The biting rate translates the average number of mosquitoes that bite humans daily. It can be estimated as the relative density of mosquitoes in relation to human density (m) multiplied by the average number of bites that a single person experiments during one day (a- man biting habit). This parameter was estimated directly from all-night human-landing collections made in Comporta region, a former malaria’s hiperendemic area where P. falciparum was the dominant parasite species. Based on a worst-scenario case this estimates was extrapolated for the whole of Portugal. Man-biting habit calculation (a) was achieved through the product of An. atroparvus biting frequency (f) plus the anthropophilic index of the species (HBI). While f was evaluated based on the feeding frequency (per day) of laboratory reared females to which was given the daily possibility of feeding on an appropriated host, HBI was assessed by an ELISA-two sites performed with the mid-gut content of freshly-fed females [9]. All biological material (larvae and females) were collected in Comporta region following the same rationale mentioned previously.

Between 2001 and 2003, numerous field surveys covering several localities along mainland Portugal were made to collect adult mosquitoes in human and animal facilities by means of electrical aspirators. The diverse surroundings of the surveyed places led to highly irregular abundance values, even between close sites. Therefore, a low abundance level does not necessarily imply that the area is less suitable. However, the opposite holds true, places with high abundance are environmentally suitable.

Moreover, the survey only gives us abundance records of the whole An. maculipennis complex because there is a high inter-species similarity between adult Anopheles mosquitoes.

An. atroparvus is the only one of the complex that can be found in the Algarve [17] and Alentejo [18] and highly prevails in central Portugal (9 to 1 proportion) [19] and Serra da Estrela Natural Park (6 to 1 proportion) [20]. Other existing studies report a majority abundance of An. atroparvus, although they do not advance quantitative data (e.g. [20,21]).

With this information, we have managed to obtain a general abundance ratio of eight An. atroparvus to one An. maculipennis. Still, because even these higher abundance values are possibly biased due to the unevenness of the surveyed facilities, they were transformed into ‘presence only’ records. Absences too were obtained. However, only the sites where other mosquito species were present but An. maculipennis complex had null/reduced values of abundance (<2%) were considered. This allowed us to remove false absences due to mosquito mitigation actions and/or facility specific characteristics. A total of 76 presence and 16 absence records were referenced.

We conducted entomological surveys in 92 locations in well-known mosquito habitats (e.g. stables, pig and cattle shelters, and other animal hutches).

Data from all collection sites associated with mosquito development, were gathered [7]. Determining potential predictive variables among the factors that affect the distribution of the species is crucial to model potential habitats [22]. Knowing the significant ecological factors that play a relevant role in the distribution of the species is important to integrate independent variables into predictive models.

The selection of the environmental data with the uppermost predictive value was based on both prior knowledge of the prevailing factors in the distribution of An. atroparvus and data availability. Therefore, five environmental factors were selected [7], namely: i) mean maximum temperature of the warmest quarter; ii) mean minimum temperature of the coldest quarter; iii) mean total annual precipitation; iv) wetland density and suitability index; and v) agricultural density and suitability index.

The temperature is included because it has direct influence on the species’ physiology and behaviour [23] or indirect effect on the access to larval sites and on the depth variability of the water bodies. Using the mean maximum temperature of the warmest quarter and the mean minimum temperature of the coldest quarter together to represent a single ecological factor avoids the spatial and temporal homogenization that comes from the application of a unique annual mean model.

The precipitation is correlated with the productivity of the mosquito breeding sites. This is expressed on [24]. The precipitation was taken into account due to the strong effects on the productivity of the Anopheles’ breeding sites. Precipitation is highly correlated with the availability and characteristics (i.e. depth of the water bodies and the existence of temporary ponds) of An. atroparvus’ habitats in the aquatic phase of its life cycle [24]. Both temperature and precipitation datasets were downloaded in raster format (1km² grid) from the WORLDCLIM project (gridded climate data) [25]. The time period of the climatological records is from 1950 to 2000. This time period expresses the climatological variability occurred in Portugal in the last decades [26].

To include data on the abundance and closeness of the wetlands, which have a direct relationship with the aquatic life cycle of An. atroparvus [27], we have used the Corine Land Cover 2006 (CLC2006) spatial raster dataset for Portugal (the resolution of the data is 100 x 100 meters) which is produced by the European Environment Agency (EEA) (available at: http://www.eea.europa.eu/data-and-maps/data/corine-land-cover-2006-raster-3) [28]. The wetland density and suitability index; and agricultural density and suitability index was based on land use classes wetland and agricultural areas, respectively, by calculating a buffer with 10 km radius. We attributed different weights to each wetland category taking into account its known suitability for larval development of An. atroparvus. The categories that were taken into account were rice fields, inland marshes, large inland water bodies, estuaries, coastal lagoons, intertidal flats, permanently irrigated areas, watercourses, and salt pans. The final index results from the product of the density values and the factors used for weighting.

Finally, the agricultural density and suitability index was addressed as an indicator of highest An. atroparvus larval productivity [29]. For instance, due to the zoophilic nature of An. atroparvus places such as cattle farms have a high suitability for the development of large populations [9]. And because of this, we have assumed that areas characterized by a high agricultural intensity have a greater probability of containing cattle. This index comprised the following classes derived from the CLC2006s nomenclature: pastures, non-irrigated arable land, permanently irrigated land, rice fields, vineyards, fruit trees and berry plantations, olive groves, annual crops associated with permanent crops, complex cultivation patterns, land principally occupied by agriculture, with significant areas of natural vegetation and agro-forestry areas [28]. The final calculation was obtained in the same way as the wetland index.

For the suitability model for An. atroparvus, we have used five different algorithms (they are the most commonly used in recent studies), three of which had already been tested in previous experiments [7], i.e. Logistic Regression, Mahalanobis distance (D2), and Artificial Neural Networks (ANN), plus two added for this study, Maximum Entropy and a Genetic Algorithm.

The majority of the predictive models working on presence/absence data are derived from well-established statistical techniques [30]. One good examples of this type of approach is the use of logistic regression that does not require the normality assumption of independent variables and is more robust when the same is not met. These models are based on the existence of a simple function for the relationship between the presence/absence of species and a set of environmental variables [31]. These strategies can produce realistic and simple models for this high function interpretability in understanding natural processes.

All the models based in presence/absence datasets can be used with pseudo absences. The use of pseudo absences can include an error rate in the model because it can include suitability areas as ‘false zeros’[32]. However, the absence of evidence is not an evidence of absence. Absence records can be due only to chance.

For the models that were initially designed for only data of presence, the best way to sort them is in relation to the degree of complexity in the processes involved. The methods of distance (or similarity environmental models) are simple representations of the ecological niche. They are based on the existence of an optimum ecological point for each species defined by the central feature of the presence points in the ecological space.

Mahalanobis distance generates an ellipsoidal envelope around the optimum point of the ecological space. Mahalanobis distance includes greater complexity than simple Euclidean distance, because it takes into account the covariance matrix between the environmental variables in the occurrence. This allows to interpret the model as an expression of the environmental constraints that the species suffers including the correlations between variables, but requires a number of sample points greater than the number of environmental variables [33].

The Maxent (Maximum Entropy) starts a list of more complex models. This is a machine learning that estimates the probability distribution closer to uniform distribution under the restriction that the expected values for each environmental variable should follow the empirical values observed in the presences. Similarly to the logistic regression, the MaxEnt weighs each variable with a constant. The principle of maximum entropy indicates that the distribution model that satisfies all constraints should be as uniform as possible, allowing to make predictions from incomplete information [34].

Artificial neural networks (ANN) and GARP (genetic algorithm for rule set production). Both share a lot of theoretical structure common to auto-learning methods, i.e. artificial intelligence. The ANN are computational models inspired by the central nervous system that are able to perform machine learning processes. They are generally presented as systems of interconnected neurons that can compute, approximate and even incorrect, quantitative data, with a gradual degradation of the response. ANN have a great power of representation of knowledge through the creation of relationships between the weighted system entries but difficulty to turn explicit the knowledge acquired by the network through a language understandable by humans, i.e. black box models [35].

Finally, the GARP represents a hybrid technique that includes statistical techniques (logistic regression) and bioclimatic envelopes within a machine learning strategy. GARP is not a modelling technique for presence data because the adjustment is done by generating a set of pseudo absences. Though, it employs sophisticated techniques to treat this problem [36].

In order to calibrate each model the records dataset of An. atroparvus was split into both calibration (called the training set) and validation (or testing set) datasets. For that, we use a k-fold cross-validation, with the original sample randomly portioned into k = 3 equal sized subsamples. This method avoids the unnecessary use of records for validation, performing better than a unique validation set, when only a small amount of records (n = 92 in this case) exists [37].

Hence, three calibration/validation sets were created, each one of them composed of 13 records (2 absences and 11 presences). This value matches a random extraction by around 15% for each record type, permitting the prevalence of the species to remain unaffected in all the calibration sets. The advantage of this method is that all observations are used for both training and validation. Furthermore, each observation is only used once for validation.

The kappa index [38] was used as predictive evaluation measure. This index demonstrates the agreement between the correct classifications achieved and the expected by chance. Its values vary from 0 and 1. The value 1 corresponds to a perfect agreement between actual and obtained results. A common approach is to set a range of thresholds and calculate the corresponding kappa value for each one of them [39], and then, using the maximum kappa value as the predictive performance of every single model. The five predictive models were partitioned in 20 intervals of equal prediction amplitude (0.05) and the kappa value calculated for each one of the intervals (Table 1).

The results of the kappa index for each model demonstrate its predictive capability. For logistic regression, the maximum kappa was 0.77 and the maximum entropy 0.72. These values are considered ‘excellent’ [40]. The artificial neural network and genetic algorithm had a kappa index of 0.51 and a maximum Mahalanobis distance of 0.42.

For the combination of models we sum all five models weight by the normalized value of their maximum kappa value. The simultaneous use of several combined models has been used as a way to decrease the uncertainty [41]. However, depending on the method used, the final result (i.e. combined model) can either benefit from most accurate models [42]. [43] produced a comparative analysis of several strategies and argued that simple means tend to produce more robust solutions, while other studies point to weighted means approaches [44–46].

The mosquito abundance model used to estimate m was computed from this combined suitability map resulting from previous section. Another possibility was to use geostatistical techniques, such as co-Kriging, to retrieve abundance by interpolating directly from the environmental variables. Recent attempts using this technique [47] have only performed fairly R² = 0.58. Therefore, we chose to test two alternative methodologies.

First, based on the final predictive model of habitat suitability, a linear rescheduling [48] of suitability levels for An. atroparvus was undertaken using the abundance values of this species in different locations in mainland Portugal.

The maximum value of abundance was determined as the arithmetic mean of the 10 highest values of An. atroparvus’ abundance as recorded in field collections. In an attempt to achieve a better correlation between the abundance model and the actual species’ distribution, we tested two different models: 1) the values of the combined model of habitat suitability rescaled on the basis of the average of the 10 highest abundance field survey records; 2) the average value of the 10 lowest and 10 highest abundance records with a linear abundance estimation using the combined model of suitability. In the first test, we rearranged (Eq 2) the resulting values of the suitability combined model (S_cm) according to the average (342.7) of the 10 highest abundance records gathered in field surveys (Table 2). Based on this estimate, we obtained an abundance predictive model (A¹_pm) with values between 51 and 321 mosquitoes.

Second, in an attempt to evaluate other abundance predictive models, a second scenario was tested (A²_pm). This consisted in calculating average values from the 10 sites with the highest and lowest values of abundance taken from the combined model of suitability (Table 2). With these two values and the corresponding suitability averages, we performed a linear regression (Eq 3) to predict abundance from the combined models of suitability (Fig 1).

From these two scenarios, we chose the one with the lowest root mean square error (RMSE). This estimate was based on the differences between the abundance field values and their counterparts in each of the two models. This method showed that the first model performed better, with an RMSE of 141.3, as compared with 146 in the second model.

The model was completed after excluding urban areas, classes represented in the Corine Land Cover [49]. Based on An. atroparvus’ bionomics, these areas were not considered highly suitable habitats for mosquitoes. This species is mainly zoophilic, with a marked preference to feed in livestock and to rest inside animal shelters [6].

The urban land cover classes were distinguished from the Corine Land Cover 2006 [49] classes referenced as ‘Artificial surfaces’. However, the so-called ‘Mine, dump and construction sites’ were not taken into consideration because they would not be attractive to An. atroparvus; and the class ‘Sport and leisure facilities’ was included only when contiguous to the other selected classes (Table 3).

This information was converted into a raster structure of 1 km² and applied as an urban binary mask (U_mask), acting as a process of excluding areas for An. atroparvus’ presence (A¹_pm). Based on Eq 4, we developed a spatially continuous predictive model of abundance (A_map), where urban areas correspond to species-refractory areas.

Due to its linear estimation background over the combined model of habitat suitability, the abundance map reveals an identical spatial pattern showing a mosquito variation between 0 and 321 (Fig 1).

To determine the final m value, predicted abundance estimates of the vector species were divided by human densities determined through the number of residents by subsection (Fig 2), i.e. urban quarter. Resident population by subsection is produced by Statistics Portugal [50] available at http://mapas.ine.pt/download/index2011.phtml (converted into raster format: 1 km²)

The daily survival rate (p) can be computed as the i₀ root of the proportion of parous females, where i₀ is the period in days of the first gonotrophic cycle [51]. The proportion of parous females in the An. atroparvus population was determined by the ratio between the number of parous females and the number of field-collected females dissected. A parous rate of 0.9 was determined for the natural population during August, the most favourable month for malaria transmission. For the first gonotrophic cycle, this parameter was estimated by Sousa (2008) as 8.5 days. This value was determined with colony specimens (29 females) by averaging the number of days between the emergence of females and their first oviposition.

The duration of the sporogonic cycle in days (n) refers to the incubation period of the parasite inside the vector [52]. The time necessary for the extrinsic incubation period to take place depends on both parasite species and temperature (Lysenko and Levitanskaya, 1952; Pavlova, 1952, cited by [53].To study this entomological component we simulated three sporogonic cycle scenarios (in days), one for each type of plasmodium identified when malaria was endemic in Portugal, i.e. Plasmodium falciparum, Plasmodium vivax, and Plasmodium malariae (6). The n calculation was based on the method proposed by Moshkovsky [53], according to the following equation: n=T/(ta−tm) (5)

Here, n is the period in days of the extrinsic cycle of Plasmodia and T and t_m are constants for each species of human parasite, assuming the values of (T = 111; t_m = 16), (T = 105; tm = 14.5) and (T = 144; tm = 16) for P. falciparum, P. vivax, and P. malariae, in this order. The variable t_a refers to the average ambient temperature for the insect during the maturation phase.

Similarly to p, in this study, n estimates were computed only for August. This information was expressed in a continuous spatial model (Fig 3) using mean temperature values for the period 1950–2000 (WorldClim project) and assuming, according to the Moshkovsky method [53], that the parasites do not develop below 16°C.

Regional vulnerability is the proportion of infected humans with forms of the parasite that are also infective in mosquitoes. For the infected humans, we used for the A0 scenario the imported cases of malaria cases for the year 2013 [55].

The malaria patients diagnosed in Portugal was an significant increase from 2010 to 2013: 54 imported cases in 2010 to 123 imported cases in 2013 (Table 4).

Currently, the reported cases of malaria in Portugal are underestimated [56]. Therefore, in order to minimize this gap, and to come as close to reality as possible, we introduced scenarios A1 and A2. In these scenarios, we increased the number of infected people: 200 for scenario A1, and 400 for scenario A2. These infected people, for each model, were introduced randomly at municipality level.