The study was carried out in the provinces of Belluno (46°08’27”N, 12°12’56”E) and Trento (46°04’00”N, 11°07’00”E), northern Italy. This mountainous area covers a large part of the Dolomites and the Southern Alps. More than 70% of the territory lies over 1,000 m a.s.l. and about 55% is covered by coniferous and deciduous forests [21]. The climate is temperate-oceanic with four main areas: sub- Mediterranean (close to Lake Garda with mild winters), subcontinental (the main valleys with more severe winters), continental (the alpine valleys) and alpine (the areas above the tree line) [21]. The human population as of 2014 is around 208,000 in the Belluno Province and 537,000 in the Trento Province with the majority of the population concentrated in the valley floors.

An entomological surveillance has been initiated in northeastern Italy since the introduction and establishment of Ae. albopictus in 1991 [22]. Furthermore, Aedes koreicus (Edwards, 1917), another invasive mosquito species, has been detected in the Belluno province in 2011 and in the Trento province in 2013 [23, 24]. Therefore, as part of the LExEM project (Laboratory of Excellence for Epidemiology and Modeling, www.lexem.eu), a mosquito monitoring focused on these two invasive Aedes species has been carried out in several localities of the provinces of Belluno and Trento ranging from 74m a.s.l. to 650m a.s.l. (see S1 Text). Seventy trapping locations in ten municipalities (Feltre, Povo, Riva del Garda, Santa Giustina, Strigno, Tenno, Tezze, Trento, Belluno and Rovereto) were selected by skilled entomologists in different places such as houses, schools, cemeteries, garden centers, public buildings, farms and tyre storage (Fig 1).

Mosquitoes were collected using Biogents Sentinel traps (Biogents AG, Regensburg, Germany) baited with BG lures and CO₂ from dry ice. Traps were placed in shaded positions sheltered from wind and rainfall as recommended by the manufacturer. All the collections were conducted in 2014. Each trap was set fortnightly for 24h from mid-April to the beginning of November except the trap of Rovereto which was set monthly from the end of June to the end of September. After each trapping session, mosquitoes were killed by freezing at -20°C and identified using taxonomic keys [25, 26] and confirmed by PCR if found in a location for the first time [26].

The MODIS sensors onboard the sun-synchronous polar-orbiting NASA satellites AQUA and TERRA are designed for global environmental monitoring, providing four records per day with a spatial resolution of 250 m to 1000 m. Most MODIS land products are accompanied by a detailed pixel-wise quality assessment, which facilitates further automated processing such as filtering and enhancement. Land surface temperature (LST) data for 2014 were obtained from the MODIS version 5 LST products MOD11A1 and MYD11A1 with four records per day and a spatial resolution of 1000 m. We applied outlier filtering and gap filling to these data and enhanced the spatial resolution to 250 m [27]. Here we used daily averages calculated from the four records per day of the reconstructed dataset.

We developed a mathematical model representing the dynamics of Ae. albopictus populations throughout the whole developmental cycle (eggs, larvae, pupae, female adults) within a single mosquito season (April to November). We adopted a compartmental structure similar to other models commonly used for Ae. albopictus [28–30] and other related species [31]. We used previous estimates of temperature-dependent rates of mortality, development from one stage to the next, and gonotrophic cycle [28] based on experimental data specific for Ae. albopictus [15]. The model is initialized at April 1^st 2014 with a fixed number of 10,000 mosquito eggs. The model robustness with respect to this assumption was verified by means of a sensitivity analysis. Abundance variability across sites was captured by local temperatures as well as by the estimation of a site-specific parameter summarizing the quantity and quality of breeding sites and representing the carrying capacity of the larval population. In other words, larval carrying capacity represents a measure of habitat suitability in our analysis. The process of capture of adults was modeled with a common capture rate across sites that was also estimated during the calibration process. We do not explicitly consider mosquito dispersal, because the average flight range of Ae. albopictus is much smaller (a few hundreds of meters [32]) than the scale of our risk predictions, which are given at the municipality level. However, the mosquito flight range was implicitly considered in the modeling of the capture process (see S1 Text). The number of captures estimated by the model was calibrated to experimental data by a Monte Carlo Markov Chain approach based on a Poisson likelihood combined over the capture sessions and ten study sites. All details are reported in the S1 Text.

We investigated the relationship between site-specific habitat suitability (encoded by values of the larval carrying capacity estimated by the population model) and two precipitation variables: the average daily rainfall (r_A) and the number of rainy days (d_r), calculated for each study site. We sampled 10,000 sets of values for the carrying capacities of the ten sites from their posterior distributions, and computed the precipitations occurring at the corresponding study sites within a given time window. We performed a correlation test with Spearman rank method between each set of carrying capacity values and the two precipitation variables. If the correlation was statistically significant (p<0.05), the value of Spearman’s rank correlation coefficient (ρ) was stored for that test; otherwise we considered the correlation coefficient to be zero. We then computed the 95% credible interval (CI) of the distribution of 10,000 correlation coefficients and considered the correlation to be robust if both boundaries resulted to have the same sign (i.e. either strictly positive or strictly negative). This procedure was iterated over 340 different temporal windows, starting on 34 different dates (between January 1^st and August 20^th 2014, with interval of one week) and with ten different window lengths (between 4 and 13 weeks). For instance, the first temporal window of 4 weeks starts on January 1^st and ends on January 28^th while the last temporal window of ten weeks starts on August 20^th and ends on November 10^th.

We assessed the potential risk of outbreaks of chikungunya and dengue caused by the introduction in the study sites of a single infectious individual, in the absence of control interventions. To this aim, we used mathematical formulae previously derived by the analysis of host-vector transmission dynamic models [33, 34]. These models assume the same SEI-SEIR epidemiological structure for both chikungunya and dengue: Ae. albopictus female adults may become infected after biting an infectious human host and start transmitting to other hosts after an incubation period and throughout the rest of their life (SEI). Human hosts may be infected by a bite of an infectious mosquito, develop symptoms after a latent period and may transmit to other mosquitoes for a given time, called infectious period (SEIR). The average number of mosquitoes infected by a single infectious human host in a population of fully susceptible mosquitoes and hosts is given by: RHV=k βVτVHωVωV+μV where k is the biting rate of mosquitoes, β_V is the probability of transmission to mosquitoes per bite, τ is the infectious period of a human host, V is the density of female adult vectors, H is the density of human hosts, ω_V is the inverse of the mosquito incubation period and μ_V is the mosquito mortality rate. Similarly, the average number of hosts infected by a single infectious mosquito introduced in a population of fully susceptible mosquitoes and hosts is given by: RVH=k βHμV where β_H is the probability of transmission to humans per bite.

The basic reproduction number (i.e. the average number of secondary human infections caused by the introduction of a single infectious host in a population of fully susceptible mosquitoes and hosts) can be simply computed as the product of these two quantities: R0=RHVRVH When a single infectious host is introduced in a population, the transmission process is stochastic and the host can heal before transmitting the infection even for values of R₀ much above the epidemic threshold, purely because of chance. In this case, transmission dies out early without causing an epidemic outbreak. The probability that an outbreak will actually take place can thus be defined, and for a SEI-SEIR model is given by [35]: pO=1−RVH+1RVH(RHV+1)

We compute the reproduction numbers and probabilities of outbreak for both chikungunya and dengue in the ten study sites at different times of introduction of the index case. In particular, the values for the transmission probabilities, host infectious period and mosquito incubation period were taken from [28] for chikungunya, and from [36] for dengue. The mosquito incubation period and the transmission probabilities for dengue (but not for chikungunya) have been shown to depend on temperature [36], according to formulae initially estimated by Focks and colleagues on Ae. aegypti [37]. We used these formulae to compute those parameter values over time based on the daily temperature recorded at each trap locations. For both chikungunya and dengue, we assumed the same biting rate of 0.09 bites per mosquito per day estimated for the chikungunya outbreak occurred in 2007 in Italy [28]. The density of human hosts was estimated by dividing the census population of municipalities considered in the study by the corresponding urban surface. Finally, the density of female adult mosquitoes was obtained by dividing model estimates of the total population by the surface of the modeled capture area (about 56 ha, see S1 Text). Differences across sites in human density, local temperatures influencing epidemiological parameters, and the estimated vector abundance translate into a geographical heterogeneity in the risk of outbreaks.

In Fig 2, we show the density of female adults over time as estimated by the model for the different study sites. The curves are substantially synchronized across sites due to the relative homogeneity of temperature patterns over time, although quantitative differences in average temperatures (see S1 Text) contribute to the geographical heterogeneity in mosquito abundance. The average peak density ranges from 17.0 (95% CI: 10.3–25.5) adult female mosquitoes per hectare in Strigno to 365 (95% CI: 264–562) in Riva del Garda. These estimates were quite robust with respect to the model assumption on the initial number of eggs (see S1 Text).

Overall, the general seasonal pattern is well reproduced both qualitatively and quantitatively by the model (see S1 Text). Fig 3 shows boxplots of the distribution of errors between the observed number of captured females and corresponding model estimates (with 95% CI) for the ten study sites, normalized by the corresponding maximum number of captured females during the season to allow comparability across sites. In Table 1, we reported two metrics to assess the goodness of fit: the value of R² between predicted and observed values and the root mean squared error, normalized by the maximum number of captured females (nRMSE). Both metrics are obtained by averaging over the 10,000 stochastic simulations. Two sites, Strigno and Belluno, are characterized by a lower R² and higher nRMSE. The poorer fit at these two sites can be explained with the low estimated local mosquito abundance (see Fig 2), resulting in a stronger variability driven by stochastic effects in the capture process. Posterior means and 95% CI of estimates for the capture rate (α₀) and the site-specific larval carrying capacities (a_s), as estimated by the MCMC procedures, are reported in Table 2.

A robust association between the average daily amount of precipitations and the estimated carrying capacities was found only in one time window, covering the period May 1^st—June 5^th, with a strong negative correlation (average Spearman’s ρ = -0.76; 95% CI: -0.69 –-0.82). When considering the number of rainy days, a negative correlation was also found for 17 time windows, covering periods between April 17^th and July 17^th (average ρ ranging between -0.70 and -0.84, depending on the time window, see S1 Text). Thus, late spring/early summer precipitations contribute negatively to local mosquito abundance and therefore to transmissibility of arboviruses. Figs 4 and 5 show the predicted peak value of R₀ in the ten study sites for chikungunya and dengue respectively, against four site-specific variables: local altitude (computed as an average between the altitudes of active traps), average daily rainfall between May 1^st and June 5^th, average temperature between April 1^st and October 31^st, and urban density. These figures summarize the effects of different local environmental factors on the geographic heterogeneity in the transmissibility of arboviral diseases. A Spearman rank correlation test between the peak value of R₀ for each disease and each variable was computed, and the results are summarized in Table 3. Lower altitudes and higher temperatures significantly increase R₀ by creating favorable conditions for the vector population. Conversely, an excess of precipitations in late spring is associated with a reduction in the larval carrying capacity and, therefore, in the amount of mosquitoes available for transmission. Finally, urban population density does not seem to have a strong effect on the transmissibility of disease, despite the fact that this variable appears directly in the denominator of R₀. This is explained by considering that, in a mountainous region such as the one under study, densely populated areas are concentrated at the bottom of the valleys, characterized by lower altitudes and warmer temperatures. Therefore, the negative effect of higher urban density on transmission is offset by the presence in the same sites of higher vector densities.

We estimated the basic reproduction number of a potential chikungunya outbreak originated by a single imported case. The peak value of R₀ is highly heterogeneous across sites, ranging from 0.25 (95%CI: 0.15–0.38) in Strigno to 2.9 (95% CI: 2.0–4.2) in Feltre and occurring, depending on the site, between mid-August and mid-September. The latter compares well with the R₀ estimated for the chikungunya outbreak occurred in the Italian region of Emilia-Romagna in 2007 [28] and suggests the existence of further areas where similar outbreaks are likely to occur. Fig 6 reports the corresponding probability of observing an outbreak for different times of importation of the index case in the ten study sites. The three sites characterized by lowest estimated mosquito abundance (Strigno, Tenno and Belluno) are, according to the model, virtually safe from possible outbreaks. For all other sites, we can define a “chikungunya season” as the period over which the probability of observing an outbreak is higher than zero. The probability of an outbreak, averaged within each site’s chikungunya season, ranges from 4.9% in Tezze over a period of just below two months (end July to mid-September), to 25% in Feltre for a duration of 4.5 months covering the whole summer and up to mid-November. The peak probability within these seasons ranges from 8.6% (95% CI: 0.0–23.2%) in Tezze to 38.3% in Feltre (95% CI: 25.0–51.2%).

Equivalent model predictions for dengue suggest generally lower values of R₀ than for chikungunya. This is due to lower average transmissibility (confirmed experimentally in Ae. albopictus from northern Italy [38] and France [3]) and longer incubation periods [37, 38], resulting in longer generation times, so that a higher proportion of mosquitoes die while in the exposed (non-infectious) phase. Peak values of R₀ range from 0.15 (95% CI: 0.09–0.22) in Strigno to 2.3 (95% CI: 1.7–3.3) in Riva del Garda and occur generally at the end of July, i.e. earlier than chikungunya. The anticipated peak of dengue transmissibility depends on the steady decrease of temperatures registered in 2014 after the end of July across all study sites (see S1 Text), which has reduced the estimated transmission probability and increased the incubation period [37], thereby offsetting the continued growth of vector abundance throughout August. Fig 7 shows the predicted probability of observing a dengue outbreak at different times of importation. Predictions are much more erratic over time than for chikungunya due to the strong temperature dependence assumed for dengue epidemiological parameters. Tezze adds to the list of virtually outbreak-free study sites, and the probability of outbreaks averaged over dengue seasons ranges from 4.2% in Trento, with a season length of one month across the end of July, to 10.8% in Riva del Garda over a two-month season that extends up to mid-September. The peak probability ranges from 12.1% (95% CI: 1.2–24.8%) in Trento to 27.8% (95% CI: 16.5–40.9%) in Riva del Garda.

A spatial interpolation of R₀ is not possible, given the small number of data points (ten, i.e. one for each study site). For the same reason, a multivariate analysis to assess the contribution of environmental factors to local mosquito abundance or transmissibility would be statistically underpowered. Therefore, to provide spatial estimates of possible ranges of the outbreak risk, we applied our model to predict vector densities within the provinces of Trento and Belluno, based on local temperature records from satellite data and considering spatially constant values of the larval carrying capacity (see S1 Text). Afterwards, we computed the corresponding outbreak risks using population density maps derived from high-resolution census data. In Fig 8, we show the peak values of the outbreak risks for both infections in the worst-case scenario, i.e. using the maximum value of the larval carrying capacity estimated among our ten study sites. Fig 8 shows that areas with highest risk are rural villages placed at the bottom of the main valleys, where vector populations are predicted to be most abundant while human density is relatively lower. Minor valleys may be considered potentially free from the risk of outbreaks because of their lower mosquito abundance, which is in turn due to lower average temperatures. In the worst-case scenario, the fraction of the population living in areas with peak outbreak risk higher than zero is up to 74% of the total for chikungunya and 50% for dengue. However, the importation of a case in the study area at the exact time of the peak has a limited probability of generating an outbreak: on average 33% for chikungunya and 16% for dengue. The fraction of the population living in areas with a risk of outbreak higher than 50% after importation of a case at the time of highest risk is 25% for chikungunya and 6% for dengue. These results are in agreement with the specific findings obtained for the 10 study sites where entomological surveillance was carried out.