Downgrading disease transmission risk estimates using terminal importations

As emerging and re-emerging infectious arboviruses like dengue, chikungunya, and Zika threaten new populations worldwide, officials scramble to assess local severity and transmissibility, with little to no epidemiological history to draw upon. Indirect estimates of risk from vector habitat suitability maps are prone to great uncertainty, while direct estimates from epidemiological data are only possible after cases accumulate and, given environmental constraints on arbovirus transmission, cannot be widely generalized beyond the focal region. Combining these complementary methods, we use disease importation and transmission data to improve the accuracy and precision of a priori ecological risk estimates. We demonstrate this approach by estimating the spatiotemporal risks of Zika virus transmission throughout Texas, a high-risk region in the southern United States. Our estimates are, on average, 80% lower than published ecological estimates—with only six of 254 Texas counties deemed capable of sustaining a Zika epidemic—and they are consistent with the number of autochthonous cases detected in 2017. Importantly our method provides a framework for model comparison, as our mechanistic understanding of arbovirus transmission continues to improve. Real-time updating of prior risk estimates as importations and outbreaks arise can thereby provide critical, early insight into local transmission risks as emerging arboviruses expand their global reach.

1. Perfect observation. In this simulation, we assume that all cases are detected. For each simulation we begin with an initial index case. That case, and all subsequent cases, infect individuals according to a negative binomial distribution of mean, R 0 , and dispersion parameter k = 0.12. We continue the simulation until there are no more newly infected individuals. We only focus on R 0 < 1 for simulation purposes, so no outbreaks grow forever.
2. Imperfect observation. In this simulation, we add the observation process to the transmission process. We therefore simulate outbreaks according to the perfect observation process described above, and then simulate the reporting process. For this, we find the total number of detected cases from the chain according to simulating a binomial detection process with probability of success equal to the reporting rate (0.0574 in this case) and total possible cases equal to the size of the chain from the transmission chain (n).
3. Imperfect Import observation. This simulation is exactly the same as the imperfect observation simulation, except for the fact that we always detect the index case. So in this case we simulate a binomial detection process with probability of success equal to the reporting rate (0.0574 in this case) and total possible cases equal to the size of the transmission chain minus one (n − 1).

R 0 estimate validation
To validate our posterior R 0 distributions, we used them to estimate the expected number of autochthonous cases from the importations data through September of 2017 (at that time, the most recent importation was detected in mid-may) and compared the estimates to the actual reported autochthonous cases. We integrated uncertainty into our estimates as follows: 1. Draw a p d from the reporting rate distribution.
2. Sum the number of importations occurring for each county-month, N , 3. Draw N , samples of the prior or posterior R 0 , distribution depending on which analysis is being conducted.
4. For each of the R 0 , values, we simulated an outbreak stemming from a single importation where each case infects individuals according to a negative binomial distribution with mean of R 0 , and dispersion parameter, k = 0.12. For each simulated outbreak, we simulate the detection process for the non-index cases as a binomial distribution with probability of success, p d . We sum the detected cases for each of the N , outbreaks, to obtain, ν, the expected number of cases detected for that sample.
5. Repeat steps 1-4 10,000 times, saving ν The distribution of ν obtained from the process described above can be compared with the true number of detected autochthonous cases from 2017 if we assume that all imported cases were reported. However, it's likely that there were a number of imported cases that were missed by surveillance. Therefore, we also analyzed a scenario with increased importations. To do so we followed the same process outlined above, except for altering step 3 to draw N * ( 1 p d ) samples to account for the missed cases rounding the resultant number to the nearest integer.

Importation-based updates of transmission risk
Hypothetically, suppose that the first 15 imported cases of Zika into Texas arrived in August into Harris County (which contains Houston) without any detected autochthonous transmission. Prior to these importations, environmental suitability models yielded a relatively high local risk estimate with median Harris county R 0 above the epidemic threshold of one (Fig S7A -dark grey). The lack of secondary cases following all 15 importations suggests that R 0 may be lower. Indeed, our updated estimates suggest that the Harris county R 0 is likely below one (Fig S7A -light grey). Our method leverages such county-level importation data to update R 0 estimates throughout the state (via a scaling factor), based on the assumption that any a priori biases will be similar across counties (Fig 7B).