1 Department of Forecasting, Provincial Meteorological Center of Villa Clara, Cuba.

2 Parasitology Department. Regional High Specialty Hospital (HARE), Dr. Juan Graham Casasús, México.

3 Department of Surveillance and Vector Control, Provincial Center of Hygiene, Epidemiology and Microbiology of Villa Clara, Cuba.

4 President of EurAsia Heart Foundation, Zurich, Switzerland.

5 Hygiene and Epidemiology Department, Faculty of Health Technology and Nursing (FHTN), University of Medical Sciences of Villa Clara (UMS-VC), Cuba.

Corresponding author email: rigoberto.fimia66@gmail.com

Article Publishing History

Received: 25/03/2026

Accepted After Revision: 19/06/2026

ABSTRACT:

The early history of infectious diseases was characterized by sudden and unpredictable outbreaks, often of epidemic proportions. The objective of the research was to model the time series and trends of the focality of Aedes aegypti, both by months and by years (2010-2025) in the short and very long term in the province of Villa Clara, Cuba. The research covered the 13 municipalities that make up the province. An ecological, retrospective, and modelling study was conducted using an Excel database (covering the period from 2010 to 2025) and Objective Regression (OR) methodology, encompassing all 13 municipalities. The sample consisted of all Ae. aegypti mosquito larval infestations collected and recorded in the database. The information gathered is based on established work cycles for vector surveillance and control. However, our research primarily focused on the urban ecosystem (related to the ecology of the vector under study).

Therefore, the maximum of the average value corresponds to October and the minimum to December. The month with the greatest variability is October, while the one with the least was May. The correlations between all months and the annual total. These correlations proved to be highly significant at the 99% confidence level for all months. Therefore, ROR modeling was performed on the totals, and simple regressions were used to calculate the models for the months in question. The year showed a significant correlation at the 95% confidence level with the months of March and May. It is concluded that it is possible to mathematically model, both in the short and very long term, the focality of the mosquito species Ae. aegypti.

KEYWORDS:

AEDES AEGYPTI; MATHEMATICAL MODELING; OBJECTIVE REGRESSIVE
REGRESSION; SHORT AND LONG TERM; VILLA CLARA.

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Rodríguez R. O, Laveaga D. D. V, Rodríguez I. D. C. G, Vogt P. R, Duarte R. F. Short and Very Long-Term Modeling for the Focality of Aedes aegypti in Villa Clara, Cuba. Biosc.Biotech.Res.Comm. 2026;19(2).

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Rodríguez R. O, Laveaga D. D. V, Rodríguez I. D. C. G, Vogt P. R, Duarte R. F. Short and Very Long-Term Modeling for the Focality of Aedes aegypti in Villa Clara, Cuba. Biosc.Biotech.Res.Comm. Biosc.Biotech.Res.Comm. 2026;19(2). Available from: <ahref=”https://shorturl.at/ZmG7b“>https://shorturl.at/ZmG7b</a>

INTRODUCTION

Throughout history, humanity has suffered from the scourge of potentially fatal viral and parasitic diseases, including Yellow Fever, Dengue, Zika, Chikungunya, Malaria, Chagas disease, Leishmaniasis, Onchocerciasis, Angiostrongylosis, and Fascioliasis, among many others. In most of these diseases, a vector organism is often a common factor (Bhatt et al., 2013; Aduh-Prah and Kofi-Tetteh, 2015; Diéguez et al., 2025a).

These diseases are widespread in the tropics, with local variations in risk, and are therefore highly dependent on factors such as rainfall, temperature, and rapid, unplanned urbanization (Bezerra et al., 2016; Benítez, 2018; Diéguez et al., 2019). Since the beginning of civilization, infectious diseases have affected humans (Gubler, 2002; Bangs et al., 2006; Fimia et al., 2022a). The early history of infectious diseases was characterized by sudden and unpredictable outbreaks, often of epidemic proportions (Lambrechts et al., 2010; Gould et al., 2017; Grubaugh et al., 2019).

Millions of people suffer from infections transmitted by arthropod vectors; among these, culicids are undoubtedly the most important in terms of hygiene and health, because they are one of the prioritized health problems in almost all tropical and subtropical regions (Turell et al., 2006; Aduh-Prah and Kofi-Tetteh, 2015; Lebl et al., 2015; Ngoagouni et al., 2015) and are responsible for the maintenance and transmission of the pathogens that cause Dengue fever, Yellow fever, West Nile fever, Chikungunya, Zika, Malaria, and Lymphatic filariosis, among other deadly and debilitating infections (Gould and Higgs, 2009; Ferguson et al., 2016; CDC, 2017; Alarcón-Elbal et al., 2019).

Dengue fever has spread in recent decades and continues to be the main arbovirus (Lambrechts et al., 2010; Bhatt et al., 2013; Diéguez et al., 2019) and Chikungunya and Zika have emerged in recent years (Cauchemez et al., 2014; Zanluca et al., 2015; Grubaugh et al., 2019). Malaria remains the world’s leading parasitic health problem (WHO, 2014; WHO, 2015). An estimated 429 000 deaths were registered in 2015. About 90% of malaria-related deaths globally, occur in Africa, 70% of which happen in children under five years old (WHO, 2016).

The emergence and re-emergence of arboviral infections are a growing phenomenon in the last decade. The changing epidemiology and the factors responsible for this dramatic resurgence of such diseases are complex (Fimia et al., 2015; Alkhaldy, 2017; Campos et al., 2022). A large proportion of human diseases are zoonotic. In addition, global and/or local demographic, social, and environmental changes have led to the spread of infection to humans (Altizer et al., 2013; Cepero et al., 2025; Diéguez et al., 2025b).

In Cuba, the incidence of these entities, both parasitic and viral, is undoubtedly a health problem (MINSAP, 2016a), with a tendency to increase the number of cases, as well as the populations of vector organisms (MINSAP, 2016b; González et al., 2026; Machado et al., 2026).

The objective of the research was to model the time series and trends of the focality of Aedes aegypti, both by months and by years (2010-2025) in the short and very long term in the province of Villa Clara, Cuba.

MATERIAL AND METHODS

Study area descriptions: The research was carried out in Villa Clara province, Cuba, whose provincial capital is Santa Clara municipality and covered the 13 municipalities that make up the province. In Villa Clara, specialists from the Provincial Unit for Surveillance and Antivectorial Fight (UPVLA) have recorded 316 370 homes and buildings in the general universe, out of which 236 391 belong to the urban universe (74.7%). They have also registered in such homes or buildings distributed over the 13 municipalities, approximately 1 581 850 water containers with conditions for the breeding, proliferation, and dissemination of the afore-mentioned Culicidae (Figure 1).

Figure 1: Administrative map of Villa Clara province

Source: Provincial Meteorological Center of Villa Clara

Type of study: An ecological, retrospective, and modelling study was conducted using an Excel database (covering the period from 2010 to 2025) and Objective Regression (OR) methodology, encompassing all 13 municipalities of Villa Clara province. The sample consisted of all Ae. aegypti mosquito larval infestations collected and recorded in the database.

Methods and techniques for the collection of data: A review of the existing statistical records and archives was made at the Provincial Unit for Surveillance and Antivectorial Struggle (UPVLA) and at the Provincial Department of Health Statistics in Villa Clara, where all the entomological history of the work cycles conceived in the 13 municipalities of the province is compiled. Such information is periodically reported in statistical tables established for such purposes by the National Directorate for Surveillance and Antivectorial Struggle (DNVLA) and the Department of Health Statistics at the Ministry of Public Health (MINSAP).

The information gathered is based on established work cycles for vector surveillance and control, focused on targeted work in homes in urban and rural areas of the province’s 13 municipalities. However, our research primarily focused on the urban ecosystem (related to the ecology of the vector under study).

Regarding the Objective Regression Methodology (ROR): To work with the Objective Regression Method (ROR) (Osés and Grau, 2011), a database is required. This database is organized by arranging the data in ascending chronological order. Then, in the first step, dichotomous variables DS, DI, and NoC are created, where:

NoC: Number of cases in the database, DS = 1 if NoC is odd; DI = 0 if NoC is even. When DI=1, DS=0, and vice versa.

DS represents a sawtooth function, and DI represents the same function but inverted, such that the variable to be modeled is trapped between these parameters, thus explaining a large amount of variance.

Next, the curves are modeled, and finally, the regressed variables with the greatest impact are added. Subsequently, the Regression analysis module of the SPSS statistical package version 19.0 (IBM Company) will be executed, specifically the ENTER method where the predicted variable and the ERROR are obtained.

Next, the autocorrelograms of the ERROR variable were obtained, paying attention to the peaks of the significant partial autocorrelations (PACF). The new variables were then calculated considering the significant lag of the PACF. Finally, these regressed variables were included in the new regression in a process of successive approximations until white noise was obtained in the regression errors.

RESULT AND DISCUSSION

Table 1 shows the descriptive statistics of the number of light sources per month. We can see the maximum value per column in red and the minimum in green. Therefore, the maximum of the average value corresponds to October and the minimum to December. The month with the greatest variability is October, while the one with the least was May. These results largely agree with those obtained by other authors for this province (Campos et al., 2022; Fimia et al., 2022b; González et al., 2026; Machado et al., 2026).

Table 1. Descriptive statistics for the number of Aedes aegypti mosquito breeding sites per months

N Minimum Maximum Media Standard deviation Year 238 2010 2026 2018.00 4.909 January 225 0.0 1522.0 127.431 293.3698 February 225 0.0 1360.0 115.484 264.4775 March 225 0.0 1541.0 109.262 258.3486 April 225 0.0 1909.0 106.578 279.8831 May 225 0.0 1420.0 111.360 258.0832 June 225 0.0 2081.0 153.262 341.6121 July 225 0.0 1936.0 119.662 273.4179 August 225 0.0 2547.0 131.040 329.3270 September 225 0.0 1643.0 138.631 312.8787 October 225 0.0 1900.0 161.751 353.8550 November 224 0.0 2012.0 141.366 315.7494 December 225 0.0 1413.0 97.138 226.5387 Total 224 0.0 17429.0 1519.089 3256.8633 N valid (by list) 223

Tables 2, 3 and 4 show the correlations between all months and the annual total. These correlations proved to be highly significant at the 99% confidence level for all months. Therefore, ROR modeling was performed on the totals, and simple regressions were used to calculate the models for the months in question. The year showed a significant correlation at the 95% confidence level with the months of March and May, results that also agree to some extent with those obtained by other researchers on this topic (Campos et al., 2022; Diéguez et al., 2025b; Diéguez et al., 2026; Lorenzo et al., 2026).

Table 2. Correlation between the total number of months (January-April) and the total number of years.

* Correlation is significant at the 0.05 level (2-tailed).
** Correlation is significant at the 0.01 level (2-tailed).

Table 3. Correlation between total months (May-July) and annual total

* Correlation is significant at the 0.05 level (2-tailed).
** Correlation is significant at the 0.01 level (2-tailed).

Table 4. Correlation between the total number of months (August-December) and the annual total
** Correlation is significant at the 0.01 level (2-tailed).

Fisher’s F is highly significant at 99% and its value was 881.74 (Table 5).

Table 5. Fisher’s F results taking into account the regression and the residual ANOVAa, b

Model Sum of squares gl mean square F Sig. 1 Regression 2703655123.809 19 142297638.095 881.740 0.000c Residue 30824118.191 191 161382.818 Total 2734479242.000d 210 a. Dependent variable: Total
b. Linear regression through the origin
c. Predictors: Lag9Total, Step70, Step56, Step42, Step112, Step210, Step196, Step182, Step140, Step65, Step93, Step51, Step205, SD, Step191, DI, Lag5Total, Lag14Total, NoC.
d. This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.

In table 6, the model coefficients and the NoC trend were found to be negative but not significant. The model depends on the regressed foci in 14 cases, 9 cases, and 5 cases. The non-significant parameters were left in the model, as they contribute to the explained variance.

Table 6. Results of the model coefficients Coefficientsa, b

Model Non-standardized coefficients Standardized coefficients T Sig. B Standard error Beta 1 DS 114.360 70.738 0.022 1.617 0.108 DI 29.755 70.460 0.006 0.422 0.673 NoC -0.547 0.479 -0.020 -1.142 0.255 Step182 4036.401 438.826 0.077 9.198 0.000 Step196 -2080.031 458.228 -0.040 -4.539 0.000 Step56 -6272.841 426.778 -0.120 -14.698 0.000 Step51 -5478.225 421.641 -0.105 -12.993 0.000 Step210 -4697.393 446.413 -0.090 -10.523 0.000 Step70 3135.044 409.868 0.060 7.649 0.000 Step93 -2818.454 414.460 -0.054 -6.800 0.000 Step205 -3684.882 429.285 -0.070 -8.584 0.000 Step42 2918.407 420.477 0.056 6.941 0.000 Step140 2882.325 425.802 0.055 6.769 0.000 Step191 -2421.659 437.930 -0.046 -5.530 0.000 Step65 2230.636 407.033 0.043 5.480 0.000 Step112 2535.747 414.498 0.048 6.118 ,000 Lag14Total 0.998 0.013 1.005 74.615 0.000 Lag5Total -0.003 0.010 -0.003 -0.332 0.741 Lag9Total 0.034 0.011 0.034 3.091 0.002 a. Dependent variable: Total
b. Linear regression through the origin

In figure 2, the histogram of the short-term model residuals shows that they do not differ from the normal distribution.

Figure 2: Histogram of waste from all light focus in Villa Clara 2010-2025 in the short term.

In table 7, the long-term model, projected one year in advance, explains 99.4% of the data, with a slightly higher but still small error than the short-term model. The Fisher F-statistic was highly significant (99%).

Table 7. Long term model Model summaryc, d

 Model summaryc, d Model R R squareb Adjusted R-squared Standard error of the estimation Durbin-Watson 1 0.994a 0.988 0.987 410.7238 1.914 a. Predictors: Lag14Total, Step65, Step70, Step93, Step112, Step42, Step205, Step51, Step191, Step56, Step140, Step182, SD, Step210, DI, Step196, NoC

b. For regression through the origin (the model without an intercept), R-squared measures the proportion of the variability in the dependent variable about the origin explained by the regression. This CANNOT be compared to the R-squared for models that include an intercept.
c. Dependent variable: Total
d. Linear regression through the origin

Regarding the long-term model coefficients, the trend was negative but not significant (Table 8). The residual statistics showed a mean of zero and a variance of almost 1.

Table 8. Results of the long-term model coefficients Coefficientsa, b

Coefficientsa, b Model Non-standardized coefficients Standardized coefficients T Sig. B Standard error Beta 1 DS 129.988 70.973 0.025 1.832 0.069 DI 54.106 71.562 0.011 0.756 0.451 NoC -0.490 0.487 -0.018 -1.006 0.315 Step182 3779.061 439.882 0.072 8.591 0.000 Step196 -2391.307 458.321 -0.046 -5.218 0.000 Step56 -6471.580 431.653 -0.124 -14.993 0.000 Step51 -5259.406 425.459 -0.101 -12.362 0.000 Step210 -4969.606 447.872 -0.095 -11.096 0.000 Step70 3020.622 415.977 0.058 7.262 0.000 Step93 -2643.789 419.956 -0.051 -6.295 0.000 Step205 -3326.303 424.396 -0.064 -7.838 0.000 Step42 2746.784 423.781 0.053 6.482 0.000 Step140 2681.711 429.995 0.051 6.237 0.000 Step191 -2013.351 429.241 -0.039 -4.690 0.000 Step65 2308.886 415.150 0.044 5.562 0.000 Step112 2377.179 419.919 0.045 5.661 0.000 Lag14Total 1.013 .012 1.020 83.502 0.000 a. Dependent variable: Total
b. Linear regression through the origin

Figure 3: Histogram of waste from all light focus in Villa Clara 2010-2025 (Long term).

Figures 4 and 5 show how the model works with its respective actual and forecasted data, both in the short and long term.

Figure 4: Actual Value vs. Forecast of Total Spotlights. Short term.

Figure 5: Actual Value vs. Forecast of Total Spotlights. Long term.

In table 9, the key statistics for the number of light focus per month and the explained variances were high, with small errors, while the Durbin-Watson statistic was close to 2 in all models; this is very beneficial for the model, as it indicates that the independent variables yielded a good model. In all cases, this variable was significant, something we already knew from the strong correlation between total light focus and each month (Campos et al., 2022; Fimia et al., 2022; Diéguez et al., 2025). Furthermore, all Fisher’s F-statistics were highly significant.

Table 9. Key statistics of the model by month. Villa Clara 2010-2025

Months R (%) Variance Explained Model error Durbin Watson F de Fisher Signification January 93.5 116.05 1.745 360.234 0.00 February 96.2 81.37 1.590 636.280 0.00 March 98.0 90.36 1.722 478.36 0.00 April 92.7 93.90 1.862 315.37 0.00 May 94.4 95.57 1.657 421.11 0.00 June 94.0 130.83 1.651 396.90 0.00 July 93.2 111.18 1.643 342.60 0.00 August 84.6 194.39 1.879 130.64 0.00 September 92.3 133.46 1.764 296.59 0.00 October 93.1 144.69 1.837 339.20 0.00 November 92.2 135.59 1.744 293.87 0.00 December 89.3 111.61 1.791 202.64 0.00 Total 99.4 401.72 1.939 881.74 0.00

CONCLUSION

The information gathered is based on established work cycles for vector surveillance and control. However, our research primarily focused on the urban ecosystem (related to the ecology of the vector under study). Therefore, the maximum of the average value corresponds to October and the minimum to December. The month with the greatest variability is October, while the one with the least was May. The correlations between all months and the annual total. These correlations proved to be highly significant at the 99% confidence level for all months. Therefore, ROR modelling was performed on the totals, and simple regressions were used to calculate the models for the months in question. The year showed a significant correlation at the 95% confidence level with the months of March and May. It is concluded that it is possible to mathematically model, both in the short and very long term, the focality of the mosquito species Ae. aegypti, the main vector transmitting arboviruses.

Compliance with ethical standards: As per guidelines

ACKNOWLEDGEMENTS

To Dr. David del Valle Laveaga for his financial contribution towards the publication of this manuscript.

Disclosure of conflict of interest: No conflict of interest exists among the authors.

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