Modeling of Dengue cases in pediatric age using the objective regression regressive methodology in Villa Clara, Cuba

Abstract

Dengue continues to be the main arbovirosis, with endemic characteristics, in at least 100 countries, affecting an average of 50 million patients per year, and with a high incidence in pediatric ages. To mathematically model the cases of Dengue in pediatric age through the methodology of the Objective Regression Regressive, during the period 2016-2021 in the province of Villa Clara, Cuba. A descriptive, retrospective, analytical-statistical (Objective Regression Regressive methodology) and prospective longitudinal study was carried out. The study area corresponded to Villa Clara province, which is located in the center of Cuba, where the population under study was the 13 municipalities that make up the province. The total number of cases of Dengue fever during the six years covered by the study was 2 013. A database was created for confirmed cases of Dengue in Villa Clara during the years 2016 to 2021, specifically for children under 18 years of age, where the data were entered in files and processed using the SPSS version 22 statistical package, which made it possible to carry out a mathematical modeling of Dengue cases, in the short and long term. The plotting of confirmed cases of Dengue fever showed that the highest incidence of cases was in the months from July to November, with an average of 28 cases studied. The short-term model depends on the cases returned in 1, 2, 7 and 14 months, which indicates a strong dependence on the previous month, so that all monitoring, surveillance, management, control and sanitation actions carried out in advance will have a positive impact on the following month, while the long-term model depended on the cases returned in 12 months, and the trend turned out to be positive and significant. It was possible to model the cases of Dengue, where the trend was to a non-significant decrease in the short term, while in the long term, this trend was to a significant increase, and for which, the cases depended on 1, 2, 7 and 14 months ago, so the best model was the long term, being able to predict the behavior of this infectious entity one year in advance, as well as the extension to longer dates in years.

Full text

* Corresponding author: Rigoberto Fimia Duarte https://orcid.org/0000-0001-5237-0810
Copyright © 2023 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0.
Modeling of Dengue cases in pediatric age using the objective regression regressive
methodology in Villa Clara, Cuba
Fimia Duarte R 1, *, Osés Rodríguez R 2, González Ronda Y 3, del Valle Laveaga D 4, Diéguez Fernández L 5,
Wilford González FM 6, Robert Vogt P 7 and González Rodríguez IC 3
1 Hygiene and Epidemiology Department, Faculty of Health Technology and Nursing (FHTN), University of Medical Sciences
of Villa Clara (UMS-VC), Cuba.
2 Prognostic Department, Provincial Meteorological Center of Villa Clara, Cuba.
3 Infectious Diseases Department, Villa Clara Provincial Center of Hygiene, Epidemiology and Microbiology (PCHEM-VC),
Cuba.
4 Parasitology Department, Regional High Specialty Hospital (HARE), Dr. Juan Graham Casasús, México.
5 Hygiene and Epidemiology Department, Faculty Technological, University of Medical Sciences of Camaguey, Cuba.
6 Biology Department, Center for Bioactive Chemicals (CBQ), Central University "Marta Abreu" of Las Villas. Villa Clara,
Cuba.
7 EurAsia Heart Foundation, Switzerland.
International Journal of Biological and Pharmaceutical Sciences Archive, 2023, 05(02), 089–098
Publication history: Received on 21 April 2023; revised on 01 June 2023; accepted on 04 June 2023
Article DOI: https://doi.org/10.53771/ijbpsa.2023.5.2.0048
Abstract
Dengue continues to be the main arbovirosis, with endemic characteristics, in at least 100 countries, affecting an average
of 50 million patients per year, and with a high incidence in pediatric ages. To mathematically model the cases of Dengue
in pediatric age through the methodology of the Objective Regression Regressive, during the period 2016-2021 in the
province of Villa Clara, Cuba. A descriptive, retrospective, analytical-statistical (Objective Regression Regressive
methodology) and prospective longitudinal study was carried out. The study area corresponded to Villa Clara province,
which is located in the center of Cuba, where the population under study was the 13 municipalities that make up the
province. The total number of cases of Dengue fever during the six years covered by the study was 2 013. A database
was created for confirmed cases of Dengue in Villa Clara during the years 2016 to 2021, specifically for children under
18 years of age, where the data were entered in files and processed using the SPSS version 22 statistical package, which
made it possible to carry out a mathematical modeling of Dengue cases, in the short and long term. The plotting of
confirmed cases of Dengue fever showed that the highest incidence of cases was in the months from July to November,
with an average of 28 cases studied. The short-term model depends on the cases returned in 1, 2, 7 and 14 months,
which indicates a strong dependence on the previous month, so that all monitoring, surveillance, management, control
and sanitation actions carried out in advance will have a positive impact on the following month, while the long-term
model depended on the cases returned in 12 months, and the trend turned out to be positive and significant. It was
possible to model the cases of Dengue, where the trend was to a non-significant decrease in the short term, while in the
long term, this trend was to a significant increase, and for which, the cases depended on 1, 2, 7 and 14 months ago, so
the best model was the long term, being able to predict the behavior of this infectious entity one year in advance, as well
as the extension to longer dates in years.
Keywords: Dengue; Pediatric age; ROR methodology; mathematical modeling; Villa Clara

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1. Introduction
At present, arbovirosis of veterinary-medical relevance continues to be a serious problem for several health programs,
since the vector species involved have a marked worldwide dispersion as a consequence of anthropic activity [1,2].
Among the determinant factors that favor the current dispersion of some species of the genus Aedes, we can mention
the wide range of containers used for breeding as a result of inadequate environmental sanitation, the intensive and
extensive use of chemicals that indirectly affects several culicid species, the increase in tourist travel by sea, land and
air [3-5], as well as changing climatic conditions, where increases in temperatures and alterations in the rainfall regime
have allowed the introduction, establishment and reproduction in places where, a priori, they were not expected [5,6].
One of the arbovirosis with great impact on health systems is Dengue, a febrile disease caused by a Flavivirus of which
four serotypes have been described (DEN-1, DEN-2, DEN-3 and DEN-4), which is transmitted to humans through the
bite of mosquitoes belonging to the genus Aedes [7]. This disease has become a growing public health problem, with
emphasis on the Caribbean and Latin America, with the pediatric age group accounting for the largest number of cases
[8-12], and was designated by the World Health Organization as one of the ten most important health threats in the
world [13].
Dengue is present with endemic characteristics in at least 100 countries, affecting 50 million sick people per year on
average [14]. In this regard, it has been described that in the Caribbean region the countries with the highest number of
cases in the last decade are Cuba, Puerto Rico, and the Dominican Republic [15,16]. This epidemiological situation has
stimulated the execution of research in several countries and regions, in order to know the behavior of Dengue episodes
in symptomatic periods, as well as to be able to make comparisons between countries and regions according to age
groups, assessing, for example, the affectations in pediatric age [17-20]. Among these studies, we can point out those
conducted in Asia [21,22] and Latin America, in which it was observed that the burden of the disease in the age range
between 9 and 12 years is higher in Asia compared to Latin America [23].
The objective of the research consisted of mathematically modeling by means of the ROR methodology, the cases of
Dengue in pediatric age during the period 2016-2021 in the province of Villa Clara, Cuba.
2. Material and methods
2.1. Study area
The research was carried out in Villa Clara province (Latitude: 22º 29'40'' N, Longitude: 79º28'30'' W), Cuba, whose
provincial capital is the Santa Clara municipality and covered the 13 municipalities that comprise it. It has geographical
limits to the north with the Atlantic Ocean, to the east with the provinces of Sancti Spiritus and Ciego de Avila, to the
south with Sancti Spiritus and to the west with the provinces of Matanzas and Cienfuegos. With a territorial extension
of 8,412 km², including 719 keys, it is the fifth largest of the 16 provinces of the national territory; its extension
represents 7.8% of the total area of the country.
2.2. Population
The 13 municipalities that make up Villa Clara province.
2.3. Total cases diagnosed by year
2016 (111), 2017 (92), 2018 (1 125), 2019 (372), 2020 (18) and 2021 (295), for a total of 2 013 cases during the six
years covered by the study.
2.4. Methods and techniques for gathering information
The documentary review of the records and statistical files existing in the Provincial Pediatric Hospital "José Luis
Miranda", located in the head municipality, as well as the files of the Provincial Department of Health Statistics of Villa
Clara, where all the health history of the 13 municipalities of the province is compiled, which is periodically reported in
statistical tables established for such purposes by the Department of National Health Statistics of the Ministry of Public
Health (MINSAP) of Cuba. All this made it possible to make a database for confirmed cases of Dengue in Villa Clara during
the years 2016 to 2021, specifically for children under 18 years of age, where the data were entered in files and
processed using the SPSS version 22 statistical package, which made it possible to carry out a mathematical modeling,
in the short and long term for these cases.

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2.5. The methodology of Objective Regressive Regression (ORR)
The prognosis was performed with the use of the Regression Objective Regression (ROR) methodology that has been
implemented in different variables such as viruses and bacteria circulating in Villa Clara province [24-27].
The modeling (ROR), is based on a combination of Dummy variables with ARIMA modeling, where only two Dummy
variables are created and the trend of the series is obtained, it requires few cases to be used and allows using also,
exogenous variables that make it possible to model and forecast in the long term, depending on the exogenous variable,
it has given better results than ARIMA in some variables, such as HIV modeling, entities of viral etiology/arbovirosis
and parasitic entities [28-34].
In the ROR methodology, dichotomous variables DS, DI and NoC are created in a first step, where:
NoC: Number of cases in the base,
DS = 1, if NoC is odd; DI = 0, if NoC is even, when DI=1, DS=0 and vice versa.
Subsequently, the module corresponding to the Regression analysis of the statistical package SPSS version 19.0 (IBM
Company) is executed, specifically the ENTER method where the predicted variable and the ERROR are obtained.
Then the autocorrelograms of the ERROR variable are obtained, paying attention to the maximums of the significant
partial autocorrelations PACF. The new variables are then calculated according to the significant Lag of the PACF.
Finally, these regressed variables are included in the new regression in a process of successive approximations until a
white noise in the regression errors is obtained.
2.6. Ethical aspects
The research was subject to ethical standards, where all the information collected and provided was used only for the
stated purpose. It did not involve physical or psychological affectations, in order to generate new knowledge without
violating the ethical principles established for these cases. On the other hand, all authors involved in the research,
publication and dissemination of the results are responsible for the reliability and accuracy of the results shown [35].
3. Results
Figures 1 and 2 show the plotting of confirmed cases, where the highest incidence of cases was in the months of July to
November, and the mean number of cases studied was close to 28 cases.
Figure 1 Plotting of Dengue cases, 2016-2021 by month for Villa Clara province

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Figure 2 Behavior of the average number of cases of Dengue fever by month
The highest value occurred in the month of October 2018 with 260 cases, and a large standard deviation (57.573 cases),
while in the short-term model 98.7 % of the variability was explained with an error of only 13.4 cases (Table 1). Fisher's
F was significant at 100 %, with a value of 97.361, and a sum of square of 286765.000d, result of the ANOVA test (a.
Dependent variable: number of confirmed with Dengue; b. Linear regression through the origin; c. Predictors: Step44,
Step62, Step33, Step36, Step61, Step47, Step45, Step34, Step31, LAG7Cases, LAG14Cases, DS, DI, LAG1Cases,
LAG2Cases, NoC and d. This total sum of squares is not corrected for the constant because the constant is zero for
regression through the origin).
Table 1 Summary of the short-term model for the number of Dengue cases
Descriptive statistics
N
Minimum
Maximum
Media
Standard
desviation
Number of
cases
72
0
260
27.96
57.573
N valid (per list)
72
Summary of the model
Model
R
R squared
R Adjusted
squared
Standard error of the
estimate
Durbin-Watson
1
0.987a
0.974
0.964
13.389
2.499
a. Predictors: Step44, Step62, Step33, Step36, Step61, Step47, Step45, Step34, Step31, LAG7Cases, LAG14Cases, DS, DI, LAG1Cases, LAG2Cases, NoC;
b. For regression through the origin (the model without intercept), R-squared measures the proportion of the variability in the dependent variable
over the origin explained by the regression. This CANNOT be compared to R-squared for models that include intercept; c. Dependent variable:
Number of confirmed with Dengue; d. Linear regression through the origin
The model in question, in the short term, depends on the cases returned in 1, 2, 7 and 14 months, which indicates a
strong dependence on the previous month, so that all monitoring, surveillance, management, control and sanitation
actions carried out in advance will have a positive impact on the following month, and in a very decisive and impacting
way; It also depends on 2, 7 and 14 months ago, which corresponds to the cycle of approximately six months that divides
the rainy and rainy periods that characterize the climate of Cuba, as well as the annual cycle. The Step variables are
cases that have an important impact on the series by greatly increasing the cases, some variables were not significant,

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but they contributed variance to the model, and for this reason they are left in the model. The trend (NoC) is small and
negative, but not significant (Table 2).
Table 2 Short-term model results based on coefficients
Coefficientsa,b
Model
Unstandardized coefficients
Standardized
coefficients
t
Sig.
B
Standard error
Beta
1
DS
5.968
5.610
0.060
1.064
0.294
DI
2.328
5.730
0.023
.406
0.687
NoC
-0.039
0.110
-0.026
-.358
0.722
LAG1Cases
0.890
0.041
0.890
21.772
0.000
LAG14Cases
0.061
0.034
0.060
1.805
0.078
LAG7Cases
-0.018
0.030
-0.018
-.620
0.538
LAG2Cases
-0.153
0.052
-0.153
-2.943
0.005
Step31
180.452
13.845
0.337
13.034
0.000
Step34
214.018
16.352
0.400
13.088
0.000
Step45
80.129
15.578
0.150
5.144
0.000
Step47
-120.264
15.068
-0.225
-7.982
0.000
Step61
96.439
13.945
0.180
6.916
0.000
Step36
-93.112
18.294
-0.174
-5.090
0.000
Step33
-65.163
17.037
-0.122
-3.825
0.000
Step62
-58.915
14.375
-0.110
-.098
0.000
Step44
50.664
13.732
0.095
3.689
0.001
a. Dependent variable: Number of confirmed with Dengue; b. Linear regression through the origin
A long-term forecast was performed, which explains 99.5% of the variance with an error of 9.9 cases; this is a tool to
have an idea of how Dengue cases will behave one year in advance, and thus be able to take prophylactic measures that
will lead to fewer cases. Fisher's F was 143, higher than in the short-term model, but still significant at 100%. This long-
term model depends on the cases regressed over 12 months (Table 3); here the trend was positive and significant.
Table 3 Long-term model results based on coefficients
Coefficientsa,b
Model
Unstandardized coefficients
Standardized
coefficients
t
Sig.
B
Standard error
Beta
1
DS
-8.082
7.578
-0.073
-1.066
0.296
DI
-13.798
7.895
-0.124
-1.748
0.092
NoC
0.0447
0.144
0.291
3.113
0.004
LAG13Casos
-0.069
0.051
-0.067
-1.334
0.194
LAG26Casos
-0.079
0.028
-0.078
-2.843
0.009

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LAG19Casos
-0.055
0.024
-0.054
-2.258
0.033
LAG14Casos
.043
.040
0.042
1.075
0.292
Step31
220.991
10.661
0.414
20.730
0.000
Step34
259.227
10.657
0.485
24.324
0.000
Step45
139.394
12.079
0.261
11.540
0.000
Step47
3.303
14.775
0.006
.224
0.825
Step61
98.467
11.420
0.184
8.622
0.000
Step36
65.075
10.628
0.122
6.123
0.000
Step33
77.673
10.577
0.145
7.344
0.000
Step62
22.620
10.420
0.042
2.171
0.039
Step44
62.189
14.408
0.116
4.316
0.000
Step35
215.856
10.529
0.404
20.501
0.000
Step32
199.596
10.756
0.374
18.557
0.000
Step46
142.538
11.446
0.267
12.453
0.000
Step30
47.750
10.844
0.089
4.,403
0.000
a. Dependent variable: Number of confirmed with Dengue; b. Linear regression through the origin.
Figures 3 and 4 show the good behavior of the actual value and its forecast, as well as the errors made, which are small.
Figure 3 Actual and predicted value in the short term

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Figure 4 Actual and predicted long-term value
4. Discussion
It was possible to corroborate the existing correlation between the cases of Dengue fever with the months of greater
larval focality and even, with the months where the population peaks occur for this mosquito species (July-November),
which is not exclusive of Villa Clara province, results that coincide with studies carried out in previous years [2,21,36],
being the month of October 2018 where the greatest number of cases (260) was presented, aspect concordant with the
rainy period for Cuba, where climatological variables have a favorable incidence on the population densities of culicidae,
both in the larval and adult phase, hence these are the months of greatest entomoepidemiological risk for these arboviral
infectious entities, which coincides with results obtained in Cuba as in other countries of the region [2,8,39-43].
The short-term model, depended on the cases returned in 1, 2, 7 and 14 months, with a strong dependence on the
previous month, also depended on 2, 7 and 14 months ago, which corresponds to the cycle of approximately six months
that, divides the rainy and little rainy periods that characterize the climate of Cuba, as well as the annual cycle 2,21,36-38.
Therefore, all monitoring, surveillance, management, control and sanitation actions carried out in advance will have a
positive, decisive and impacting repercussion on the following month [25,26,33].
The long-term prognosis explained 99.5% of the variance with an error of 9.9 cases; this model depends on the cases
regressed in 12 months, and here the trend was positive and significant, so it is an excellent tool to take into account for
the evolution of Dengue cases one year in advance, and thus be able to take prophylactic measures that lead to fewer
cases [2,26,34,36-38].
5. Conclusion
It was possible to model the cases of Dengue, observing a trend in the short term to a non-significant decrease, while in
the long term, this trend is to a significant increase, where the cases depend on 1, 2, 7 and 14 months ago, so the best
model was the long term one. The behavior of this infectious entity can be predicted one year in advance. This is a study
that could be extended to a longer date in years to see the impact of the solar cycle, which is approximately 11 years.
Compliance with ethical standards
Acknowledgments
To all the members of the Statistics Department of the Provincial Pediatric Hospital of Villa Clara province, who kindly
gave us all the data for the research.

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Disclosure of conflict of interest
The authors express that there is no conflict of interest.
Statement of ethical approval
The present research paper does not contain any studies conducted on animals/humans by any of the authors. We
worked with a database provided by the colleagues in charge of recording and controlling the database of the Pediatric
Provincial Hospital of Villa Clara.
Statement of informed consent
The Declaration of Informed Consent did not apply to this study, since we worked with numerical data obtained from a
digital database.
Author’s declaration
The authors hereby declare that the work presented in this article is original and that they will bear any liability for
claims relating to the content of this article.
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http://www.urp.edu.pe/facultad-de-biologia/index.php?urp=revistas-investigacion

International Journal of Biological and Pharmaceutical Sciences Archive, 2023, 05(02), 089–098
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Authors short biography
Lic. Rigoberto Fimia Duarte, MSc., Ph.D. Born in 1966 in the current province of Sancti Spíritus,
Cuba. Graduated in 1989 in Biology Science. Professor and Researcher at the Central University
"Marta Abreu" of Las Villas. Currently works at the University of Medical Sciences of Villa Clara
(UCM-VC), Cuba. President of the Territorial Tribunal for the main teaching categories (Assistant
Professor and Full Professor) of the University of Medical Sciences of Villa Clara. Member of the
Society of Microbiology and Parasitology of Cuba and Cuban Society of Zoology. He has to his credit,
506 scientific results/publications, of which, he is the author of 360 scientific articles in specialized
journals of recognized prestige and impact, both in Cuba and abroad, many of them indexed in
group 1 and Web of Science (WoS) databases, as well as 27 books. He has taught at the Central
University "Marta Abreu" of Las Villas, Institute of Tropical Medicine "Pedro Kourí" (IPK),
University of Medical Sciences of Villa Clara and the Universities of Medical Sciences of the
provinces of Cienfuegos, Sancti Spíritus and Ciego de Avila. ORCID Code: https://orcid.org/0000-
0001-5237-0810; ID Scopus: 23472337200.