Real-time Zika risk assessment in the United States

27 Recent Zika Virus (ZIKV) outbreaks in southern Florida have heightened public health concern 28 across the southern United States. As autochthonous (locally-acquired) cases accumulate within the US, 29 policymakers seek early and accurate indicators of self-sustaining transmission to inform intervention 30 efforts in high risk areas. However, given ZIKV’s low reporting rates and the geographic variability in 31 both importations and transmission potential, a small cluster of reported cases may reflect diverse 32 scenarios, ranging from multiple self-limiting but independent introductions to a self-sustaining local 33 epidemic. We developed a stochastic model that captures variation and uncertainty in ZIKV case 34 reporting, importations, and transmission, and applied it to assess county-level epidemic risk throughout 35 the state of Texas. For each of the 254 counties, we estimated the future epidemic risk as a function of 36 reported autochthonous cases and evaluated a national recommendation to trigger interventions 37 immediately following the first two reported cases of locally-transmitted ZIKV. Our analysis suggests 38 that the regions of greatest risk for sustained ZIKV transmission include 21 Texas counties along the 39 Texas-Mexico border, in the Houston Metro Area, and throughout the I-35 Corridor from San Antonio to 40 Waco. Variation in vector habitat suitability and importation risk drives epidemic risk variation. Upon 41 detection of two locally transmitted cases in a spatiotemporal cluster, the threat of epidemic expansion 42 depends critically on local vulnerability. For high risk Texas counties, we estimate this likelihood to be 43 64%, assuming an August 2016 risk projection and a 20% reporting rate. With reliable estimates of key 44 epidemiological parameters, including reporting rates and vector abundance, this framework can help 45 optimize the timing and spatial allocation of public health resources to fight ZIKV in the US. 46 47 48 49 50 51 52 Author Summary 53 Given the growing threat of Zika Virus (ZIKV) in the southern US and the critical importance of 54 early intervention, public health decision makers seek early and accurate indicators of local transmission. 55 However, given ZIKV’s low reporting rates and the geographic variability in both importations and 56 transmission potential, a small cluster of reported cases may reflect diverse scenarios, ranging from 57 multiple self-limiting but independent introductions to a self-sustaining local epidemic. To support real58 time risk assessment of emerging ZIKV outbreaks at a county level, we developed a quantitative 59 framework that estimates current ZIKV burden and future epidemic threat based on recent reported cases 60 and the underlying risks of ZIKV importation and transmission. We assessed ZIKV risk in Texas and 61 found that 21 of the 254 counties are potentially vulnerable to locally-transmitted ZIKV outbreaks. The 62 high risk region includes much of the Texas-Mexico border, the Houston Metro Area, and patches along 63 the I-35 Corridor from San Antonio to Waco. If two locally transmitted and epidemiologically linked 64 cases are detected in one of these counties, we estimate a 64% risk of imminent epidemic expansion. 65 66 Introduction 67 In February 2016, the World Health Organization (WHO) declared Zika virus (ZIKV) a Public 68 Health Emergency of International Concern [1]. As of 18 August of 2016, the WHO confirmed 69 mosquito-transmitted cases in 70 countries and territories, with over 500,000 suspected and confirmed 70 cases in the Americas alone [2,3]. In the US, the 46 reported autochthonous (local) ZIKV cases all 71 occurred in Southern Florida, but the potential range of a primary ZIKV vectors, Aedes aegypti, may 72 include over 30 states [4,5]. Texas is a particularly vulnerable state, given its suitable climate, 73 international airports, and geographical proximity to affected countries [4,6–10]. Of the 2,487 imported 74 ZIKV cases in the US that have been identified, 137 have occurred in Texas through the end of August. 75 While these importations have yet to spark autochthonous transmission within the state, Texas has 76 historically sustained several small, autochthonous outbreaks (ranging from 4 25 confirmed cases) of 77 another arbovirus vectored by Ae. Aegypti—dengue (DENV) [11–13]. 78 As peak mosquito season continues in the US and more cases are introduced via international 79 travelers from the Americas, public health decision makers will face considerable uncertainty in gauging 80 the severity of the threat and in effectively initiating interventions, given the large fraction of undetected 81 ZIKV cases (asymptomatic and symptomatic) as well as the challenge in estimating the economic tradeoff 82 of disease prevention versus disease response [14–17]. Depending on the ZIKV symptomatic fraction, 83 reliability and rapidity of diagnostics, importation rate, and transmission rate, the detection of five 84 autochthonous cases in a single Texas county, for example, may indicate a small chain of cases from a 85 single importation, a self-limiting outbreak, or even a large, hidden epidemic underway (Fig 1). These 86 diverging possibilities have historical precedents. In French Polynesia, a handful of suspected ZIKV cases 87 were reported by October 2013; two months later an estimated 14,000-29,000 individuals had been 88 infected [14,15]. By contrast, Anguilla had 17 confirmed cases from late 2015 into 2016 without a 89 subsequent epidemic, while many surrounding countries experienced large ZIKV epidemics [18]. To 90 address the uncertainty, the CDC recently issued conservative guidelines for state and local agencies; they 91 recommend initiation of public health responses following local reporting of two non-familial 92 autochthonous ZIKV cases [19]. 93

importation scenario, in which the first quarter cases (27) in Texas represent only the 137 symptomatic (20%) imported cases, corresponding to a projected third quarter statewide 138 importation rate of 4.5 cases per day. 139 2. We defined county-specific import risk as the probability that the next imported case in Texas 140 will occur in that county. To build a predictive model for import risk, we fit a probabilistic model 141  (Tables S3-S4). 159

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Estimating County Transmission Risk 161 The risk of ZIKV emergence following an imported case will depend on the likelihood of 162 mosquito-borne local transmission. For each Texas county, we used the Ross-Macdonald formulation to 163 estimate the ZIKV reproduction number (R 0 ), which is the average number of secondary infections caused 164 by the introduction of a single infectious individual into a fully susceptible population (Supplement §1.2) 165 [27]. To parameterize the model (Table S5) To transmit ZIKV, a mosquito must bite an infected human, the mosquito must get infected with 175 the virus, and then the infected mosquito must bite a susceptible human. We assumed that mosquito-borne 176 transmission would be the main driver of epidemic dynamics, so we did not include sexual transmission 177 in our model. Rather than explicitly model the full transmission cycle, we aggregated the two-part cycle 178 of ZIKV transmission (mosquito-to-human and human-to-mosquito) into a single exposure period where 179 the individual has been infected by ZIKV, but not yet infectious, and do not explicitly model mosquitos. 180 For the purposes of this study, we need only ensure that the model produces a realistic human-to-human 181 generation time of ZIKV transmission. 182 The resultant model thus follows a Susceptible-Exposed-Infectious-Recovered (SEIR) 183 transmission process stemming from a single ZIKV infection using a Markov branching process model 184 ( Fig S2). The temporal evolution of the compartments is governed by daily probabilities of infected 185 individuals transitioning between S, E, I, and R states, and new ZIKV cases arising from importations or 186 autochthonous transmission (Table S6). We treat days as discrete time steps, and the next disease state 187 progression depends solely on the current state and the transition probabilities. We assume that infectious 188 cases cause a Poisson distributed number of secondary cases per day (via human to mosquito to human 189 transmission), but this assumption can be relaxed as more information regarding the distribution of 190 secondary cases becomes available. We also assume infectious individuals are introduced daily according 191 to a Poisson distributed number of cases around the importation rate. Furthermore, Infectious cases are 192 categorized into reported and unreported cases according to a reporting rate. We assume that reporting 193 rates approximately correspond to the percentage (~20%) of symptomatic ZIKV infections [16] and occur 194 at the same rate for imported and locally acquired cases. Additionally, we make the simplifying 195 assumption that reported cases transmit ZIKV at the same rate as unreported cases. We track imported 196 and autochthonous cases separately, and conduct risk analyses based on reported autochthonous cases 197 only, under the assumption that public health officials will have immediate and reliable travel histories for 198 all reported cases [28]. 199 To accurately model the timing of ZIKV outbreaks, we fit the ZIKV generation time to recent 200 estimates (Supplement §2.4) [29]. The generation time measures the average duration from initial 201 symptom onset to the subsequent exposure of a secondary case, and is estimated to range from 10 to 23 202 days for ZIKV [29]. In our model, the generation time corresponds to the exposure period followed by 203 half of the infectious period. First, we fit the infectious period in our model to human ZIKV estimates for 204 duration of viral shedding, which we assumed to be the length of the infectious period, but may be an 205 underestimate of the total length. Specifically, we solved for transition rates of a Boxcar Model [30] that 206 produce an infectious period with mean duration of 9.88 days (Table S6)  For each county risk scenario, defined by a specified importation rate, transmission rate, and 217 reporting rate, we ran 10,000 stochastic simulations. Each simulation began with a single imported 218 infectious case and terminated either when there were no individuals left in either the Exposed or 219 Infectious classes or the cumulative number of autochthonous infections reached 2,000. We classified 220 simulations as either epidemics or self-limiting outbreaks; epidemics were all simulations that fulfilled 221 two criteria: reached 2,000 cumulative autochthonous infections and had a maximum daily prevalence 222 (which we defined as the number of current infectious cases) exceeding 50 autochthonous cases (Fig S3). 223 The second criterion distinguishes simulations resulting in large self-sustaining outbreaks (that achieve 224 substantial peaks) from those that accumulate infections through a series of small, independently sparked 225 clusters (that fail to reach the daily prevalence threshold). The latter occurs occasionally under low R 0 s 226 and high importation rates scenarios. 227 For simulations resulting in epidemics, the cumulative reported autochthonous infections may 228 include cases from several co-occurring or proximate transmission clusters, as might occur in actual 229 outbreaks. To verify that our simulations do not aggregate cases from clusters with clear temporal 230 separation, we calculated the distribution of times between sequential cases (Fig S4). In our simulated Policymakers must often make decisions in the face of uncertainty, such as when and where to 237 initiate ZIKV interventions. Our stochastic framework allows us to provide real-time county-level risk 238 assessments as reported cases accumulate. For each county, we found the probability that an outbreak will 239 progress into an epidemic (reach 2,000 cases with a maximum daily prevalence over 50), as a function of 240 the number of reported cases. We call this epidemic risk. To solve for epidemic risk in a county following 241 the xth reported autochthonous case, we first find all simulations (of 10,000 total) that experience at least 242 x reported autochthonous cases, and then calculate the proportion of those that are ultimately classified as 243 epidemics. For example, consider a county in which 1,000 of 10,000 simulated outbreaks reach at least 244 two reported autochthonous cases; the remaining 9,000 simulations dissipate with only one or zero case 245 reports. If only 50 of the 1,000 simulations ultimately fulfill the two epidemic criteria, then the estimated 246 epidemic risk following two reported cases in that county would be 5%. This simple classification scheme 247 performs quite well, only rarely misclassifying a string of small outbreaks as an epidemic, with the 248 probability of such an error increasing with the importation rate. For example, epidemics should not occur 249 when R 0 =0.9. If the importation rate is high, however, overlapping series of moderate outbreaks may 250 occasionally meet the two epidemic criteria. Even under the highest importation rate we considered (0.3 251 cases/day), only 1% of outbreaks were misclassified. 252 This method can be applied to evaluate universal triggers (like the recently recommended two-253 case trigger) or derive robust triggers based on local importation and transmission risks as well as the risk 254 tolerance of public health agencies. For example, if a policymaker would like to initiate interventions as 255 soon as the risk of an epidemic reaches 30%, we would simulate local ZIKV transmission and solve for 256 the number of reported cases at which the probability of an epidemic first exceeds 30%. Generally, the 257 recommended triggers decrease as the policymaker threshold for action decreases (for example, 258 policymakers would act sooner (fewer reported cases) for a 10% versus 30% threshold) and as the local 259 transmission potential increases (e.g. R 0 = 1.5 versus R 0 = 1.2). A policymaker wishing to trigger 260 interventions early, upon even a low probability of epidemic spread, has a low tolerance for failing to 261 intervene but may waste resources on unnecessary interventions; a policymaker willing to wait longer, 262 has a higher risk tolerance, but may implement interventions too late in the course of the outbreak. 263

County Uncertainty Analysis 265
We took two approaches to addressing uncertainty in the model parameters. First, we conducted a 266 sensitivity analysis to address the considerable uncertainty regarding several inputs into our estimation of 267 R 0 , including mosquito biology, ZIKV epidemiology, and human-mosquito interactions (Supplement §4). 268 For most factors, the county estimates of R 0 simply scale linearly with changes in the factor. However, 269 county-specific human-mosquito contact rates can change relative county risks based on assumptions 270 regarding the socioeconomic effect on human-mosquito interactions (Fig S6-7), and county risk moves 271 southward as the summer heat subsides (Fig S8). Second, given the considerable uncertainty regarding 272 ZIKV epidemiology, we examined a scenario where the absolute values of both R 0 and importation rate 273 are unknown, but lie within plausible ranges for Texas. To do so, we randomly sampled 10,000 274 simulations from the high risk Texas county outbreaks (counties with estimates of R 0 >1), creating an 275 amalgamous high risk county, and completed the outbreak analysis as we do with individual counties. 276 277

Results 278
To develop a ZIKV risk assessment framework for Texas counties, we first estimate county-level 279 ZIKV importation and transmission rates for August 2016. ZIKV importation risk within Texas is 280 predicted by variables reflecting urbanization, mobility patterns, and socioeconomic status (Table S3), 281 and is concentrated in metropolitan counties of Texas (Fig 2A). The two highest risk counties--Harris, 282 which includes Houston and has an estimated 27% chance of receiving the next imported Texas case, and 283 Travis, which includes Austin and has a 10% chance of the next importation--contain international 284 airports. Other high risk regions include Brazos County, the Dallas and San Antonio metropolitan areas, 285 and several counties along the Texas-Mexico border. 286

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and yellow increasing to red counties indicate R 0 s > 1 (See Fig S7-11 for sensitivity analysis).

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Our county-level estimates of autochthonous ZIKV transmission risk (Fig 2B) suggest that the 294 majority of Texas counties (87%) have an estimated R 0 below one, and thus are unlikely to sustain 295 epidemics. The Southeast region of Texas has the highest estimated transmission risk, driven primarily by 296 high mosquito habitat suitability. These estimates are sensitive to uncertainty in several parameters (Fig  297   S7-11), and can be updated as we learn more about ZIKV. While the average transmission risk may be 298 higher or lower than our baseline assumption, and certainly varies seasonally, the relative high and low 299 risks areas of the state are robust (Fig S7-11), and allow us to conduct plausible case studies and identify 300 at risk areas for enhanced surveillance and preparedness efforts. However given the uncertainty 301 underlying specific county R 0 estimates, we also aggregate the 21 highest absolute estimates into a 302 plausible distribution for any high risk Texas county, ranging from R 0 = 1.0 to R 0 = 2.2 with a median of 303

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Under a single set of epidemiological conditions, wide ranges of outbreaks are possible (Fig 3A). 305 The relationship between what policymakers can observe (cumulative reported cases) and what they wish 306 to know (current underlying disease prevalence) can be obscured by such uncertainty, and will depend 307 critically on both the transmission and reporting rates (Fig 3B). If key drivers, such as R 0 , can be 308 estimated with confidence, then the breadth of possibilities narrows, enabling more precise surveillance. 309 For example, under a known high risk R 0 scenario and with a 20% reporting rate, ten linked cumulative 310 autochthonous reported cases corresponds to 6 currently circulating cases with a 95% CI of 1-16; under 311 an unknown but high risk R 0 scenario, the same number of cases corresponds to an expected daily 312 prevalence of 10 cases with a much wider 95% CI of 2-32 ( Fig 3B).

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We apply our model to characterize time-varying epidemic risk as cases accumulate in a given 325 county. Under both a known and unknown high risk scenario, we track the probability of epidemic expansion following each additional reported case (Fig 3C). Across the full range of reported cases, the 327 probability of epidemic spread is always higher in the unknown, compared with the known high risk 328 scenario showing more sensitivity to the reporting rate. These curves can support both real-time risk 329 assessment as cases accumulate and the identification of surveillance triggers indicating when risk 330 exceeds a specified threshold. For example, suppose a policymaker wanted to initiate an intervention 331 upon two reported cases and thought the reporting rate was 20%, this would correspond with a 64% 332 probability of an epidemic in the unknown high risk county but only 35% in the known high risk county. 333 Alternatively suppose a policy maker wishes to initiate an intervention when the chance of an epidemic 334 exceeds 50%. In the unknown high risk scenario, they should act immediately following the 1st 335 autochthonous reported case; in the known high risk scenario, the corresponding trigger ranges from two 336 to seven autochthonous reported cases, depending on the reporting rate. As the policymaker's threshold 337 (risk tolerance) increases, the recommended surveillance triggers can be adjusted accordingly. 338 To evaluate a universal intervention trigger of two reported autochthonous cases, we estimate 339 both the probability of a trigger event (two such cases) in each county and the level of epidemic risk at the 340 moment a trigger event occurs (second case reported) in each county. Assuming a baseline importation 341 rate extrapolated from recent importations to August 2016 and a 20% reporting rate, only a minority of 342 counties are likely to experience a trigger event (Fig 4A). While 231 of the 254 counties (91%) have non-343 zero probabilities of experiencing two reported autochthonous cases, only 63 counties have at least a 10% 344 chance of such an event, with the remaining 168 counties having a median probability of 0.017 (range 345 0.0004 to 0.089). Next, assuming that a second autochthonous case has indeed been reported, we find that 346 the underlying epidemic risk varies widely among the 231 counties, with most counties having near zero 347 epidemic probabilities and a few counties far exceeding a 50% chance of epidemic expansion. For 348 example, two reported autochthonous cases in Starr County, along the Texas-Mexico border, correspond 349 to a 99% chance of ongoing transmission that would proceed to epidemic proportions without 350 intervention. The greater San Antonio metropolitan region appears to be the highest risk metropolitan 351 region with four of its eight counties having a higher than 25% probability of experiencing two reported 352 autochthonous cases; in those four counties, the epidemic risk upon detection of a second case ranges 353 from 19-90%. Houston metropolitan region is also a high risk region with its second (Fort Bend) and 354 fourth (Brazoria) largest counties having a 39% and 45% chance of sustaining two reported 355 autochthonous cases, respectively, with corresponding epidemic risks of 67% and 86% thereafter.

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White counties never reach two reported cases across all 10,000 simulated outbreaks; light gray counties reach two cases, but 361 never experience epidemics. (C) Recommended county-level surveillance triggers (number of reported autochthonous cases)

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indicating that the probability of epidemic expansion has exceeded 50%. White counties indicate that fewer than 1% of the 363 10,000 simulated outbreaks reached two reported cases. All three maps assume a 20% reporting rate and a baseline importation

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Given that a universal trigger may signal highly disparate levels of ZIKV risk, policy makers 368 might seek to adapt their triggers to local conditions. Suppose a policymaker wishes to design triggers 369 that indicate a 50% chance of an emerging epidemic (Fig 4C). Under the baseline importation and 370 reporting rates, only 21 of the 254 counties in Texas are expected to reach a 50% epidemic probability, 371 with triggers ranging from one (Starr County) to 21 (Dimmit County) reported autochthonous cases, with 372 a median of two cases. The remaining counties have less than a 1% chance of experiencing sustained 373 ZIKV transmission. Under an elevated importation scenario, assuming that only one fifth of ZIKV importations (the symptomatic proportion) have been observed, we find that the recommended triggers