Throughout history, humanity has faced multiple potentially deadly viral and parasitic diseases, including yellow fever, dengue, zika, chikungunya, and malaria, which are closely related because they are transmitted by a mosquito (Diptera: Culicidae). These diseases are highly prevalent in tropical areas and the risk of contracting them depends, to a large extent, on rainfall, temperature and the living conditions of each place.²

Mosquitoes are considered one of the most versatile living organisms in the world as they can breed in any pool of water, such as puddles or tanks; however, their reproduction is influenced by certain biotic and abiotic factors.^3,4These insects need the blood of humans and/ or other vertebrates to make their eggs fertile and viable, so they represent a threat to humanity since they are vectors of pathogenic microorganisms of several vector-borne diseases that can become burdens for many countries from the health, economic and social point of view.^5,6

Natural disasters threaten the safety of people, hurricanes being the most destructive phenomenon in the tropics because of all that their passage entails.^7-10 Since the frequency of these events is on the rise, knowing their behavior is essential; for this reason, in Cuba, seasonal forecasts are constantly made based on the oceanic and atmospheric conditions that preceded the past hurricane seasons (active or inactive), as they provide useful information about trends that could be observed in similar future seasons.¹¹

Although the occurrence of hurricanes cannot be predicted accurately, their impact can be determined in advance. Moreover, research in this area has made significant progressin recent years, so much so that in 2012, for the first time, it was possible to forecast an event of this type a year in advance.¹² To this end, high-quality forecasts are made using the regressive objective regression (ROR) methodology, which, due to its simplicity and accuracy, can be useful to know the future of climate variables or daily data years in advance.^13,14 Forecast times can extend to 11 years of the solar cycle or other longer cycles known in nature.

By using the ROR methodology, the population dynamics of insects such as mosquitoes, and their interactions with certain environmental variables, can also be modeled. This is helpful to establish timely control and prophylactic measures in epidemiological surveillance programs.^12,13,15

In this sense, the objective of this research was to assess the impact of atmospheric pressure on mosquito population density in the province of Villa Clara, Cuba, through mathematical models based on the ROR methodology.

In the present research work, 43 species of mosquitoes of 13 genera were identified in Villa Clara. Several of these species had marked ubiquity (Table 1).

Table 1

Mosquito species	Classification and year	Municipalities *	Total number of municipalities
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
Anopheles atropos	Dyar & Knab, 1906	5, 6	2
Anopheles grabhamii	Theobald, 1901	5 , 6,11	3
Anopheles vestitipennis	Dyar & Knab, 1906	3, 5, 6, 7, 8, 9, 11	7
Anopheles 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
Aedes albopictus	Skuse, 1894	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13	13
Aedes mediovittatus	Coquillett, 1906	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13	13
Aedes scapularis	Rondani, 1848	2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13	12
Aedes sollicitans	Walker, 1856	1, 3, 4, 5, 6, 7, 10, 11	8
Aedes taeniorhynchus	Wiedemann, 1821	1, 2, 3, 4, 5, 6, 7, 10, 11	9
Aedes tortilis	Theobald, 1903	3, 4, 5, 7, 9	5
Aedes walkeri	Theobald, 1901	2, 6, 11, 12	4
Coquillettidia nigricans	Coquillett, 1904	9, 11	2
Culex americanus	Neveu-Lemaire, 1902	6, 9	2
Culex atratus	Theobald, 1901	4, 5, 6, 8, 9, 10	6
Culex bahamensis	Dyar & Knab, 1906	6, 8	2
Culex cancer	Theobald, 1901	1, 5 , 6	3
Cx. chidesteri	Dyar, 1921	1, 2, 6, 8, 9, 11, 12	7
Culex corniger	Theobald, 1903	2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 13	12
Culex erraticus	Dyar & Knab, 1906	4, 5, 6, 7, 8, 9, 10, 12, 13	9
Culex iolambdis	Dyar, 1918	8, 9	2
Culex nigripalpus	Theobald, 1901	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13	13
Culex pilosus	Dyar & Knab, 1906	1, 3, 4, 5, 6, 8, 13	7
Culex quinquefasciatus	Say, 1823	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13	13
Culex sphinx	Howard, Dyar & Knab, 1915	6	1
Culex secutor	Theobald, 1901	8, 13	2
Mansonia titillans	Walker, 1848	3, 6, 8, 9, 10, 11, 12	7
Limatus durhamii	Theobald, 1901	9, 12	2
Orthopodomyia signifera	Coquillett, 1896	8, 12	2
Psorophora ciliata	Fabricius, 1794	1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13	12
Psorophora confinnis	Lynch Arribálzaga, 1891	1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13	13
Psorophora howardii	Coquillett, 1901	6, 7, 8, 9, 10, 12, 13	7
Psorophora johnstonii	Grabham, 1905	6	1
Psorophora pygmaea	Theobald, 1903	1, 4, 5, 6, 7, 9, 10, 13	8
Psorophora santamarinai	González Broche, 2000	6	1
Psorophora insularia	Dyar and Knab, 1906	6	1
Psorophora infinis	Dyar and Knab, 1906	8	1
Toxorhynchites portoricensis	von Roder, 1885	5, 6	2
Uranotaenia sapphirina	Osten-Sacken, 1868	3, 4, 5, 6, 7, 8, 9, 11, 12	9
Wyeomyia vanduzeei	Dyar & Knab, 1906	9	1
Wyeomyia mitchellii	Theobald, 1905	8, 9	2

* Each municipality was identified with a number: 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.

Table 2 presents the descriptive statistics for the number of breeding sites per municipality; it is possible to see that the highest mean and standard deviation (σ) are found in the municipality of Santa Clara and that the lowest are in Encrucijada. The maximum value obtained for the time series (11 years of annual data) was 8 778 in Santa Clara, while the minimum value was 0 in Corralillo, Quemado de Güines, Encrucijada and Caibarién. The overall average number of breeding sites in the province was 7 143, with a σ of 2 165.

Table 2

Municipalities	N	Minimum	Maximum	Mean	σ
Corralillo	11	0.00	44.00	12.72	15.49
Quemado de Güines	11	0.00	117.00	17.00	34.33
Sagua la Grande	11	4.00	1 199.00	475.27	468.07
Encrucijada	11	0.00	14.00	6.36	5.35
Camajuaní	11	1.00	108.00	44.36	36.37
Caibarién	11	0.00	54.00	18.81	18.55
Remedios	11	1.00	249.00	52.00	76.57
Placetas	11	10.00	438.00	89.45	126.31
Santa Clara	11	3 734.00	8 778.00	5 987.63	1 549.21
Cifuentes	11	3.00	78.00	25.72	25.29
Santo Domingo	11	5.00	204.00	91.09	80.06
Ranchuelo	11	36.00	675.00	185.81	214.27
Manica ragua	11	6.00	381.00	137.09	145.17
Provincia	11	4 497.00	10 806.00	7 143.36	2 165.59

σ: standard deviation; N: number of years studied from 2007 to 2017.

The ROR model was chosen because, during the investigation, it was concluded that by combining lags 1, 2 and 6 (corresponding to 1 year, 2 years and 6 years, respectively) a perfect model could be obtained for each municipality but the parameters of influence could not be measured since there were divisions by zero. The proposed model proved to be perfect according to the analyzed data since no standard error was observed and no autocorrelation was detected in the residues by means of the Durbin Watson statistic. The analysis of variance (ANOVA) for the model indicated that Fisher's F could not be determined because the error was zero, and to calculate this statistic, it is necessary to divide by the error, which creates a mathematical uncertainty.

Figure 2 shows the result of the modeling for the province; it is possible to see that the predicted value has excellent coincidence with the real value from 2013 to 2017.

Figure 2 Source: Own elaboration.

The highest variance explained was the same for all municipalities (100%), but there was an upward trend in Cifuentes since the NoC coefficient was positive, while the trend was downward in Caibarién and Ranchuelo since the NoC coefficient was negative (Table 3). NoC coefficient was recorded when it was not significant. The ANOVA was only doneforthe larval stage.

Table 3

Municipality and significance of larval density	Durbin Watson	S	IS	NoC	Lag2*	Lagl *	Lag6 *
Corralillo 0.002	1.459	16.99	2.709		-1.09	1.936	-2.198
Quemado de Güines 0.001	1.889	22.85	3		0.148	-3.889	18.407
Sagua la Grande 0.003	0.892	2 400	3 919		-2.359	-1.363	6.348
Encrucijada 0.004	2.184	5.968	6.437		-0.482	0.378	-0.194
Camajuaní 0.023	1.655	141.74	65.98		-1.996	0.802	0.534
Caibarién 0.014	2.044		-14.877	-4.604	3.378	-1.375	5.901
Remedios 0.025	1.328	160.44	300.25		-2.887	-0,601	6.846
Placetas 0.004	1.808	126.88	-14.28		-2.776	-1.447	12.969
Santa Clara 0.005	1.397	13 432	12 753		-0.431	-0.755	0.008
Cifuentes 0.032	1.567	143.35	-136.42	19.708	0.807		-0.986
Santo Domingo 0.002	1.570	356.31	399.82		-0.751	-1.998	15.040
Ranchuelo 0.004	1.630	-78.03	-130.33	-33.253		0.253	10.685
Manicaragua 0.004	2.415	418.46	467.47		-1.296	-0.151	0.482
Province	1.268	14 114	12 952		-0.546	-0.886	0.875

S: sawtooth; IS: inverted sawtooth; NoC: number of cases.

The forecast values obtained using the atmospheric pressure prediction in the Santo Domingo station showed a behavior similar to that calculated without it (Figure 3).

Figure 3 Source: Own elaboration.

From the 70 species of mosquitoes identified in Cuba so far,^16,24 43 were found in Villa Clara in the present study.

The most common genera with the highest presence in the municipalities studied were Anopheles, Culex and Psorophora, while the most common and widely distributed species were Anopheles albimanus, Culex quinquefasciatus, Culex nigripalpus, Aedes mediovittatus, Psorophora confinnis, Aedes aegypti and Aedes albopictus (found in the 13 municipalities), followed by Culex corniger, Aedes scapularis and Psorophora ciliata (found in 12 of the 13 municipalities). The most common species were An. albimanus, Anopheles crucians, Culex atratus, Cx. quinquefasciatus, Cx. nigripalpus and Ps. Confinnis, which were found in practically all the ecosystems sampled and in relatively high abundance, a fact that coincides with what was reported by Mar-quetti-Fernández,²⁵ specifically for Cx. quinquefasciatus in urban ecosystems. The great phenotypic plasticity of the mosquitoes was also evident since it was found that they are capable of exploiting any habitat.^16,26-30

Ae. aegypti and Ae. albopictus are largely found in Villa Clara, which is noteworthy because they are high-risk entomoepidemiological species due to their involvement in infectious diseases such as dengue fever, yellow fever, West Nile fever, chikungunya and Zika virus.^31-34 Currently, these two species are present practically in the entire Cuban territory and they are increasingly expanding because human activity generates an important number of breeding sites.³³ This expansion shows their high phenotypical plasticity and great capacity of adaptation to different ecological niches.^35-37

According to the descriptive statistics, there is great variability between municipalities regarding the number of breeding sites per municipality (Table 2), which may be explained by the physical and geographical characteristics of each place, as well as the quality of the samples, aspects that are consistent with the results of previous research.^30,31

Considering that the value obtained in the present study using the Fisher's F test was high, the model designed here to establish mosquito population density is extremely good since the higher the Fisher's F, the higher the probability of having a good model in the ANOVA. ^38,39

During the research, influence parameters could not be measured because they were divided by zero, so it was necessary to resort to mathematical definitions made by other authors and even for other organisms.^40,41 The greatest variance explained was the same for all municipalities and it was 100%. Moreover, as mentioned above, there was a trend towards a decrease in the number of breeding sites in Caibarien and Ranchuelo, while there was an upward trend in Cifuentes. The most significant predicted lags were at 1 year, 2 years and 6 years (Table 3), which coincides with other studies where similar results were obtained and good modeling results were achieved through ROR models.^42-44

The impact of the atmospheric pressure predicted in the four stations using the ROR methodology explains 100% of the variance in this new model. From all the pressure measurements per station obtained, the model selected the atmospheric pressure registered in the Santo Domingo station, which resulted in an impact coefficient of 13.84. Therefore, as atmospheric pressure increased in Santo Domingo, the number of breeding sites in the provinces increased; this coincides with previous works carried out in other municipalities of the province to measure larval density^9,12,40 and confirms the impact of atmospheric pressure and, consequently, the performance of the North Atlantic anticyclone, which is the main climate modulator in the island of Cuba.

There is a close relationship between atmospheric pressure and mosquito population density since both total and specific larval densities increase as atmospheric pressure increases. These findings confirm the possibility of mathematically modeling the effect of atmospheric pressure on mosquito population density (Diptera: Culicidae) in Villa Clara, Cuba.