The analysis presented here gives a comprehensive description of the distributions of the incubation periods of yellow fever virus in humans and Ae. aegypti mosquitoes and quantifies the effect of temperature on the extrinsic incubation period. The information gleaned from the models presented significantly enhances the understanding of these critical measures of yellow fever activity.
Data relevant to these incubation periods are scarce because of the fact that they were mostly obtained in unrepeatable experiments and through observations made at a time when yellow fever was more common and little was known about its etiology.2
Because of the paucity of these data, we were meticulous and cautious in our approach to data collection, using available descriptions to substantiate observations from studies when the mode of exposure was not yet known, and excluding cases where too little information was available. We also estimated the average temperature for some of the observations and accounted for the considerable uncertainty of all the temperature data using a Bayesian approach. Furthermore, we used time-to-event models to allow various forms of time-censored data to be explicitly incorporated.
In this analysis, we defined the intrinsic incubation period as the time from exposure to illness. Although this definition is clinically relevant, it does not inform us about the course of infection in asymptomatic infections nor does it necessarily relate to the probability or timing of the human becoming infectious, a critical component for understanding the possibility of continued transmission. We would have liked to describe this time period as well, but the data on human infectiousness are extremely limited. The only pertinent observations we found were those discussed by Hindle,21
who demonstrated that human blood is not infectious during the intrinsic incubation period but that it is infectious during the first 3–4 days of fever. This suggests that the infectious period likely begins at roughly the same time as the onset of fever in symptomatic cases.
We compared four models to describe each period. The single-parameter exponential model implies a constant hazard rate, unlike the other three models. In terms of the intrinsic incubation-period model fitted here, this means that approximately 18% of exposed people become symptomatic each day post-exposure, regardless of if it is the first or tenth day. Although this may be a reasonable model and is often used because of its simplicity, it provided the worst fit of the models used here. The other three models were qualitatively similar, with the log-normal model having the best fit as measured by the DIC. The median intrinsic incubation period for the log-normal model was estimated to be 4.3 days with the middle 95% of symptomatic yellow fever cases having an illness onset between days 2.2 and 8.6 post-exposure. These estimates are similar to a previously published range of 3–6 days.23
The parametric model, however, gives a more comprehensive picture of the whole distribution, while also allowing further calculations, such as the cumulative probability of becoming ill within the first 3 days post-exposure (15%) or the range over which the middle 50% of cases develop symptoms (3.4–5.5 days).
As expected based on previous work with yellow fever21,25
and other flaviviruses,26,45,46
the extrinsic incubation period varied with temperature. The fitting of a parametric model in this case has the same advantages as described above for the intrinsic incubation period with the added benefit of being able to characterize the temperature dependence and thus, predict the period under different temperature conditions. The effect of temperature is of high importance compared with the expected life span of Ae. aegypti
mosquitoes. The lowest temperature at which yellow fever infectiousness has been observed to develop in a mosquito is approximately 16.5°C.21
Although the model predicts that it may occur at lower temperatures, the estimated life span of a mosquito is 30–50 days under ideal conditions,47
and it is shorter at lower temperatures,48
making it unlikely for a mosquito to survive a complete incubation period. At higher temperatures, in contrast, the probability of a mosquito surviving the much shorter incubation period is correspondingly greater. Temperatures greater than 35°C, however, also negatively affect Ae. aegypti
activity and survival,48
and it is, therefore, unlikely that model estimates for temperatures in this range have biological significance.
The analysis presented here has several potential uses including mathematical modeling, which is increasingly used to simulate transmission scenarios or identify vaccination targets.49,50
Use of appropriate models for incubation periods is vital to constructing reasonable models. Selection of exponential models for incubation periods when other models are more appropriate, for example, can lead to significant underestimation of transmission potential.51
This incubation-period analysis is also useful in clinical settings and the management of outbreaks. It enables the estimation of past and future transmission risk and may help in diagnosing yellow fever virus infections in individuals who have traveled from endemic areas or who have become ill during an outbreak. More specifically, when a patient presents with yellow fever-compatible symptoms, knowledge of where they were in the previous 2–9 days can eliminate or support a diagnosis, with added weight given to a positive diagnosis when the onset of fever is closest to the median time of 4.3 days. Many diseases may present similarly to yellow fever, and some, such as viral hepatitis, have much longer incubation periods of 2 or more weeks.52
When a case of yellow fever is diagnosed, these models provide a tool to estimate when and where exposure may have occurred (if unknown a priori
) and where further risk may be present. Furthermore, because the incubation periods regulate the speed of transmission cycles, they are useful in determining the time frame for declaring that an urban outbreak is over and for assessing the success of or need for interventions. The temperature dependence of the extrinsic incubation period in particular is very important because of the influence of geographical and temporal temperature variation on the transmission cycle.