probable evolution of the series over the 
next years. 

The demand forecast from the time series 
analysis is a tool that should be used to improve the 
analysis of processes and decision making in health 
services, thus contributing to the more efficient use 
of the public budget related to health. Studies 
indicate that public health expenditures in Brazil in 
relation to PIB consume about 2.8% of all wealth 
generated in the country. The correct and efficient 
administration of these resources by public entities 
becomes a preponderant factor for improving the 
health of society and managing disbursements 
(SIMÕES; SILVA, 2017). 

In another approach, the reflex of the 
Primary Health Care units closed at weekends was 
evaluated to verify a possible overhead in the 
emergency department. Thus, patients classified as 
green were divided into two groups, those who were 
seen during the week and those who were seen at 
the weekend. Following, the daily average of care 
for these two groups was obtained. The Graph 2 
shows the evolution of the daily average care of the 
two groups in the period studied. 

 

 
 

Graph 2. Time series for the daily average of patients during the week and the weekend 
 
In this graph 2, similar behavior is observed 

for the two groups, with the average number of 
visits at the weekend being slightly lower than the 
average number of visits during the week. This 
statement was confirmed by the unilateral Z test (p-
value = 0.0251). Thus, it can be seen that even APS 
units providing support for urgency and emergency 
services during the weekdays, there is still a 
significant demand for green patients at weekends, 
which is slightly lower than during the week. 

The population believes that the urgency 
and emergency service provides fast, safe and 
effective care, for being able to attend the most 
serious cases. This, together with dissatisfaction 
with the Primary Health Care services, leads to 

overcrowding of urgency and emergency services 
(CHEN et al., 2015). 

An analysis of Primary Health Care 
practiced in Unified Health System shows a 
privilege of uniprofessional attention, strongly 
focused on the doctor, and carried out through 15 
minute consultations (MENDES, 2011). There is 
even a very widespread programming parameter of 
four medical consultations per hour (SESMG, 
2007). 

In national or international experiences, it is 
a common reality that the urgency and emergency 
service is the main doorway of the user to the health 
system (FRANGO et al., 2018). A study carried out 
in southern Brazil showed that 58.2% of the patients 
reported have been looking for the first aid because 



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they believed that this service would be better able 
to serve them than the Primary Health Care units 
(CARRET et al., 2007). 

The time series used in this study was 
limited four years ago because during the survey 
there was no further information available. 
Although there is no allowance in the literature for a 
minimum number of data, further studies should be 
performed with a larger set of observations ordered 
over time. 
 
CONCLUSIONS 

 
Using the time series for the number of 

patients classified by the Manchester Screening 
Protocol as green, the results of the present study 
suggest that the ARIMA model (1,1,1) presents a 
better fit for this prediction. The predictions of this 
model are values close to those observed, for the 
number of patients attended that ranges between 
1780.4 and 1796.6 patients per month. 

It emphasizes the importance of the use of 
mathematical models of forecasting in Integrated 
Delivery Systems. The application of these models 
should be seen by the managers as a tool to aid 

decisions, so it should subsidize processes of 
management, planning and evaluation of public 
policies. 

On the other hand, the demand of patients 
classified as green at the weekend is slightly lower 
than that of the weekend, but it is still an expressive 
demand. This demand for patients who do not fit as 
an urgent case during the weekdays shows that PHC 
does not always act as a gateway to the health care 
system in cases of less complexity. However, 
Primary Health Care should be the fundamental 
level of Unified Health System, being the first 
contact of the population with this system. 

Thus, it is necessary to rethink the practice 
of Integrated Delivery Systems in the scope of the 
Unified Health System. The emergency department 
should work in a coordinated manner with the 
Primary Health Care and all other health care points 
of the Integrated Delivery Systems so that the 
patient has the necessary care, according to his need, 
at the point of appropriate attention of care. The 
mathematical models for demand forecasting can 
improve care management tools and services, thus 
making an extraordinary contribution to the 
scientific and technological development. 

 
 

RESUMO: Este estudo apresenta um modelo matemático para realizar as previsões de demanda em 
relação aos pacientes classificados como verdes no departamento de emergência de um município de Minas 
Gerais. Além disso, outra abordagem investigará se a demanda dos pacientes verdes permanece a mesma no 
final de semana, em relação aos dias da semana, uma vez que não há apoio das unidades de Atenção Primária 
de Saúde no final de semana. Um estudo retrospectivo do serviço de emergência no município de Monte 
Carmelo foi realizado no período de janeiro de 2014 a dezembro de 2017. A série temporal dos pacientes 
classificados como verdes durante o acolhimento pelo enfermeiro, segundo o Sistema de Triagem de 
Manchester, foi analisada no domínio temporal para a construção de um modelo paramétrico com a finalidade 
de realizar a previsão de demanda. O Sistema de Triagem de Manchester foi adotado na maioria dos serviços de 
emergência como instrumento orientador para a classificação de risco, priorizando os casos mais graves. O 
processamento de dados foi realizado usando o Software R Versão 3.4. O modelo ARIMA (1,1,1) apresentou 
melhor ajuste para essa previsão. As previsões deste modelo são valores próximos aos observados para o 
número de pacientes atendidos que variam de 1780.4 a 1796.6 pacientes por mês. Em relação à demanda de 
pacientes classificados como verdes no final de semana, constatou que é ligeiramente inferior a do fim de 
semana, mas ainda é uma demanda expressiva. A aplicação dos modelos deve ser vista pelos gestores como 
uma ferramenta para auxiliar as decisões, portanto, deve apoiar processos de planejamento, gestão e avaliação 
de políticas públicas. Nesse contexto, os modelos matemáticos para previsão de demanda são um instrumento 
de atendimento e serviços gerenciais. 
 

PALAVRAS CHAVE: Triagem. Necessidades e demandas de serviços de saúde. Saúde pública. 
 
 
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