Relevant literature was collected by searching the PubMed, Ovid, and the Armed Forces Pest Management Board Literature Retrieval System databases using combinations of search terms including Aedes aegypti, Stegomyia fasciata (previous name for Ae. aegypti), Aedes albopictus, dengue, experiment, import, incubation, transmission, temperature, and travel. We did not restrict the search based on time of publication or language. Further material was found by reviewing references from identified papers.

The moment when a mosquito becomes infectious is not directly observable, so observations of the EIP are restricted to the window between exposure(s) and transmission experiment(s), defined by a minimum and maximum EIP. For example, if a mosquito is shown to be infectious 10 days after exposure, the EIP must be between 0 and 10 days. If the same mosquito is tested at day 5 and does not transmit DENV at that time, the EIP is between 5 and 10 days. For each observation, the maximum EIP was defined as the time from the first infectious blood meal to the first successful transmission of DENV. If transmissibility was tested and never successful, the maximum EIP is unknown. The minimum EIP was the time from the last infectious blood meal to the last negative transmission experiment or zero if there were no negative transmission experiments.

Acceptable transmission assays involved the confirmation of transmission to a naïve individual as evidenced by the onset of dengue or by laboratory evidence of infection such as hemagglutination inhibition or plaque reduction neutralization assays. Because dengue is used as an indicator, there may be some false-negative tests resulting from asymptomatic infections. We initially assume that all negative tests are truly negative and revisit this assumption later.

Observations of the EIP were limited to those in which Ae. aegypti or Ae. albopictus were fed on viremic humans or non-human primates. We also excluded observations in which infection of the mosquito was attained by injection or by feeding on animal blood or artificial media seeded with DENV, as these may not realistically mimic natural transmission.

Temperature data were recorded for each EIP observation when available. For observations with no temperature data, we obtained temperature data for the location of the study at the time of year when the study was undertaken from the Climate Research Unit 30-year mean climatology dataset (CL 2.0) [27]. The available temperature data was used to calculate a spatially and seasonally matched mean temperature for each observation.

The IIP analysis was restricted to events in which humans became sick after being experimentally infected by Ae. aegypti or Ae. albopictus or after being naturally exposed to DENV within a defined period of time by travelling into or out of an area with ongoing DENV transmission. In this case, the end event, the onset of symptoms, was always observed, but the exact exposure time is only known in the case of experimental infections. In those cases, the IIP was directly observed and therefore uncensored. In other cases, the maximum and minimum IIP were defined as the time from the first and last potential exposures, respectively, to the onset of illness. For example, a traveler who became sick 3 days after returning from a 10-day trip may have been exposed at any time during the trip, so the IIP must be between 3 and 13 days.

Further ancillary data collected for the analyses included the serotype of virus when known. The data is available in Text S1.

The EIP and IIP data were both analyzed using censored time-to-event models. For the IIP observations with a single exposure and a known time of illness onset, the data are uncensored. For observations of EIP or IIP defined by an interval, the event is interval-censored, i.e. the event occurred sometime between the minimum and maximum times defined by the observations. Observations with only a minimum time are treated as right-censored data.

For each incubation period, we analyzed four common time-to-event models: exponential, Weibull, gamma, and log-normal. The specific formulations of each are given in Table 1. For each model, we assumed multiplicative hazards using linear covariates, defined by βX. For the EIP, we incorporated a covariate for temperature (T) to estimate the temperature sensitivity and a random effect (z) to control for inter-study (i) variation which may arise from unique study designs and unknown properties of a particular human, monkey, mosquito, or virus population:(1)

The IIP models only included the intercept β₀ and random effect, not the temperature covariate. We also evaluated possible differences between serotypes using a dummy variable for each serotype.

We fitted the models using Markov Chain Monte Carlo methods. We used weakly informative priors for all coefficients (Text S2). To improve sampling, the random effects were hierarchically centered on the intercept estimate and the temperature variable was mean-centered. Thus equation 1 becomes:(2)

The β₀ coefficient that we report is adjusted for this and the between-study variation so that it may be used directly without centering: . The IIP is only adjusted for between-study variation: . The between-study variation adjustment is necessary because e^βX is log-normally distributed such that this variance contributes to the expected mean.

We initialized three Markov Chain Monte Carlo chains for each model and ran them until convergence based on visualization and the Gelman-Rubin statistic [28]. We then continued sampling, using thinning to reduce first-order autocorrelation to below 0.1, until we had at least 1,000 independent samples for estimation of the posterior distributions. Model fit was compared using the deviance information criterion (DIC) [29]. The DIC rankings were further assessed via bootstrapping (Text S3). The analyses were performed in R 2.15.0 (www.r-project.org). OpenBUGS Version 3.2.1 [30] using R2OpenBUGS [31] (www.openbugs.info).

We identified 38 studies reporting relevant observations of natural EIP and IIP [3], [5], [12], [13], [14], [16], [17], [18], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61]. The crude data and further details regarding selection or exclusion of specific observations can be found in Text S1.

The EIP data included 146 observations from 8 studies published between 1905 and 1987 [3], [5], [12], [13], [14], [16], [32], [33]. In 109 instances, the EIP observation was interval-censored and in 37, right-censored. For 5 studies including 27 observations, serotype was unknown. The other three studies consisted of DENV-1 (49 observations), DENV-2 (38 observations), and DENV-4 (32 observations). Ae. aegypti were used for 140 of the observations and Ae. albopictus, for 6. The average temperature was reported for 54 observations and estimated for the remaining 92 based on average climate for the particular location and time of year. Overall, the average temperature ranged from 16.4 to 35.0°C with a median of 26.5°C.

For the IIP, 204 observations were collected from 35 studies published between 1903 and 2011 [3], [12], [13], [14], [16], [17], [18], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61]. The 8 studies prior to 1940 were experimental and included uncensored and some interval-censored observations. The other 27 studies occurred after 1970 and were all travel-related. These included only interval-censored and right-censored observations related to the period of travel. Altogether there were 131 uncensored observations, 58 interval-censored observations, and 15 right-censored observations. Serotype was not reported for 14 studies, totaling 39 observations (19%). DENV-1 was reported for 102 observations in 12 studies, DENV-2 for 6 observations in 6 studies, DENV-3 for 5 observations in 3 studies, and DENV-4 for 52 observations in 2 studies.

To characterize the EIP, we fitted four time-to-event models with temperature as a covariate and a random effect for each study. The models incorporating temperature and random effects (DIC range: 75–91) fitted better than models without temperature (DIC range: 104–116) and models without random effects (DIC range: 119–129). The 95% credible intervals (CI) for β_T (Table 2) indicate that the association between increased temperature and decreased EIP (Figure 1A–D), is significant for each model. Figure 1 shows the temperature-dependent mean and middle 95% of the respective distributions using the mean parameter estimates (Table 2). Qualitatively, the middle 95% of each estimated distribution crossed through the majority of the observed EIP intervals. The mean estimate for the EIP at 30°C ranged from 4.7 days in the Weibull model to 6.5 days in the log-normal model (Table 2). As measured by DIC, the model with the best fit was the log-normal model, followed by the gamma, Weibull, and exponential models, in order. Due to the close DIC values we performed a bootstrap analysis and found that the log-normal model consistently fit the data better than the other models (Text S3).

Assessment of mosquito infectivity relies on the demonstration of transmission, generally evidenced in this data as dengue in an experimentally exposed individual. Thus, some negative tests of infectivity may be incorrect. We repeated the analysis for the EIP without any of the negative observations which may have resulted from asymptomatic infection. The mean EIP at 30°C was similar to the model with the complete data, but the estimated effect of temperature was reduced (Table 2, Figure 2).

Only three studies contained serotype information for EIP observations, each implicating a single serotype. Because of the limited number of studies, each estimated coefficient was highly correlated with the random effect of the respective study such that inter-study variation could not be separated from potential inter-serotype variation. As only 6 observations were made using Ae. albopictus, we did not compare the EIP between species.

Using all of the data and omitting serotype information, the mean estimate for the EIP decreased from 15 days (95% CI: 10, 20 days) at 25°C to 6.5 days (95% CI: 4.8, 8.8 days) at 30°C (Figure 1D) in the log-normal model. To characterize the expected range of EIPs at a given temperature, we estimated the middle 95% of the posterior distribution. At 25°C, the middle 95% of the distribution was from 5 days (95% CI: 3, 8 days) to 33 days (95% CI: 23, 48 days). At 30°C, this range was 2.4 days (95% CI: 1.6, 3.3 days) to 15 days (95% CI: 10, 21 days).

Because of the differences between the pre-1940 and post-1970 observations, we modeled these subsets of data as well as the complete dataset independently using each of the 4 models and a random effect for each study. Inclusion of the random effects improved the fit of each model and dataset, with the exception of the exponential model and the post-1970 data (Text S3). The IIP data included multiple observations of each serotype in various studies, but covariates for serotype were not significant and did not improve the fit of the models (Text S3).

As shown in Figure 3, the estimated distributions for the completely censored post-1970 data are flatter than those for the pre-1940 data, likely reflecting the censoring in the observations rather than a change in the IIP. Furthermore, the post-1970 data contributes little to the fit of the complete dataset (Figure 3), so we focus our analysis on the 153 observations from the 8 pre-1940 studies. For this dataset, the gamma model provided the best fit followed by the log-normal, Weibull, and exponential distributions (Table 3). However, for bootstrapped samples of the pre-1940 datasets, the log-normal model provided a better fit in 71 out of 100 samples (Text S3). Thus, while the gamma model may fit the complete dataset better, the log-normal model may better fit any given subset of the data.

The gamma and log-normal models had similar qualitative fits (Figure 4) and equivalent mean expected IIPs of 5.9 days (Table 3). The middle 95% of the log-normal IIP distribution was 3.4 days (95% CI: 3.0, 3.7 days) to 10 days (95% CI: 9, 11 days). For the gamma distribution, the range was similar, from 3.4 days (95% CI: 2.9, 4.0 days) to 9 days (95% CI: 8, 11 days).