Mathematical Modeling and Climate: Incidence, Repercussion and Impact on Communicable Entities and Vector Organisms


Rigoberto Fimia Duarte*1, Phd, Ricardo Osés Rodríguez2, Msc, David del Valle Laveaga3, Msc and Donald A. Yee4, Phd


1*Faculty of Health Technology and Nursing (FTSE), University of Medical Sciences of Villa Clara (UCM-VC), Cuba

2Provincial Meteorological Center of Villa Clara, Cuba

3Academic Area of Health, Maya World University, México

4School of Biological, Environmental & Earth Sciences, University of Southern Mississippi, EUA


*Corresponding Author

Rigoberto Fimia Duarte

Article History: | Received: 28.06.2022 | Accepted: 24.07.2022 | Published: 25.08.2022|


Abstract: Humanity has suffered throughout history the scourge of potentially fatal diseases, and where climate has a marked and decisive influence. The objective of the study consisted in demonstrating the existing relationship between the transmissible infectious entities Dengue and Malaria with climate by means of mathematical modeling in Villa Clara province, Cuba. The research covered two fundamental aspects: the influence exerted by some meteorological variables on the larval populations of culicidae, and on the Dengue entity. The mathematical model used was the Objective Regressive Regression (ORR) model, where the response variables were defined, as well as the explanatory variables. The general and specific larval densities showed a cyclical and seasonal behavior. Temperature, relative humidity, mean wind speed and atmospheric pressure proved to be excellent predictors of the population dynamics of entomoepidemiological important culicidae. A significant correlation of the infectious entity Dengue with minimum temperature (R=0.332; p=0.023) and water vapor tension (R=0.298; p=0.042) was obtained, as well as an inverse relationship with atmospheric pressure (R=-0.317; p=0.030). It is concluded that there is a close relationship between the infectious entities analyzed and the species of vector organisms with climate, which was corroborated by the mathematical modeling ROR, so it is possible to model and predict, in the short, medium and long term, both the population dynamics of culicidae with entomoepidemiological importance and the incidence of cases of Dengue.


Keywords: climate, Dengue, entomoepidemiological, Objective Regressive Regression (ORR) methodology, mathematical modeling, Villa Clara.

Copyright @ 2022: This is an open-access article distributed under the terms of the Creative Commons Attribution license which permits unrestricted use, distribution, and reproduction in any medium for non commercial use (NonCommercial, or CC-BY-NC) provided the original author and source are credited.


Introduction:

Humanity has suffered throughout history from the scourge of potentially fatal viral and parasitic diseases, including: Yellow Fever, Dengue, Zika, Chikungunya, Malaria, Chagas, Leishmaniosis, Onchocercosis, Angiostrongylosis, Fasciolosis, among many others, and most of them often involve a vector organism as a common factor (Guzmán & Kourí 2002, WHO, 2019). These diseases are widespread in the tropics, with local variations in risk, so they are highly dependent on rainfall, temperature and rapid unplanned urbanization, among others (Troyo et al., 2008; Gould et al., 2017; Benavides et al., 2021).


To these problems, we can now add global warming and the intensification of extreme meteorological disturbances, which has brought about changes in the behavior of diseases and their transmissions, with the establishment of vector species in places never recorded before (Gore, 2007; Fajardo et al., 2016; Real, 2017). Climate change is considered one of the main environmental problems, and its effects undoubtedly have a negative impact on human health (Gore, 2007; Ehelepola et al., 2015; Sharmin et al., 2015; Márquez et al., 2019). There are several studies that relate climatic variables with the increase of infectious diseases, where arbovirosis has been one of the most studied, and it has been shown that there is a positive relationship between climate variation and the incidence of these infectious entities (García et al., 2012; Osés et al., 2017a; Sánchez et al., 2017; Osés et al., 2018a; Fimia et al., 2020a).


The relationship between the incidence of Dengue and climatological variables is mainly given in the characteristics of the vector, its life cycle and the conditions that favor the proliferation of the vector (Brenda et al., 2000; Marquetti, 2006; Fimia et al., 2015, Wilke et al., 2016). Among the most influential climatic variables, elevated temperature, humidity and precipitation volume are reported (Osés et al., 2016, Osés et al., 2018b, Machado, 2019; Fimia et al., 2020b).


All vector-borne diseases in the world have very high incidence rates; for example, it is estimated that between 50-100 million cases of Dengue fever occur each year (Ortega, 2001; Guzmán et al., 2013; Gould et al., 2017). This viral entity has been considered for many years as a public health problem in the world, especially in tropical countries where the influences of environmental variables favor the increase of cases each year (Service, 1992; Guzmán et al., 2013; Gould et al., 2017).


However, the main health problem in terms of vectors continues to be Malaria, with 500 million reported cases and three million deaths each year, of which one million are children under five years of age (Service, 1992; Das & Amalraj, 1997; Dia et al., 2003); this entity causes the death of one person every 60 seconds (Dia et al., 2003; Póvoa et al., 2003; Beck-Johnson et al., 2013; Fimia et al., 2017a). Cuba, due to its geographic location and climatological characteristics, has a wide fauna of culicidae with proven vectorial capacity, making them of great interest for human and other animal health (Marquetti, 2006; Fimia et al., 2017a).


Efforts to control vector-borne diseases have been hampered in part by the development of drug-resistant etiologic agents, insecticide-resistant mosquitoes, environmental contamination, residual effect of chemicals, high prices of insecticides in the market and operational failures (Das & Amalraj, 1997; Guzmán et al., 1999; Ayala et al., 2008; Ngoagouni et al., 2015; Fimia et al., 2016; Alarcón et al., 2017).


There is the possibility of making forecasts of high quality, precision and certainty using several methodologies, among which stands out, the methodology of Regressive Objective Regression (ROR), which due to its simplicity and accuracy can open an important window to know the future of climate variables or daily data, years in advance (Osés et al., 2017b; Osés et al., 2018a, b); this cycle can be extended to the 11 years of the solar cycle, or to higher cycles, which are known in nature; the population dynamics of mollusks and insects, such as culicidae and their interactions with certain environmental variables, can also be modeled, with the aim of establishing prophylactic and timely control measures in epidemiological surveillance programs (Fimia et al., 2017b; González et al., 2017; Machado et al., 2018). Consequently, there is a growing need to develop and implement other strategies for the control of infectious entities and their vectors, which can complement existing methods in a more effective and efficient way.


The objective of the research was to demonstrate the relationship between the transmissible infectious entities Dengue and Malaria with climate through mathematical modeling in Villa Clara province, Cuba.


MATERIALS AND METHODS

Study area

The research was carried out in Villa Clara province, Cuba, whose provincial capital is Santa Clara municipality and covered the 13 municipalities that comprise it (Figure 1). Villa Clara province is located in the central region of the island of Cuba (Latitude: 22º 29'40'' N, Longitude: 79º28'30'' W), and has the following geographical limits; to the west, with Matanzas province, to the east, with Sancti Spíritus province and to the south, with Cienfuegos province (Figure 1).


Figure Image is available at PDF file

Figure 1. Political-administrative map of Cuba with the 13 municipalities of Villa Clara province


Period of study and data collection

The research covered the period from 2008 to 2020. Retrospective data on the main species of culicidae identified in the 304 permanent breeding sites and 218 temporary breeding sites in the province were collected from the existing control sheets/records kept in the Statistical Department of the Provincial Unit of Surveillance and Antivectorial Control (UPVLA) of Villa Clara province. The method used to collect mosquito larvae was the ladle method (WHO, 1982). Likewise, the mosquito species to which the larvae belonged were identified by means of the MSB-9 stereo microscope, using specialized keys (Pérez-Vigueras, 1956; Méndez et al., 2005; González, 2006) and taking into account all recent changes in the systematics and taxonomy of Culicidae (Reinert, 2000, 2001 and 2004).


In the case of Dengue, a cross-sectional descriptive research was conducted in the province of Villa Clara, Cuba, from January 2017 to December 2020. The universe consisted of all patients who contracted Dengue fever during that period. The selected sample coincided with the total population under study. Monthly data corresponding to the number of Dengue cases in the province were used, and for the same period, a climatic database was created, which included variables from the Yabú meteorological station, located in Santa Clara municipality, capital of Villa Clara province. Both qualitative and quantitative variables were taken into account:

N of monthly cases

Incidence by municipality

Incidence rates by municipality

Average temperature (T. media)

Maximum temperature (T. max)

Minimum Temperature (T. min)

Average Humidity (Med. R.H. Med)

Maximum Relative Humidity (RHx)

Minimum Relative Humidity (RHn)

Precipitation (Prec)

Wind speed (Vmed)

Station Atmospheric Pressure (Patm)

Cloudiness (Nub)

Saturation Deficit (Dsat)

Water Vapor Tension (Tva)


The technique for obtaining and collecting data was based on the use of the "Panorama of Diseases" register, which is obligatory, as well as the Provincial Meteorological Center's record of observations during the study period. The information obtained from these records was entered into a database, which was processed in the SPSS software, version 25. The Pearson coefficient was calculated and the Chi-square test was applied; in addition, the cases of Dengue were modeled in the short and long term using the methodology of the Regressive Objective Regression (ROR), with climatic variables (minimum temperature and precipitation).


Determination of time series and trends

In addition to collecting data on the main species of culicidae identified in the province, data were collected on larval densities, both general and specific (Anopheline) in each of the 13 municipalities of the province during the aforementioned study period. These data were organized in the Windows Excel application by years and months; that is, three columns were placed: the first with the years, the second with the 12 months that make up each year and the third with the values of the General Larval Density (GLD) and Specific Larval Density (SLD). This procedure was done for each municipality in the province. After organizing the data, we proceeded to obtain the time series and trend for each of the aforementioned variables, which was reflected in the line figures prepared for all the municipalities.


Development of Predictive Models for Culicidae Population Dynamics

Objective Regressive Regression (ORR) modeling was used to develop the predictive model. The following were defined as response variables: General Larval Density (GLD) and Specific Larval Density (SLD), and as explanatory variables: meteorological variables: Maximum Relative Humidity (RHX), Mean Relative Humidity (MRH), Minimum Relative Humidity (MRH), Maximum Temperatures (TX), Mean Temperatures (MT), Minimum Temperatures (MT), Provincial Precipitation (Prec.), Cloudiness (Nub.), Average Wind Speed (VMV), Atmospheric Pressure (PA). Data for both response and explanatory variables are from the same time period (2008-2015). The data of the meteorological variables were requested to the Provincial Meteorological Center of Villa Clara and they come from the four Meteorological stations of Villa Clara province, located in the municipalities of Santa Clara, Manicaragua, Caibarién and Sagua La Grande. The data obtained were processed by means of Pearson correlations and Student's t-test, as a statistical significance test. The statistical package SPSS ver. 13.


Objective Regressive Regression methodology (ORR)

In this methodology, the dichotomous variables DS, DI and NoC must be created first, where: NoC: Number of cases of the base (its coefficient in the model represents the trend of the series). DS = 1, if NoC is odd; DI = 0, if NoC is even, and vice versa. DS represents a sawtooth function and DI this same function, but in inverted form, so that the variable to be modeled is trapped between these parameters and a large amount of variance is explained.


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 maximum of the significant partial autocorrelations (PACF), and then the new variables are calculated, taking into account the significant Lag of the PACF. Finally, these variables are included in the new regression, regressed in a process of successive approximations until a white noise in the regression errors is obtained. In the case of atmospheric pressure, the lags of one year in advance were used.


RESULTS AND DISCUSSION

To date, 43 species of mosquitoes distributed in 15 genera have been identified in Villa Clara province, being the best represented and distributed species Anopheles albimanus (Wiedemann, 1821), Culex quinquefasciatus (Say, 1823), Cx. nigripalpus (Theobald, 1901), Gymnometopa mediovittata (Coquillett, 1906), Psorophora confinnis (Lynch Arribálzaga,1891), Aedes aegypti (Linnaeus, 1762) and Ae. albopictus (Skuse, 1894) (present in all 13 municipalities of this province), followed by Culex corniger (Theobald, 1903), Ochlerotatus scapularis (Rondan, 1848) and Psorophora ciliata (Fabricius, 1794) (in 12 of the 13 existing municipalities), all of which are shown in table 1.


Table 1. Distribution of mosquito species identified by municipality

Species of mosquitoes


Municipios

Total

Aedeomyia squamipennis

(Lynch Arribálzaga,1878)

9, 12

2

Anopheles albimanus

(Wiedemann, 1821)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

An. atropos

(Dyar y Knab, 1906)

5,6

2

An. grabhamii

(Theobald, 1901)

5,6,11

3

An. vestitipennis

(Dyar y Knab, 1906)

3,5,6,7,8,9,11

7

An. crucians

(Wiedemann, 1828)

5,8,12

3

Aedes aegypti

(Linnaeus, 1762)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

Ae. albopictus

(Skuse, 1894)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

Howardina walkeri

(Theobald, 1901)

2, 6,11,12

4

Coquillettidia nigricans

(Coquillett, 1904)

9,11

2

Culex atratus

(Theobald,1901)

4,5,6,8,9,10

6

Cx. bahamensis

(Dyar y Knab, 1906)

6,8

2

Cx. cancer

(Theobald, 1901)

1,5,6

3

Cx. chidesteri

(Dyar, 1921)

1,2,6,8,9,11,12

7

Cx. corniger

(Theobald, 1903)

1, 2, 3, 4, 5, 6, 7, 8,9,10,12,13

12

Cx. erraticus

(Dyar y Knab, 1906)

4, 5, 6, 7, 8,9,10,12,13

9

Cx. iolambdis

(Dyar, 1918)

8,9

2

Cx. nigripalpus

(Theobald, 1901)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

Cx. pilosus

(Dyar y Knab, 1906)

1,3,4,5,6,8,13

7

Cx. quinquefasciatus

(Say, 1823)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

Cx. sphinx

(Howard, 1915)

6

1

Cx. secutor

(Theobald, 1901)

8,13

2

Cx. americanus

(Neveu-Lemaire, 1902)

6,9

2

Gymnometopa mediovittata

(Coquillett, 1906)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

Mansonia titillans

(Walker, 1848)

3,6,8,9,10,11,12

7

Limatus durhamii

(Theobald, 1901)

9,12

2

Ochlerotatus scapularis

(Rondan, 1848)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12

12

Oc. sollicitans

(Walker, 1856)

1,3,4,5,6,7,10,11

8

Oc. taeniorhynchus

(Wiedemann, 1821)

1, 2, 3, 4, 5, 6, 7, 10,11

9

Oc. tortilis

(Theobald, 1903)

3,4,5,7,9

5

Orthopodomyia signifera

(Coquillett, 1896)

8,12

2

Psorophora ciliata

(Fabricius, 1794)

1, 2, 3, 4, 6, 7, 8,9,10,11,12,13

12

Ps. confinnis

(Lynch Arribálzaga,1891)

1, 2, 3, 4, 5, 6, 7, 8,9,10,11,12,13

13

Ps. howardii

(Coquillett, 1901)

6,7,8,9,10,12,13

7

Ps. johnstonii

(Grabham, 1905)

6

1

Ps. pygmaea

(Theobald, 1903)

1,4,5,6,7,9,10,13

8

Ps. santamarinai

(González Broche, 2000)

6

1

Ps. insularia

(Dyar y Knab, 1906)

6

1

Ps. infinis

(Dyar y Knab, 1906)

8

1

Toxorhynchites portoricensis

(von Röder, 1885)

5,6

2

Uranotaenia sapphirina

(Osten-Sacken, 1868)

3,4,5,6,7,8,9,11,12

9

Wyeomyia vanduzeei

(Dyar y Knab, 1906)

9

1

Wy. mitchelli

(Theobald, 1905)

8,9

2


Legend: List of municipalities of Villa Clara province: 1 Corralillo, 2 Quemado de Güines, 3 Sagua la Grande, 4 Encrucijada, 5 Camajuaní, 6 Caibarién, 7 Remedios, 8 Placetas, 9 Santa Clara, 10 Cifuentes, 11 Santo Domingo, 12 Ranchuelo and 13 Manicaragua.

Of the 69 species of mosquitoes registered for Cuba (González, 2013), in Villa Clara, the number of identified species is 43/62.31 %, so that species was collected in all the fluvial ecosystems sampled, which evidenced the great ecological plasticity of the entomofauna of culicidae existing in our country, in spite of being an archipelago, which corroborates the results obtained by García (1977) and González (1985).


The genera best represented and with a marked presence in the municipalities studied were Anopheles, Culex and Psorophora, while the species best represented and distributed in this province were An. albimanus, Cx. quinquefasciatus, Cx. nigripalpus, Gy. mediovittata, Ps. confinnis, Ae. aegypti and Ae. albopictus (present in all 13 municipalities of this province), followed by Culex corniger, Ochlerotatus scapularis and Psorophora ciliata (in 12 of the 13 existing municipalities), being the most common and best represented species in this investigation: An. albimanus, An. crucians, Cx. atratus, Cx. quinquefasciatus, Cx. Nigripalpus and Ps. confinnis, because they were distributed in almost all the ecosystems sampled, where they appeared in relatively high abundance, a fact that agrees with the results obtained by Marquetti (2006), specifically for Cx. quinquefasciatus in the urban ecosystem; this result also confirms the criteria of Mattingly (1962), Scorza (1972) and Cruz & Cabrera (2006) in relation to the extraordinary adaptive capacity and high ecological plasticity of Cx. quinquefasciatus in the most diverse and possible habitats provided by man.


The fact that Ae. aegypti and Ae. albopictus are gaining ground and space in Villa Clara province is notorious and relevant. These species are of high entomoepidemiological risk because of their involvement in several infectious entities (Komar, 2003; Mackenzie et al., 2005; Pupo et al., 2011; Guzmán et al., 2013), among which Dengue, Yellow Fever, West Nile virus, Chikungunya and Zika virus stand out; but reality has shown us, that at present, these two species are practically present throughout the length and breadth of the national geography, expanding increasingly, colonizing an important number of breeding sites generated by human activity together with environmental variables (Bangs et al., 2006), thus showing their high ecological plasticity and high capacity to adapt to the most dissimilar ecological niches (Marquetti, 2006; Fimia et al., 2015).


When mathematically modeling the influence of the meteorological variables under study on the Specific Larval Density (An. albimanus) in the hatcheries (Table 2), it was observed that the correlations between anopheline larval density and temperatures were positive and highly significant for minimum and mean temperatures, which indicates that as temperatures increase, specific larval densities also increase, results that coincide with those reached by García et al. (2012) and Beck-Johnson et al. (2013), who state that temperatures rather than rainfall play an important role in increasing anopheline larval density and malaria transmission. Both maximum and minimum temperatures have a positive association with anopheline larval densities and could be used as a predictor of the rate of Anopheles spp. infestation (Zhang et al., 2010).


Table 2. Modeling of temperature on Specific Larval Density (SLD)

Modeling variables

Mean temperature

Maxime temperature

Minimum temperature

Anopheline Larval Density (ALD)

0.09 (**)

0.08 (*)

0.10 (**)

** Pearson's correlation significant at the 0.01 level (bilateral)

* Pearson's correlation significant at the 0.05 level (bilateral)

Source: Statistical records of the Institute of Meteorology of Villa Clara.


The association between temperature and population dynamics of culicidae has been investigated in many studies, particularly in tropical and sub-tropical areas. The results of this study are consistent with previous studies in other regions of the world (Zhou et al., 2004; Zhang et al., 2015).


The correlations between specific larval density with Relative Humidity were also positive and highly significant. Indicating, that as relative humidity increases, larval density increases (Table 3). We agree with Farajzadeh et al. (2015), who define relative humidity as a vital meteorological variable in the survival of mosquitoes of the genus Anopheles. These researchers further found relative humidity and temperature to be strong predictors of Anopheles mosquito abundance. Wilke et al. (2016) found associations between mosquito abundance and meteorological variables. In addition, they consider that predictive models based on meteorological variables can provide important information on the population dynamics of culicidae. Average relative humidity is a suitable predictor of anopheline larval density, and thus malaria transmission (Aduh-Prah & Kofi-Tetteh, 2015; Alkhaldy, 2017).


Table 3. Modeling of Relative Humidity on Larval Specific Density

Modeling variables

Mean relative humidity

Maximum relative humidity

Minimum relative humidity

Anopheline Larval Density (ALD)

0.07 (*)

0.09 (**)

0.10 (**)

* Pearson's correlation significant at the 0.05 level (bilateral)

** Pearson's correlation significant at the 0.01 level (bilateral).

Source: Statistical records of the Institute of Meteorology of Villa Clara.


In Table 4, when correlating the climatological variables (precipitation, cloudiness and average wind speed), no correlation was observed between anopheline larval density with precipitation and cloudiness. Mean wind speed had a negative and highly significant correlation, indicating that as mean wind speed decreases, larval density increases. These findings are in agreement with those found by Bezerra et al. (2016), who did not find a positive association between Anopheles spp. larval density and rainfall. The highest larval densities determined by them were found in the months of the rainy period. This can be explained by the fact that, in the rainy season, the frequently high levels of rainfall could modify the life cycle of the culicidae, since an excessive increase in water levels in the breeding sites could contribute to the immature forms of the mosquito escaping or dying, and not being able to complete their life cycle. In addition, we agree with Aduh-Prah & Kofi-Tetteh (2015) who, despite finding that there was no significant association between rainfall and larval densities, consider that there is evidence that rainfall is an important predictor of larval density.


Table 4. Modeling of rainfall, cloud cover and mean wind speed on anopheline larval density

Modeling variables

Precipitations

Cloudiness

Mean wind speed

Anopheline Larval Density (ALD)

0.02

0.05

0.09 (**)

** Correlation significant at the 0.01 level (bilateral).

Source: Statistical records of the Institute of Meteorology of Villa Clara.


Table 5 shows that atmospheric pressure is a good predictor of culicidae larval densities, since a positive and significant association was found between both variables. As well as the influence exerted by the North Atlantic anticyclone, which dictates the behavior of atmospheric pressure in Cuba.


Table 5. Modeling of atmospheric pressure on General Larval Density (GLD) in the municipality of Corralillo

Modeling Variable

Unstandardized coefficients

Standardized coefficients

t

Sig.

B

Standard error

Beta


Atmospheric Pressure

.002

.001

3.744

3.123

.003


This finding can be explained by the fact that oxygen taken under partial or total gas pressures is only regulated by changes in spiracle movements. At reduced oxygen tensions, both the opening and the time the spiracles remain open increases. At low atmospheric pressures, the spiracles remain permanently open, so that dehydration may be the main cause of mortality at low atmospheric pressures (Galun & Fraenkel, 1961).


This finding constitutes a really novel result of the present work, since atmospheric pressure is a meteorological variable scarcely studied in terms of the influence that it can exert on the larval densities of culicidae of entomoepidemiological importance, since most of the investigations reviewed at national and international level address in their models the following meteorological variables: temperature, relative humidity and precipitation; however, atmospheric pressure has remained a scarcely studied variable, perhaps because of the very narrow range in which its values fluctuate over time. In fact, we were forced to find a biological explanation for the influence of atmospheric pressure on the General Larval Density (GLD) of culicidae, and we found the article by Galun & Fraenkel (1961) who investigated the influence of atmospheric pressure on mosquito larval densities artificially, since they had to create a team to achieve this purpose.


Effects of some meteorological variables on Dengue fever in Villa Clara province

In relation to the calculation of Pearson's correlation coefficient and its statistical significance, between the incidence of Dengue cases and the climatological variables, it should be noted that there was a significant correlation (r=0.332; p=0.023) between this variable and the Minimum Temperature, as this increases, the cases of Dengue increase, and in the case of Atmospheric Pressure it was also significant (r=-0.317; p=0.030), since as this increases, the cases of Dengue decrease. Water Vapor Tension was significant (r=-0.298; p=0.042), as it increases, cases of Dengue also increase. The other variables were not significant (Table 6).

Table 6. Correlation of climatological variables with the incidence of Dengue cases. Villa Clara 2017-2020

Climatological Variables

Pearson correlation

Sig. (bilateral)

Mean temperature

0.268

0.069

Maximum temperature

0.194

0.192

Minimum temperature

0.332

0.023

Maximum relative humidity

-0.23

0.412

Minimum relative humidity

0.155

0.299

Mean relative humidity

0.127

0.396

Saturation density

0.002

0.991

Atmospheric pressure

-0.317

0.030

Cloudiness

0.079

0.596

Average wind speed

-0.013

0.933

Precipitations

-0.120

0.423

Water Vapor Tension

0.298

0.042

Source: Provincial Meteorological Center and Overview of notifiable diseases. Villa Clara 2017-2020.


Regarding the relationship of climatological variables with the incidence of Dengue. It was observed that the distributions of confirmed cases increased in the summer months and decreased considerably in the winter months. The intervals in which the considerable increase in cases was observed also coincided with the cyclonic season in Cuba, so it is inferred that there is a relationship in terms of the meteorological determinants that determine this period in the national territory and the incidence of Dengue, which is consistent with results obtained by other researchers, both in Villa Clara province and in other locations in Cuba (Rodríguez et al., 2006; Fimia et al., 2012; Diéguez et al., 2015; Fimia et al., 2016; Machado et al., 2018).


In relation to the geographical distribution, a higher incidence was identified in the municipality of Santa Clara, which corresponds to an urban area with a higher population density, so it should be considered that the urbanization factor has a positive influence on the number of reported cases, which is consistent with results obtained by other authors, both in Cuba and in countries of the American continent (Diéguez et al., 2015; Fajardo et al., 2016; González et al., 2019; Ayala et al., 2021; Rydzanicz et al., 2021).


Dengue cases were modeled in the short term using the ROR methodology (Table 7) with the climatic variables (Tmin and Prec), the latter variable was used even though no significant relationship was found in the study, because it is widely used in the studies consulted, due to its demonstrated incidence in the vector's life cycle. This model explains 95.4% of the variance, with an error of 135 cases, the Durbin Watson statistic is close to 2, so we are in the presence of a valid model; there is no more information on the errors.


Table 7. Summary of the model using the ROR methodology

Model summary c, d

Model

R

R squaredb

R squared adjusted

Standard error of estimation

Durbin-Watson

1

.954a

.911

.866

134.963

2.182

a. Predictors: Lag17Prec, Lag8Total, Lag14Total, DS, Lag2Total, Lag10Total, DI, Lag1Total, NoC, Lag1Tmin.

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: Total

d. Linear regression through the origin


In relation to the analysis of climatological variables, there was concordance between the results of the study and others reviewed, in which temperature and relative humidity are variables with high correlation with the incidence of Dengue (Osés et al., 2018a, b; Fimia et al., 2019; Machado, 2019; Fimia et al., 2020a, b).

Temperature, humidity and wind directly influence the occurrence of Dengue outbreaks; high temperature with average humidity and low winds create conditions conducive to an increase in the intensity of disease transmission (Garcia et al., 2012; Osés et al., 2018a, b; Fimia et al., 2019; Fimia et al., 2020b). The influence of environmental temperature on the Aedes spp mosquito and the transmission of the Dengue virus, has postulated that, due to the action of climate change, the mosquito has appeared and adapted in places where it was not frequent, allowing the viruses to spread uncontrolled in different regions, potentiated by climatic variables (precipitation and humidity), which influence the infestation of areas in tropical and subtropical regions, related to a greater availability of breeding sites, and a higher frequency of feeding under conditions of water stress, which is a modulating factor in the emergence of epidemics and increase virus transmission (Diéguez et al., 2015; Osés et al., 2018a, b; Fimia et al., 2019; Fimia et al., 2020b).


The model was significant at 100 % (Table 8), with a Fisher's F of 20, significant at 100 %.


Table 8. Analysis of Variance of the model for short-term Dengue

ANOVAa,b

Model

Sum of squares

gl

Quadratic mean

F

Sig.

1

Regression

3727352.201

10

372735.220

20.463

.000c

Residue

364301.799

20

18215.090



Total

4091654.000d

30





a. Dependent variable: Total

b. Linear regression through the origin

c. Predictors: Lag17Prec, Lag8Total, Lag14Total, DS, Lag2Total, Lag10Total, DI, Lag1Total, NoC, Lag1Tmin.

d. This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.


The ROR model in question (Table 9) consists of the following variables: DS (sawtooth) and DI (inverted sawtooth), which are dichotomous variables and the number of Dengue cases in backward steps in 1, 2, 8, 8, 10 and 14 months (Lag1Total, Lag2Total, Lag8 Total,Lag10 Total, lag14 Total), also depends, on the Tmin regressed on 1 month (Lag1Tmin), and the Prec regressed on 17 months (Lag17Prec), as this increases, the cases of Dengue increase, for example, when the precipitation is 100 mm, the number of cases of Dengue increases by 131 cases in the month, the trend was significant to increase in 41 cases. All variables were significant.


Table 9. ROR modeling for Dengue cases regressed over time with some climatic variables

Coefficients a,b

Model

Unstandardized coefficients

Standardized coefficients

t

Sig.

B

Standard error

Beta

1

DS

-3105.190

439.709

-5.945

-7.062

.000

DI

-2974.767

431.547

-5.696

-6.893

.000

Tendency

41.202

7.518

3.752

5.480

.000

Lag1Total

.321

.141

.321

2.285

.033

Lag2Total

-.447

.143

-.430

-3.132

.005

Lag8Total

-.458

.142

-.440

-3.212

.004

Lag10Total

-.577

.137

-.555

-4.229

.000

Lag14Total

-1.526

.239

-1.038

-6.397

.000

Lag1Tmin

103.065

16.538

5.845

6.232

.000

Lag17Prec

1.312

.283

.606

4.637

.000


a. Dependent variable: Total

b. Linear regression through the origin


Variations in the water temperature in which mosquito larvae develop influence their survival. Thus, the development of Ae. aegypti is reduced when the water temperature decreases or increases due to the physiological optimum range, which oscillates between 16 and 35 °C (Sharmin et al., 2015; Benítez, 2018; Márquez et al., 2019; Fimia et al., 2019). The effect of climate change has been evaluated on different aspects of Ae. aegypti biology, where precipitation and temperature have been reported as factors that influence not only the population dynamics of this species, but also its ability to transmit different types of viruses (Fimia et al., 2015; Sharmin et al., 2015; Osés et al., 2016; Wilke et al., 2016; Benítez, 2018; Márquez et al., 2019).


Moreover, precipitation plays an important role as a predisposing factor for Dengue, because while temperature influences virus replication, precipitation is related to mosquito habitat (Garcia et al., 2012; Xu et al., 2014; Sharmin et al., 2015; Wilke et al., 2016; Márquez et al., 2019). Although the increase in temperatures generates that humans store more water, so that the vector can spread more easily to urban areas; when the La Niña phenomenon occurs, soil moisture and naturally accumulated water residues are conducive to the vector's reproductive cycle (Troyo et al., 2008; Diéguez et al., 2015; Bezerra et al., 2016; Fajardo et al., 2016; Machado et al., 2018).


The inverse relationship between the incidence of Dengue and atmospheric pressure could be due to the fact that the higher the atmospheric pressure, the lower the probability of rainfall. On the other hand, the direct relationship of dependence between cloudiness and temperature with the increase of Dengue cases is due to the fact that the higher the temperature, the higher the cloudiness, and with it, also increases the probability of rainfall, creating favorable conditions for the proliferation of the vector (Fimia et al., 2015; Osés et al., 2016; Fimia et al., 2019; Machado et al., 2019).


A long-term model was performed, that is, with a lag of 12 months (1 year) to search in advance in the forecast, obtaining a model that explains 82.9 %, with an error of 306 cases, where Fisher's F was 3.6, significant at 95 % (Table 10).


Table 10. Long-term modeling on a 12-month basis

ANOVAa,b

Model

Sum of squared

gl

Quadratic mean

F

Sig.

1

Regression

2679044.400

8

334880.550

3.569

.021c

Residue

1219818.600

13

93832.200



Total

3898863.000d

21




a. Dependent variable: Total

b. Linear regression through the origin

c. Predictors: Lag14Patm, Lag26Total, Lag20Total, DI, Lag14Total, Lag13Total, NoC, Lag13Tmin.

d. This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.


Below are the results of the long-term model. In red the predicted value for the year 2021, where an increase is expected in the month of February to decrease from March to July, then from August to December, the values will increase greatly (Table 11).


Table 11. Long-term modeling for the year 2021

Case summariesa


Years/ Months

Total

Unstandardized Predicted Value

Unstandardized residual

27

201903.00

0

263.17511

-263.17511

28

201904.00

67

65.31128

1.68872

29

201905.00

58

320.96671

-262.96671

30

201906.00

321

618.48470

-297.48470

31

201907.00

709

512.88789

196.11211

32

201908.00

544

719.47803

-175.47803

33

201909.00

888

512.70928

375.29072

34

201910.00

1221

602.22787

618.77213

35

201911.00

607

391.42575

215.57425

36

201912.00

51

335.65956

-284.65956

37

202001.00

144

81.85423

62.14577

38

202002.00

19

-87.79324

106.79324

39

202003.00

92

-32.54104

124.54104

40

202004.00

59

-89.12622

148.12622

41

202005.00

75

-45.43644

120.43644

42

202006.00

87

294.02186

-207.02186

43

202007.00

0

356.46147

-356.46147

44

202008.00

0

20.81879

-20.81879

45

202009.00

0

112.73595

-112.73595

46

202010.00

541

430.91737

110.08263

47

202011.00

0

100.10287

-100.10287

48

202012.00

.

-183.01860

.

49

202101.00

.

-186.50764

.

50

202102.00

.

110.59928

.

51

202103.00

.

-777.22693

.

52

202104.00

.

-557.63272

.

53

202105.00

.

-649.93080

.

54

202106.00

.

-673.56864

.

55

202107.00

.

-159.39669

.

56

202108.00

.

873.05625

.

57

202109.00

.

1305.09638

.

58

202110.00

.

1225.58847

.

59

202111.00

.

1342.80937

.

60

202112.00

.

1866.51432

.

Total

N

100

47

34

21

a. Limited to the first 100 cases.


Figure 2 shows the good coincidence of the model, despite the fact that we are in the presence of a model 1 year in advance, a significant increase in Dengue cases in the province is expected for the second half of the year, a matter that should be treated with caution, so taking preventive measures would be very beneficial.


Figure Image is available at PDF file

Figure 2. Long-term forecast for Dengue cases in Villa Clara, Cuba


The ROR methodology consists of several steps and allows not only to mathematically model the larval densities of mosquitoes, as well as the population dynamics of mollusks, but goes beyond (possibility of modeling infectious entities of different etiologies, such as HIV/AIDS, Cholera, Influenza, Acute Respiratory Infections (ARI), Acute Bronchial Asthma (CAAB), Fasciolosis, Angiostrongylosis and even, in the estimation of the length and area of the universe, monthly forecasting of precipitation and extreme temperatures, forecasting of meteorological disturbances (hurricanes), prediction of the latitude and longitude of earthquakes, search for information on white noise, modeling of the Equivalent Effective Temperature (TEE) and Atmospheric Pressure (PA) up to the electricity consumption of a municipality, province and/or nation) (Osés & Grau, 2011; Osés et al., 2017b; Osés et al., 2018c; Osés et al., 2019).


CONCLUSIONS

It is concluded that there is a close relationship between the infectious entities analyzed and the species of vector organisms with the climate, demonstrated by means of the predictive model for the specific and general larval densities of culicidae, and the mathematical modeling ROR for the Dengue entity, so that it is possible to model and predict, Thus, it is possible to model and predict, in the short, medium and long term, both the population dynamics of culicidae with entomoepidemiological importance and the incidence of cases of Dengue, with very good results, making the ROR methodology an excellent predictive tool not only for transmissible entities of viral and parasitic etiology.


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