Abstract In the event of a new infectious disease outbreak, mathematical and simulation models are commonly used to inform policy by evaluating which control strategies will minimize the impact of the epidemic. In the early stages of such outbreaks, substantial parameter uncertainty may limit the ability of models to provide accurate predictions, and policymakers do not have the luxury of waiting for data to alleviate this state of uncertainty. For policymakers, however, it is the selection of the optimal control intervention in the face of uncertainty, rather than accuracy of model predictions, that is the measure of success that counts. We simulate the process of real-time decision-making by fitting an epidemic model to observed, spatially-explicit, infection data at weekly intervals throughout two historical outbreaks of foot-and-mouth disease, UK in 2001 and Miyazaki, Japan in 2010, and compare forward simulations of the impact of switching to an alternative control intervention at the time point in question. These are compared to policy recommendations generated in hindsight using data from the entire outbreak, thereby comparing the best we could have done at the time with the best we could have done in retrospect. Our results show that the control policy that would have been chosen using all the data is also identified from an early stage in an outbreak using only the available data, despite high variability in projections of epidemic size. Critically, we find that it is an improved understanding of the locations of infected farms, rather than improved estimates of transmission parameters, that drives improved prediction of the relative performance of control interventions. However, the ability to estimate undetected infectious premises is a function of uncertainty in the transmission parameters. Here, we demonstrate the need for both real-time model fitting and generating projections to evaluate alternative control interventions throughout an outbreak. Our results highlight the use of using models at outbreak onset to inform policy and the importance of state-dependent interventions that adapt in response to additional information throughout an outbreak.

Author summary Mathematical and simulation models may be used to inform policy in the early stages of an infectious disease outbreak by evaluating which control strategies will minimize the impact of the epidemic. In these early stages, significant uncertainty can limit the ability of models to provide accurate predictions, and policymakers do not have the luxury of waiting for data to alleviate this state of uncertainty. For policymakers, however, what is most important is the selection of the optimal control intervention, rather than accuracy of model predictions. We fit an epidemic model to observed, spatially-explicit, infection data at weekly intervals throughout two historical outbreaks of foot-and-mouth disease, UK in 2001 and Miyazaki, Japan in 2010, and compare forward simulations of the impact of alternative control interventions. These are compared to policy recommendations generated in hindsight using data from the entire outbreak. Our results show that the optimal control policy is identified accurately from an early stage in an outbreak, despite high levels of uncertainty in projections of epidemic size, and that the relative performance of control strategies is strongly mediated by our understanding of the locations of infected farms, rather than improved estimates of transmission parameters.

Citation: Probert WJM, Jewell CP, Werkman M, Fonnesbeck CJ, Goto Y, Runge MC, et al. (2018) Real-time decision-making during emergency disease outbreaks. PLoS Comput Biol 14(7): e1006202. https://doi.org/10.1371/journal.pcbi.1006202 Editor: Katia Koelle, Emory University, UNITED STATES Received: July 24, 2017; Accepted: May 15, 2018; Published: July 24, 2018 This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication. Data Availability: UK farm demography data is available at a national level via the RADAR system by emailing RADAR@apha.gsi.gov.uk. Data on the 2010 Miyazaki FMD outbreak are commercially sensitive and shared by a third-party, the Miyazaki government. Data are available from Dr Hisashi Aratake, Ph.D., Intellectual Property Office, Center for Collaborative Research & Community Cooperation, University of Miyazaki, 1-1 Gakuen Kibanadai-nishi, 889-2192, Japan, chizai-s@of.miyazaki-u.ac.jp. All parameter estimate data and simulation output are available via the Dryad Digital Repository with DOI of doi:10.5061/dryad.gr656gk. We provide Python code for generating the figures in the manuscript at the following website: https://github.com/p-robot/fmd_realtime_decisionmaking. Excluded from this repository are code for figures that depend upon confidential data (S1, S2, S7 and S8 Figs). All data for S2 and S8 Figs is available if researchers follow the access details we have provided for the Miyazaki data. S1 and S7 Figs, however, rely on the outbreak data for the UK outbreak in 2001. Data on the 2001 UK FMD outbreak are available on request from the Department for Environment, Food, and Rural Affairs (DEFRA) of the government of the United Kingdom. Access to this data, including appropriate DEFRA contact information, is accessed through the following website https://www.gov.uk/government/organisations/department-for-environment-food-rural-affairs. Code for the MCMC algorithm is available under the GPLv3 license at http://fhm-chicas-code.lancs.ac.uk/InFER/InFER/tags/InFERfmd-v1.0. Funding: This work was supported by a grant from the Biotechnology and Biological Sciences Research Council (BB/K010972/4; www.bbsrc.ukri.org), and from the Ecology and Evolution of Infectious Disease program of the National Science Foundation (www.nsf.gov) and the National Institutes of Health (1 R01 GM105247-01; www.nih.gov). MJT, MJF and CJ received funding by the Research and Policy for Infectious Disease Dynamics (RAPIDD) program of the Science and Technology Directorate of the Department of Homeland Security. CJ thanks the NVIDIA Corporation (www.nvidia.com) for a hardware donation of a NVIDIA K40 GPU Accelerator. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction The responsibilities of policymakers during infectious disease outbreaks include the difficult task of choosing between multiple control interventions based on an uncertain future. Mathematical and simulation models have proved a useful tool to aid decision-making during disease outbreaks by both generating forecasts of outbreak severity and comparing different control strategies [1–6]. Using mathematical and simulation models, however, requires estimation of model parameters, and in the early stages of an outbreak, when decisions are most critical and data are most scarce, significant parametric uncertainty may limit the ability of models to provide informed advice. Recent research has outlined frameworks that combine Bayesian parameter estimation and a mathematical model for generating real-time forecasts of outbreak severity throughout the course of an epidemic, aiming to assimilate available surveillance data into model estimates as rapidly as possible [7–10]. The efficacy of these frameworks has typically been evaluated using the accuracy of forecasts. For decision-makers, however, the accuracy of model forecasts per se, are not the best measure of success, it is the selection of the optimal control interventions in the face of uncertainty that counts, and ultimately what they are judged on. However, projections of the impact of alternative control interventions are not always performed alongside projections of the burden of infection. For several infectious diseases it is not possible, or relevant, to include projections of control interventions, for instance when interventions are directly related to estimates of the burden of disease or when control interventions are related to the timing of the peak of an epidemic (such as in influenza). Including projections of interventions does allow disease control problems to be phrased as optimization problems and therefore allows the determination of whether optimal control choice is dependent upon the underlying state of the outbreak. In contrast to real-time forecasting approaches, we demonstrate real-time decision-making, which requires integration of all information until now plus the potential future impact of candidate control interventions. In this work, we simulated the process of real-time decision-making by fitting a dynamic epidemic model to the observed (confirmed), herd-level, infection data at weekly intervals throughout two historical outbreaks of foot-and-mouth disease (FMD), a viral disease of economically important livestock, and compared forward simulations of the impact of alternative culling and vaccination interventions under a management objective of minimizing total culls so as to gain disease-freedom. We repeated these forward simulations at each time point using parameter estimates from a model fitted to the complete outbreaks, thereby comparing the best we could have done at the time with the best we could have done in retrospect. Forward simulations predicted the final total culls (number of animals culled) from having taken a single control intervention from a particular date into the future. Control interventions included culling of infected premises only (IP), culling of infected premises and dangerous contacts (IPDC), culling of infected premises, dangerous contacts and contiguous premises (IPDCCP), ring culling in areas surrounding infected premises at 3 and 10 km radii (RC3 and RC10 respectively), and vaccination in areas surrounding infected premises at 3 and 10km radii (V3 and V10 respectively) (see Materials and Methods for further details of the control interventions). This set of intervention strategies includes those that governments have implemented, or considered, in the past and that are consistent with other studies on foot-and-mouth disease. In contrast to previous work in real-time forecasting [7–10], we used an individual-based model and included uncertainty regarding the location of infected and undetected farms [11,12]. As surveillance data become available, we improve our understanding, in a cumulative manner, of both how the outbreak is unfolding, via estimates of transmission parameters, and of where likely new infections may be located, via estimates of the spatial distribution of infected but undetected farms. Forward simulations are therefore conditional upon both the actual state of the outbreak (i.e. the pattern of confirmed infected cases and the pattern of inferred, undetected infections) and having enacted the actual outbreak controls until the time point in question. The outbreaks of FMD in the UK in 2001 and Miyazaki, Japan in 2010 contrast in a number of ways and thus provide a valuable comparison for investigating how policy recommendations are affected by additional information throughout an outbreak. Firstly, the UK outbreak had over 2000 infected premises over an area that included England, Wales, and Scotland (roughly 230000km2) [13] whereas the outbreak in Miyazaki affected only 290 premises contained within the Miyazaki prefecture (less than 8000km2) [14,15]. Secondly, at the time of confirmation of FMD, there were multiple foci of infection dispersed throughout the UK but only one focus of infection in the Miyazaki outbreak (although additional foci occurred later). Finally, control interventions deployed during each outbreak were different; UK control interventions only included culling strategies whereas control of the outbreak in Miyazaki began with culling and shifted to vaccination after 5 weeks, necessitated by constraints on the disposal of accumulating carcasses [16].

Discussion Our results have shown that policy recommendations using real-time parameter estimates and forward simulations can be correct from an early stage in an outbreak despite highly uncertain projections of epidemic severity, in line with previous research on one-time decisions for the control of Ebola [18]. Projections from mathematical and simulation models are useful for informing policy-making insofar as they help to identify what is the best course of action and we have included two summaries of how simulation results may be communicated, dependent upon whether policymakers have an objective of 1) optimizing an expectation in outbreak severity (Figs 2B and 3B) or 2) optimizing the number of times that an intervention was predicted to be optimal (Figs 2C and 3C). In many situations, estimating the burden of infection and selection of the optimal control intervention are directly related. However, our results are a reminder that this may not always be the case; in many cases it is how projections influence change in the recommended control intervention, rather than the value of projections themselves, that matter and so, where appropriate, it is important to include projections of intervention efficacy when making real-time projections of disease burden. Our results showed that changes in the estimated relative performance of control interventions was strongly influenced by the spatial distribution of both observed and undetected infectious premises and culled premises (the state of the outbreak). Although our analysis only looked at one change in control intervention (from what was being applied historically) this dependence highlights that, should one allow multiple changes of control through time, then the optimal policy is likely to be dynamic. In our results, even if accurate parameter estimates had been available from the first confirmed case (such as those derived from the whole outbreak), it would still have been necessary to perform state-dependent control to find the best choice of control intervention as the outbreaks evolve. In practice, estimating the state of the outbreak (i.e. prediction of locations of undetected infections) depends on estimates of transmission parameters and, therefore, continual re-evaluation of control interventions alone makes little sense without also re-evaluating, and re-fitting, model parameters. Thus, control recommendations should adapt to the changing state of an outbreak. Our results included a marked stabilization in recommended control interventions in simulations for the outbreak in the UK. It remains an avenue for future research to investigate what are the drivers of such stabilization in recommendations in control intervention, and whether it is logistically feasible to measure (and therefore act upon) such drivers, beyond an in silico experiment. Such analyses would require a more general approach to seeding outbreaks, and generating landscapes, to more thoroughly explore the state-space of potential future outbreaks. Here, we only investigated two outbreaks, simulations for each of which were seeded from historical starting points. Often, the need for rapid response during an outbreak is discussed in terms of the initial response [13], but not as often in terms of adapting as circumstances change throughout an outbreak. In both outbreaks we investigated, there was significant variability in epidemiological predictions during the early stages of disease outbreaks highlighting that real-time updating of parameters is vital in order to obtain accurate predictions of epidemic size and extent. However, additional foci of infection may be seen as independent outbreaks and, therefore, the rapid response that is called for at the start of an outbreak needs to be reapplied when such foci are discovered. For the outbreaks that we investigated, identifying the locations of undetected infected premises was of greater importance to determining the best course of action than identifying the underlying disease dynamics; this calls for increased vigilance in surveillance during an outbreak and highlights the importance of methodology for predicting undetected infections (e.g. [11,12]), assimilating surveillance data into parameter estimates for individual-based models, and of confirming negative cases, especially when such premises are in locations that would be considered as additional foci of infection. Simply because an outbreak has progressed beyond its initial stages does not mean that the need to act swiftly according to changes in the outbreak are in any way diminished. At a coarse level, for one-time decisions, the idea of state-dependent control has already been adopted or discussed by several agencies, such as the Department for Environment, Food, and Rural Affairs, UK (DEFRA) and the United States Department of Agriculture (USDA) in flowcharts for determining when to perform emergency vaccination [19,20], the dependence of different phases in smallpox eradication upon smallpox prevalence [21], management of wildlife diseases [22], and the use of adaptive surveillance of herds in the eradication of rinderpest [23]. Decision-making frameworks, such as adaptive management, have also highlighted the utility of modeling and optimization as tools for generating state-dependent policies [24]. We note that optimization methods such as dynamic programming or reinforcement learning would be required to generate state-dependent policies and that such methodologies, although a more complex optimization than what we have presented, would allow the possibility of changing control intervention repeatedly through time, or generating optimal interventions that are a combination of those defined here, such as county-specific interventions (e.g. [25]). Our analysis shows there is potential to make large gains in the effectiveness of the response to an outbreak by adopting state-dependent control that is on a much more nuanced scale than one-time binary decisions, and that mathematical and simulation models can play a significant role in policy preparedness by investigating such strategies before an outbreak occurs.

Materials and methods We used data augmentation Markov chain Monte Carlo (MCMC) to fit a 3-species (cattle, sheep, pigs) SEINR (Susceptible-Exposed-Infected-Notified-Removed) model to the observed infection and intervention data at the farm-level at weekly time points throughout the epidemics [11,12]. The analysis started one week after the first confirmed case (one week after 19 February 2001 and 20 April 2010 for the outbreaks in UK and Miyazaki respectively). Data for the UK included location and farm demography for approximately 188000 premises. Data for Miyazaki included location and farm demography for approximately 9000 premises. In the case of the UK outbreak, we changed the timescale to 28-day time points after 11 June 2001 until 3 September 2001. A final model fit represents all information that could have been garnered from the outbreak (on 24 December 2001 for the UK outbreak and 6 July 2010 for the outbreak in Miyazaki). Each model fit included an estimate of a joint posterior distribution of 16 parameters (only 12 parameters had changing estimates in Miyazaki since no sheep were affected in this outbreak) and an estimate of the infection time of infected, but as yet undetected, premises (so-called ‘occult’ infections). To reproduce a comparable level of initial uncertainty, the same uninformative prior distributions were used for each parameter at the start of the two outbreaks, while a uniform prior was used for the initial infection times of the undetected but infected farms. At each time point, parameter estimates were used within a previously-validated farm-level simulation model [1,26], to make forward projections under various control interventions. Each set of parameter values in the posterior distribution also had an associated set of infection times of undetected infections. These were combined with the confirmed infections from the real outbreak data and used to seed the infectious status of each farm in simulations. Predictions were therefore conditional on the actual state of the outbreak at that point in time as well as our estimate of parameters and which farms were infected. Forward projections were made twice for each time point: once with parameter estimates (and the associated distribution of infection times of undetected infections) based only upon the data available at that time point, denoted ‘accrued information’; and once with analogous estimates made using all the data from the entire outbreak, denoted ‘complete information’. Six (Miyazaki) or seven (UK) control interventions were compared in the forward simulations (Table 1). The performance of culling infected premises only (IP) was included as the least severe strategy possible, and the culling of infected premises and dangerous contacts only (IPDC) was included as the minimum required under European Union [27] and Japanese [28] law. In the UK simulations, the control of culling contiguous premises of infected farms (IPDCCP) was also included beyond controls used in the simulations for Miyazaki; this is most similar to that which was implemented during the 2001 outbreak [1]. Simulations for both outbreaks included ring culling around infected premises at 3km (RC3) and 10km (RC10) radii. Two emergency vaccination strategies, only targeting cattle, were also included at 3km and 10km around infected premises (V3 and V10 respectively), and were assumed to be vaccinate-to-live policies; where vaccinated cattle enter the food chain and are not included in counts of total animals culled. Note that a vaccinate-to-live policy was not applied in the outbreak in Miyazaki but it may be a future possibility in the UK [19]. These vaccination radii were used because 1) they aided in comparison with ring culling interventions; 2) they spanned a range that includes the optimal ring radius for reactive vaccination in the UK [4], and; 3) they included the radius (10km) at which vaccination was actually implemented in Miyazaki [14]. All parameter estimate data and simulation output are available via the Dryad Digital Repository: https://doi.org/10.5061/dryad.gr656gk [29]. PPT PowerPoint slide

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larger image TIFF original image Download: Table 1. Summary of control interventions used in the simulations. https://doi.org/10.1371/journal.pcbi.1006202.t001 Model Both outbreaks used a similar model structure. The infectious pressure, λ j (t), on a susceptible farm j at time t is where and are the sets of infected and notified farms at time t respectively (t = 0, 1, 2, … T). Models of similar structure have been previously used for modeling FMD (e.g. [1,4,11]). A summary of notation used to describe the model is given in Table 2. Notification time is assumed to mean the time of laboratory confirmation of FMD, and removal time is assumed to mean the date when the farm is both culled and disposed of. We count t in days; day 0 is the first confirmed infected case in the data and T is the day of the final parameter estimate (24 December 2001 for the UK outbreak and 6 July 2010 for the outbreak in Miyazaki). By including both and , as the sets of susceptible and removed farms at time t respectively, we then have four sets essentially giving the state of the epidemic on the population at a given point in time, . The infection time of the kth farm is denoted I k , while N k and R k denote notification and removal times of farm k respectively. Note that in the next section we assume that for I t , N t , and R t , the t subscript denotes the set of infection, notification, or removal times of all premises respectively; here the time subscript is dropped for succinctness. All times are listed in days unless otherwise specified. Infectious pressure can be decomposed into contributions from infectious (but not yet notified) farms, (1) and contributions from notified farms . We define and to be the ‘infectivity’ of farm i and ‘susceptibility’ of farm j respectively, where c k , p k , and s k are the numbers of cattle, pigs, and sheep on farm k, with mean numbers of cattle, pigs, and sheep, denoted by . The effect of distance is captured using a Cauchy-type kernel where ρ ij is the Euclidean distance between farms i and j, and δ the decay of transmission rate with distance. Baseline infectious pressure distinguishes between periods before and after the movement ban was implemented, and the latency of the disease was modeled using the function An estimate at time t of the complete parameter set, of 16 parameters (12 parameters in Miyazaki), is denoted θ t . Parameter ω was assumed fixed at 1.3 in both outbreaks, as were the initial priors. The priors for each parameter were elicited via expert opinion and assigned the following distributions: π 0 (δ)∼Gamma(4,8),π 0 (ϵ 1 ),π 0 (ϵ 2 )∼Gamma(1E−7,1), π 0 (ψ 1 ),π 0 (ψ 2 ),π 0 (ψ 3 ),π 0 (ϕ 1 ),π 0 (ϕ 2 ),π 0 (ϕ 3 ),π 0 (ξ 2 ),π 0 (ξ 3 ),π 0 (ζ 2 ),π 0 (ζ 3 ) ∼Gamma(0.5,1),π 0 (γ 1 ),π 0 (γ 2 )∼Gamma(1E−4,1). Gamma(a, b) is the gamma distribution with shape parameter a and rate parameter b. PPT PowerPoint slide

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larger image TIFF original image Download: Table 2. Summary table of mathematical symbols used. https://doi.org/10.1371/journal.pcbi.1006202.t002 Infection to notification time was assumed to be distributed according to a Gamma distribution such that N i → I i = d i ∼Gamma(4,b) with parameter b = 0.5 governing the scale of the probability distribution. Notification to removal time is an observed quantity since both events are recorded. Parameter estimation Let the data (demographics and event history) observed up to time t be , with denoting the joint posterior distribution of the model parameters and infection times (including infection times of undetected infections) immediately at time t. We assume that infections occurred according to a continuous-time non-homogeneous Poisson process, where infection rate is assumed to be λ j (t) as above. Let I, N, and R be vectors of infection, notification, and removal times for individuals 1, …, n I who were infected by observation time T obs . Conditioning on this event time, the joint posterior distribution over parameters θ = {ϵ 1 ,ϵ 2 ,γ 1 ,γ 2 ,ξ,ζ,ψ,ϕ,δ,b} is where the first line represents the infection process, the second line represents the detection (infected to notified) process, and the third line represents independent prior distributions for all components of θ. represents the time immediately before the infection time of the jth premises. Parameters in bold, represent the corresponding set of species-specific parameters, e.g. ζ = {ζ 2 ,ζ 3 }. κ denotes the initial infective, and P denotes the set representing all individuals in the population. The joint posterior distributions used in the forward simulations and figures of the instantaneous risk of onward spread represent the MCMC output sub-sampled to 2000 parameter coordinates. MCMC algorithm Multisite adaptive Metropolis-Hastings was used to draw from the conditional posterior distributions of {ϵ 1 ,ϵ 2 ,γ 1, ,γ 2 ,δ}, ψ and ϕ. Furthermore, since the infection times are unobserved, we updated them component-wise using Metropolis-Hastings, with a reversible-jump update to explore the posterior over the presence of undetected infections. See [11,12] for further details. Updating species effects ξ and ζ The introduction of the 3-species model (in comparison to [11] and [1]) results in a non-linearly correlated posterior distribution, particularly between γ 1 and both of ξ and ζ. This presents particular difficulties for Metropolis-based MCMC algorithms, since the optimal proposal distribution scale changes with location in the posterior parameters space. To approximately orthogonalize the posterior distribution, and hence improve the convergence properties of our adaptive Metropolis algorithm, we employed the following non-centered update for ξ and ζ. To construct an efficient proposal distribution for ξ, we seek to exploit the shape of the posterior distribution with respect to γ 1 . This can be thought of as a joint update of γ 1 and ξ, respecting the contour of the joint posterior. First, we write the equation for q(i;ξ) (see above) as where and similarly for P i and S i . We then let We then propose and where, with probability 0.05, B = I 2 the 2x2 identity matrix, and with probability 0.95, B = Σ k the empirical covariance matrix of the MCMC samples for (A 1 ,A 2 )T up to iteration k (see [30]). We then solve for γ 1 and ξ. Similarly, we update γ 1 and ζ. Instantaneous risk of onward spread Uncertainty in the joint posterior distribution of transmission parameters was summarized using a measure of the instantaneous risk of onward spread, defined as the instantaneous force of infection from an average-sized infectious farm to an average-sized susceptible farm at time t (g t ). This risk measure was calculated at each time point as the integral over the joint posterior distribution of parameters at that point in time and over a distance of 20km (from the infectious to the susceptible farm): The equation for the instantaneous risk of onward spread is taken from the equation for the infectious pressure (Eq 1) substituting the average number of cattle, pigs, and sheep for c i , p i , and s i respectively. Forward simulations Each control intervention, a, is evaluated according to the expected total number of animals culled, U(Y t |a), where the Bayesian predictive distribution of the ongoing epidemic, Y t , is given by the integral This was estimated by simulating forward from using draws from . The above formulation is using parameter estimates from the time point in question, so-called ‘accrued information’. Forward simulations were also generated with parameters estimated using all data, , so-called ‘complete information’, which were generated in an analogous fashion instead using draws from in the above integral. The optimal control strategy is chosen as that which minimizes the mean expected total animals culled Vaccine efficacy was assumed to be 90%, whereby animal numbers on a vaccinated farm were reduced by 90% after a delay until conferment of immunity of 4 days. Delay from infection to notification time was simulated as 9 days, with a 4-day latency period. Notification to removal time was simulated as 1 day for infected premises and 2 days for culling of dangerous contacts or contiguous premises. Software The MCMC algorithm above was implemented in C++ (GCC version 4.8.3) embedded within an R package. General-purpose graphics processing unit (GPU) using NVIDIA CUDA 7.5 was used to implement the calculation of the likelihood and speed up inference. The software is available under the GPLv3 license at http://fhm-chicas-code.lancs.ac.uk/InFER/InFER/tags/InFERfmd-v1.0.

Acknowledgments The authors thank the Miyazaki government for provision of the data on the Miyazaki outbreak, and the UK Department for Environment Food and Rural Affairs for data on the UK 2001 outbreak. The authors wish to acknowledge the expertise of Ruri Ushijima who was consulted regarding the outbreak in Miyazaki. The authors wish to thank attendants of a RAPIDD workshop in Merida, Mexico in August 2015, and two external reviewers for their valuable comments. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.