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Ballistic imaging systems can help solve crimes by comparing images of cartridge cases, which are recovered from a crime scene or test-fired from a gun, to a database of images obtained from past crime scenes. Many U.S. municipalities lack the resources to process all of their cartridge cases. Using data from Stockton, CA, we analyze two problems: how to allocate limited capacity to maximize the number of cartridge cases that generate at least one hit, and how to prioritize the cartridge cases that are processed to maximize the usefulness (i.e., obtained before the corresponding criminal case is closed) of hits. The number of hits can be significantly increased by prioritizing crime scene evidence over test-fires, and by ranking calibers by their hit probability and processing only the higher ranking calibers. We also estimate that last-come first-served increases the proportion of hits that are useful by only 0.05 relative to first-come first-served.

The April 7, 2020, Wisconsin election produced a large natural experiment to help understand the transmission risks of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). As of April 14, 2020, 1 551 711 total votes were cast (https://bit.ly/2yWPhlF),1 and 1 138 491 absentee ballots were returned as of April 21, 2020,1 suggesting that approximately 413 220 people voted in person. Waiting times in Milwaukee averaged 1.5 to 2 hours.2 Poll workers had surgical masks and latex gloves, hand sanitizer was made available to voters, isopropyl alcohol wipes were used to clean voting equipment, and painting tape and signs were used to facilitate social distancing.1 (Am J Public Health. Published online ahead of print June 18, 2020: e1-e2. doi:10.2105/AJPH.2020.305770).

Firearms identification imaging systems help solve crimes by comparing newly acquired images of cartridge casings or bullets to a database of images obtained from past crime scenes. We formulate an optimization problem that bases its matching decisions not only on the similarity between pairs of images, but also on the time and spatial location of each new acquisition and each database entry. The objective is to maximize the detection probability subject to a constraint on the false positive rate. We use data on all cartridge casings matches detected in Israel during 2006-2008 to estimate most of the model parameters. We estimate matching accuracy from two different studies and predict that the optimal use of extraneous information would increase the detection probability from 0.931 to 0.987 and from 0.707 to 0.844, respectively. These improvements are achieved by favoring pairs of images that are closer together in space and time.

The U.S. is the main country in the world that delivers its food assistance primarily via transoceanic shipments of commodity-based in-kind food. This approach is costlier and less timely than cash-based assistance, which includes cash transfers, food vouchers, and local and regional procurement, where food is bought in or nearby the recipient country. The U.S.’s approach is exacerbated by a requirement that half of its transoceanic food shipments need to be sent on U.S.-flag vessels. We estimate the effect of these U.S. food assistance distribution policies on child mortality in northern Kenya by formulating and optimizing a supply chain model. In our model, monthly orders of transoceanic shipments and cash-based interventions are chosen to minimize child mortality subject to an annual budget constraint and to policy constraints on the allowable proportions of cash-based interventions and non-US-flag shipments. By varying the restrictiveness of these policy constraints, we assess the impact of possible changes in U.S. food aid policies on child mortality. The model includes an existing regression model that uses household survey data and geospatial data to forecast the mean mid-upper-arm circumference Z scores among children in a community, and allows food assistance to increase Z scores, and Z scores to influence mortality rates. We find that cash-based interventions are a much more powerful policy lever than the U.S.-flag vessel requirement: switching to cash-based interventions reduces child mortality from 4.4% to 3.7% (a 16.2% relative reduction) in our model, whereas eliminating the U.S.-flag vessel restriction without increasing the use of cash-based interventions generates a relative reduction in child mortality of only 1.1%. The great majority of the gains achieved by cash-based interventions are due to their reduced cost, not their reduced delivery lead times; i.e., the reduction of shipping expenses allows for more food to be delivered, which reduces child mortality.

BACKGROUND: Recent studies show that transfusing older blood may lead to increased mortality. This raises the issue of whether transfusing fresher blood can be achieved without jeopardizing blood availability. STUDY DESIGN AND METHODS: We propose a simple family of policies that is defined by a single threshold: rather than transfusing the oldest available blood that is younger than 42 days, we transfuse the oldest blood that is younger than the threshold, and if there is no blood younger than the threshold then we transfuse the youngest blood that is older than the threshold. To assess this policy, we build a simulation model using data from Stanford University Medical Center. We focus on the tradeoff between the mean age of transfused blood and the fraction of transfused blood that is imported. RESULTS: For hospitals in which the local supply is greater than demand, our policy with a threshold of 14 days leads to a decrease of 10 to 20 days in the mean age of transfused blood while increasing the fraction of imported blood to less than 0.005 (i.e., 0.5%). If the health benefits from transfusing fresher blood can be confirmed by randomized clinical trials, then conservative assumptions suggest that this policy could reduce the annual number of transfused patients who die within 1 year by 20,000. CONCLUSION: The proposed allocation policy with a threshold of 14 days could allow many US hospitals to significantly reduce the age of transfused blood, thereby possibly reducing morbidity and mortality, while having a negligible impact on supply chain operations. T he allocation of available red blood cells (RBCs) for transfusion to patients is a difficult problem: compatibility between donor and recipient must be maintained, and the age and quantity of available RBCs need to be accounted for. More specifically, while there is a tendency to use older available blood to prevent outdating, stored RBCs undergo biochemical changes that impact RBC function, and the age of transfused blood has been reported to be associated with an increased risk of infection, postoperative complications, and/or short-term and long-term mortality.

We superimpose a radiation fallout model onto a traffic flow model to assess the evacuation versus shelter-in-place decisions after the daytime ground-level detonation of a 10-kt improvised nuclear device in Washington, DC. In our model, approximately 80k people are killed by the prompt effects of blast, burn, and radiation. Of the approximately 360k survivors without access to a vehicle, 42.6k would die if they immediately self-evacuated on foot. Sheltering above ground would save several thousand of these lives and sheltering in a basement (or near the middle of a large building) would save of them. Among survivors of the prompt effects with access to a vehicle, the number of deaths depends on the fraction of people who shelter in a basement rather than self-evacuate in their vehicle: 23.1k people die if 90% shelter in a basement and 54.6k die if 10% shelter. Sheltering above ground saves approximately half as many lives as sheltering in a basement. The details related to delayed (i.e., organized) evacuation, search and rescue, decontamination, and situational awareness (via, e.g., telecommunications) have very little impact on the number of casualties. Although antibiotics and transfusion support have the potential to save approximately 10k lives (and the number of lives saved from medical care increases with the fraction of people who shelter in basements), the logistical challenge appears to be well beyond current response capabilities. Taken together, our results suggest that the government should initiate an aggressive outreach program to educate citizens and the private sector about the importance of sheltering in place in a basement for at least 12 hours after a terrorist nuclear detonation. Language: en

Motivated by the cost and disruption involved in changing from a two-finger to a ten-finger biometric system for matching U.S. visitors to a watchlist of criminals and terrorists, we investigate whether any two-finger multistage biometric strategies would fix the inadequate matching performance of poor-quality prints that plagues the U.S. Government's original two-finger, single-stage biometric system. For several multistage strategies, we solve the Stackelberg game in which the U.S. Government chooses the biometric threshold levels to maximize the detection probability subject to constraints on the false positive probability and on the mean time per visitor to perform biometric screening, and the terrorist chooses the fingerprint image quality to minimize his detection probability. The first stage of all the strategies uses the current minutiae-based fingerprint matching system, but with thresholds that depend on image quality, which in isolation achieves a detection probability of 0.771. Using face recognition (based on 2002 data) in the second stage increases the detection probability to 0.841, whereas using a slower and more thorough texture-based fingerprint matcher in the second stage leads to a detection probability of at least 0.913 and perhaps significantly higher. (Data for the texture matcher is only available for the poorest-quality prints and we assume that this is its performance for all prints.) Adding face recognition as a third stage to this latter system does not improve performance. The two-finger, two-stage strategy may be comparable in performance to the ten-finger, single-stage strategy (which has a detection probability of 0.937), is robust against gaming and poor image acquisition, requires no additional hardware, and would generate no visible changes from the original two-finger, single-stage system from a visitor's viewpoint. The uncertainty in our performance estimates needs to be better quantified, ideally with raw data on similarity scores, before recommending this strategy for implementation.

This paper is the archival record of the INFORMS Philip McCord Morse Lecture delivered in 2008. It describes the author's research on four topics in homeland security and public health: preparedness and response to a bioterror anthrax attack, preparedness and response to a bioterror attack on the food supply, routes of transmission and infection control for pandemic influenza, and biometrics (e.g., fingerprint matching) to prevent terrorists from entering the country. The paper focuses on the modeling, policy recommendations, and implementation of these recommendations. The author draws lessons about policy implementation from these examples and from examples from his other homeland security work with colleagues, including a bioterror smallpox attack, preventing nuclear weapons from entering the country on a shipping container, preventing nuclear weapons from entering a city, and preventing terrorists from crossing the border between the United States and Mexico.

We develop a mathematical optimization model at the intersection of homeland security and immigration, that chooses various immigration enforcement decision variables to minimize the probability that a terrorist can successfully enter the United States across the U.S.-Mexico border. Included are a discrete choice model for the probability that a potential alien crosser will attempt to cross the U.S.-Mexico border in terms of the likelihood of success and the U.S. wage for illegal workers, a spatial model that calculates the apprehension probability as a function of the number of crossers, the number of border patrol agents, and the amount of surveillance technology on the border, a queueing model that determines the probability that an apprehended alien will be detained and removed as a function of the number of detention beds, and an equilibrium model for the illegal wage that balances the supply and demand for work and incorporates the impact of worksite enforcement. Our main result is that detention beds are the current system bottleneck (even after the large reduction in detention residence times recently achieved by expedited removal), and increases in border patrol staffing or surveillance technology would not provide any improvements without a large increase in detention capacity. Our model also predicts that surveillance technology is more cost effective than border patrol agents, which in turn are more cost effective than worksite inspectors, but these results are not robust due to the difficulty of predicting human behavior from existing data. Overall, the probability that a terrorist can successfully enter the United States is very high, and it would be extremely costly and difficult to significantly reduce it. We also investigate the alternative objective function of minimizing the flow of illegal aliens across the U.S.-Mexico border, and obtain qualitatively similar results.

Motivated by the ease with which online customers can bid simultaneously in multiple auctions, we analyze a system with two competing auctioneers and three types of bidders: those dedicated to either of the two auctions and those that participate simultaneously in both auctions. Bidding behavior is specified and proven to induce a Bayesian Nash equilibrium, and a closed-form expression for the expected revenue of each auctioneer is derived. For auctioneers selling a single item, partial pooling—i.e., the presence of some cross-auction bidders—is beneficial to both auctioneers as long as neither one dominates the market (e.g., possesses more than 60%–65% of the market share). For multi-item auctions, pooling is mutually beneficial only if both auctioneers have nearly identical ratios of bidders per items for sale; otherwise, only the auctioneer with the smaller ratio benefits from pooling. Pooling's impact on revenue decreases with the number of bidders, suggesting that popular auction sites need not be overly concerned with mitigating bidding across auctions.

We formulate and analyze an optimal stopping problem concerning a terrorist who is attempting to drive a nuclear or radiological weapon toward a target in a city center. In our model, the terrorist needs to travel through a two-dimensional lattice containing imperfect radiation sensors at some of the nodes, and decides at each node whether to detonate the bomb or proceed. We consider five different scenarios containing various informational structures and two different sensor array topologies: the sensors are placed randomly or they form an outer wall around the periphery of the city. We find that sensors can act as a deterrent in some cases, and that the government prefers the outer wall topology unless the sensors have a very low detection probability and the budget is tight (so that they are sparsely deployed).

We formulate and solve an optimization problem in which a terrorist is attempting to drive a nuclear weapon toward a city center, but needs to travel through an array of imperfect neutron radiation sensors that form a wall around the periphery of the city. A fleet of interdiction vehicles are available to chase, and attempt to interdict, vehicles that set off a sensor alarm. In our model, the government chooses the thickness (in terms of number of sensors) of the radiation wall, the neutron threshold in the sensors, and the number of interdiction vehicles to minimize the expected damage inflicted by a terrorist, subject to a budget constraint on sensors and interdiction vehicles. The terrorist observes the wall thickness and at each node he updates his likelihood of passing through a sensor without triggering an alarm and decides whether to proceed through the sensor or stop and detonate the bomb. Our results suggest that for an annual cost ranging from several million dollars to several tens of millions of dollars, depending upon the city's roadway topology, a single layer of sensors placed tens of miles from the city center and 10-20 dedicated interdiction vehicles could mitigate the damage from an unshielded or lightly-shielded plutonium weapon, but not from a uranium weapon or a radiological dispersal device.

Background Fecal microbiota transplantation is an effective treatment for recurrent Clostridium difficile infection and is being investigated as a treatment for other microbiota-associated diseases. To facilitate these activities, an international public stool bank has been created, which screens donors and processes stools in a standardized manner. The goal of this research is to use mathematical modeling and analysis to optimize screening and donor management at the stool bank. Results Compared to the current policy of screening active donors every 60 days before releasing their quarantined stools for sale, costs can be reduced by 10.3 % by increasing the screening frequency to every 36 days. In addition, the stool production rate varies widely across donors, and using donor-specific screening, where higher producers are screened more frequently, also reduces costs, as does introducing an interim (i.e., between consecutive regular tests) stool test for just rotavirus and C. difficile. We also derive a donor release (i.e., into the system) policy that allows the supply to approximately match an exponentially increasing deterministic demand. Conclusions More frequent screening, interim screening for rotavirus and C. difficile, and donor-specific screening, where higher stool producers are screened more frequently, are all cost-reducing measures. If screening costs decrease in the future (e.g., as a result of bringing screening in house), a bottleneck for implementing some of these recommendations may be the reluctance of donors to undergo serum screening more frequently than monthly. Electronic supplementary material The online version of this article (doi:10.1186/s40168-015-0140-3) contains supplementary material, which is available to authorized users.

We develop a mathematical model to find the optimal inspection strategy for detecting a nuclear weapon (or nuclear material to make a weapon) from being smuggled into the United States in a shipping container, subject to constraints of port congestion and an overall budget. We consider an 11-layer security system consisting of shipper certification, container seals, and a targeting software system, followed by passive (neutron and gamma), active (gamma radiography), and manual testing at overseas and domestic ports. Currently implemented policies achieve a low detection probability, and improved security requires passive and active testing of trusted containers and manually opening containers that cannot be penetrated by radiography. The annual cost of achieving a high detection probability of a plutonium weapon using existing equipment in traditional ways is roughly several billion dollars if testing is done domestically, and is approximately five times higher if testing is performed overseas. Our results suggest that employing high-energy x-ray radiography and elongating the passive neutron tests at overseas ports may provide significant cost savings, and several developing technologies, radiation sensors inside containers and tamper-resistant electronic seals, should be pursued aggressively. Further effort is critically needed to develop a practical neutron interrogation scheme that reliably detects moderately shielded, highly enriched uranium.

To aid in understanding how best to respond to a bioterror anthrax attack, we analyze a system of differential equations that includes a disease progression model, a set of spatially distributed queues for distributing antibiotics, and vaccination (pre-event and/or post-event). We derive approximate expressions for the number of casualties as a function of key parameters and management levers, including the time at which the attack is detected, the number of days to distribute antibiotics, the adherence to prophylactic antibiotics, and the fraction of the population that is preimmunized. We compare a variety of public health intervention policies in the event of a hypothetical anthrax attack in a large metropolitan area. Modeling assumptions were decided by the Anthrax Modeling Working Group of the Secretary's Council on Public Health Preparedness. Our results highlight the primary importance of rapid antibiotic distribution and lead us to argue for ensuring post-attack surge capacity to rapidly produce enough anthrax vaccine for an additional 100 million people.

We developed a mathematical model of a cows-to-consumers supply chain associated with a single milk-processing facility that is the victim of a deliberate release of botulinum toxin. Because centralized storage and processing lead to substantial dilution of the toxin, a minimum amount of toxin is required for the release to do damage. Irreducible uncertainties regarding the dose–response curve prevent us from quantifying the minimum effective release. However, if terrorists can obtain enough toxin, and this may well be possible, then rapid distribution and consumption result in several hundred thousand poisoned individuals if detection from early symptomatics is not timely. Timely and specific in-process testing has the potential to eliminate the threat of this scenario at a cost of

To aid in understanding how best to respond to a bioterror anthrax attack, we analyze a system of differential equations that includes an atmospheric release model, a spatial array of biosensors, a dose-response model, a disease progression model, and a set of spatially distributed tandem queues for distributing antibiotics and providing hospital care. We derive approximate closed-form expressions for the number of deaths as a function of key parameters and management levers, including the size of the attack, the time at which the attack is detected via symptomatic patients, the number of days to distribute antibiotics, the efficacy (both for treatment and prevention) of antibiotics, the prophylactic antibiotic distribution strategy, the prioritization of the antibiotics queue, and the detection limit, deployment density, and delay time of biosensors.

To evaluate existing and alternative proposals for emergency response to a deliberate smallpox attack, we embed the key operational features of such interventions into a smallpox disease transmission model. We use probabilistic reasoning within an otherwise deterministic epidemic framework to model the 'race to trace', i.e., attempting to trace (via the infector) and vaccinate an infected person while (s)he is still vaccine-sensitive. Our model explicitly incorporates a tracing/vaccination queue, and hence can be used as a capacity planning tool. An approximate analysis of this large (16 ODE) system yields closed-form estimates for the total number of deaths and the maximum queue length. The former estimate delineates the efficacy (i.e., accuracy) and efficiency (i.e., speed) of contact tracing, while the latter estimate reveals how congestion makes the race to trace more difficult to win, thereby causing more deaths. A probabilistic analysis is also used to find an approximate closed-form expression for the total number of deaths under mass vaccination, in terms of both the basic reproductive ratio and the vaccination capacity. We also derive approximate thresholds for initially controlling the epidemic for more general interventions that include imperfect vaccination and quarantine.

To the Editor: In a recent article (1), Kaplan et al. addressed the problems in detecting a bioterror attack from blood-donor screening. The main point of this comment is the "early approximation" used by Kaplan et al. to derive the probability of detecting an attack. The simplification used by Kaplan et al. leads to a probability that does not account for the size of the exposed population and can lead to incorrect results and misinterpretations. Consider a single bioterror attack that infects a proportion p of an exposed population of size N at time τ = 0, such that the initial number of infected is I0= Np. The quantity of interest is the probability D(τ) of finding at least one positive blood donation and detecting the attack within time τ. For attacks conducted with contagious agents that could lead to an epidemic, Kaplan et al. used the early approximation solution of the classic epidemic models (2) to describe the progression of the number of infected persons. Consequently, the resulting probability of attack detection [noted Des(τ)] is dependent only upon the initial size of the release I0 , the basic reproductive number R0 (the mean number of secondary cases per initial index case), and other variables (the blood screening window ω, the mean number k of blood donations per person and per unit of time, and the mean duration of infectiousness 1/r) (Appendix). Early approximation can lead to unreliable results because it is valid only at earlier stages of the epidemics and in the limit where the proportion p of initially infected is much smaller than the intrinsic steady proportion (R0 – 1) / R0 of the epidemics (Appendix). Relaxing this approximation and using the full solution for the progression of the number of infected persons leads to the probability D(τ)that takes into account the size of the exposed population (Appendix). The latter is important because, in contrast to Des(τ)that leads to the same conclusion, D(τ) indicates that the probabilities of detecting an attack within two exposed populations of different sizes, but with the same numbers of initially infected, are not identical. As illustrated in the Figure, when the other variables are fixed, D(τ)decreases as the proportion p of initially infected increases because the epidemic size decreases as p approaches the threshold (R0 – 1) / R0 . These subtleties of a simple epidemic model are even less reliable when using the blood screening to detect a bioterror attack with agents that cause diseases of very short incubation period. Figure Probability of attack detection delay for a contagious agent. Dashed line represents the early approximation Des(τ), solid lines the full solution (where the numbers represent the fraction p of the population initially infected), and the symbol ... Nonetheless, detecting a bioterror attack is very similar to detecting the response of pathogen-specific immunoglobulin M antibodies (as an indicator of recent contact of hosts with pathogens) within a population of hosts by using serologic surveys. Therefore, the reasoning developed for a bioterror attack can be extended and applied to detect and time the invasion or early circulation of certain pathogens within a population. In that perspective, it might be useful to develop an analysis that includes more details of the epidemic progression within this framework.

We developed a mathematical model to compare various emergency responses in the event of an airborne anthrax attack. The system consists of an atmospheric dispersion model, an age-dependent dose–response model, a disease progression model, and a set of spatially distributed two-stage queueing systems consisting of antibiotic distribution and hospital care. Our results underscore the need for the extremely aggressive and timely use of oral antibiotics by all asymptomatics in the exposure region, distributed either preattack or by nonprofessionals postattack, and the creation of surge capacity for supportive hospital care via expanded training of nonemergency care workers at the local level and the use of federal and military resources and nationwide medical volunteers. The use of prioritization (based on disease stage and/or age) at both queues, and the development and deployment of modestly rapid and sensitive biosensors, while helpful, produce only second-order improvements.

Motivated by the recent development of highly specific agents for brain tumours, we develop a mathematical model of the spatio-temporal dynamics of a brain tumour that receives an infusion of a highly specific cytotoxic agent (e.g. IL-4-PE, a cytotoxin comprised of IL-4 and a mutated form of Pseudomonas exotoxin). We derive an approximate but accurate mathematical formula for the tumour cure probability in terms of the tumour characteristics (size at time of detection, proliferation rate, diffusion coefficient), drug design (killing rate, loss rate and convection constants for tumour and tissue), and drug delivery (infusion rate, infusion duration). Our results suggest that high specificity is necessary but not sufficient to cure malignant gliomas; a nondispersed spatial profile of pretreatment tumour cells and/or good drug penetration are also required. The most important levers to improve tumour cure appear to be earlier detection, higher infusion rate, lower drug clearance rate and better convection into tumour, but not tissue. In contrast, the tumour cure probability is less sensitive to a longer infusion duration and enhancements in drug potency and drug specificity.

In the event of a smallpox bioterrorist attack in a large U.S. city, the interim response policy is to isolate symptomatic cases, trace and vaccinate their contacts, quarantine febrile contacts, but vaccinate more broadly if the outbreak cannot be contained by these measures. We embed this traced vaccination policy in a smallpox disease transmission model to estimate the number of cases and deaths that would result from an attack in a large urban area. Comparing the results to mass vaccination from the moment an attack is recognized, we find that mass vaccination results in both far fewer deaths and much faster epidemic eradication over a wide range of disease and intervention policy parameters, including those believed most likely, and that mass vaccination similarly outperforms the existing policy of starting with traced vaccination and switching to mass vaccination only if required.

Fecal microbiota transplantation is being assessed as a treatment for chronic microbiota-related diseases such as ulcerative colitis. Results from an initial randomized trial suggest that remission rates depend on unobservable features of the fecal donors and observable features of the patients. We use mathematical modeling to assess the efficacy of pooling stools from different donors during multiple rounds of treatment. In the model, there are two types of patients and two types of donors, where the patient type is observable and the donor type (effective or not effective) is not observable. In the model, clinical outcomes from earlier rounds of treatment are used to estimate the current likelihood that each donor is effective, and then each patient in each round is treated by a pool of donors that are currently deemed to be the most effective. Relative to the no-pooling case, pools of size two or three significantly increase the proportion of patients in remission during the first several rounds of treatment. Although based on data from a single randomized trial, our modeling suggests that pooling of stools - via daily cycling of encapsulated stool from several different donors - may be beneficial in fecal microbiota transplantation for chronic microbiota-related diseases.

Motivated by India's nationwide biometric program for social inclusion, we analyze verification (i.e., one-to-one matching) in the case where we possess similarity scores for 10 fingerprints and two irises between a resident's biometric images at enrollment and his biometric images during his first verification. At subsequent verifications, we allow individualized strategies based on these 12 scores: we acquire a subset of the 12 images, get new scores for this subset that quantify the similarity to the corresponding enrollment images, and use the likelihood ratio (i.e., the likelihood of observing these scores if the resident is genuine divided by the corresponding likelihood if the resident is an imposter) to decide whether a resident is genuine or an imposter. We also consider two-stage policies, where additional images are acquired in a second stage if the first-stage results are inconclusive. Using performance data from India's program, we develop a new probabilistic model for the joint distribution of the 12 similarity scores and find near-optimal individualized strategies that minimize the false reject rate (FRR) subject to constraints on the false accept rate (FAR) and mean verification delay for each resident. Our individualized policies achieve the same FRR as a policy that acquires (and optimally fuses) 12 biometrics for each resident, which represents a five (four, respectively) log reduction in FRR relative to fingerprint (iris, respectively) policies previously proposed for India's biometric program. The mean delay is [Formula: see text] sec for our proposed policy, compared to 30 sec for a policy that acquires one fingerprint and 107 sec for a policy that acquires all 12 biometrics. This policy acquires iris scans from 32-41% of residents (depending on the FAR) and acquires an average of 1.3 fingerprints per resident.

Motivated by the lack of randomized controlled trials with an intervention-free control arm in the area of child undernutrition, we fit a trivariate model of weight-for-age z score (WAZ), height-for-age z score (HAZ) and diarrhea status to data from an observational study of supplementary feeding (100 kCal/day for children with WAZ [Formula: see text]) in 17 Guatemalan communities. Incorporating time lags, intention to treat (i.e., to give supplementary food), seasonality and age interactions, we estimate how the effect of supplementary food on WAZ, HAZ and diarrhea status varies with a child's age. We find that the effect of supplementary food on all 3 metrics decreases linearly with age from 6 to 20 mo and has little effect after 20 mo. We derive 2 food allocation policies that myopically (i.e., looking ahead 2 mo) minimize either the underweight or stunting severity - i.e., the sum of squared WAZ or HAZ scores for all children with WAZ or HAZ [Formula: see text]. A simulation study based on the statistical model predicts that the 2 derived policies reduce the underweight severity (averaged over all ages) by 13.6-14.1% and reduce the stunting severity at age 60 mo by 7.1-8.0% relative to the policy currently in use, where all policies have a budget that feeds [Formula: see text]% of children. While these findings need to be confirmed on additional data sets, it appears that in a low-dose (100 kCal/day) supplementary feeding setting in Guatemala, allocating food primarily to 6-12 mo infants can reduce the severity of underweight and stunting.

We analyse the sequence in which the three most commonly prescribed cancer treatments--surgery (S), chemotherapy (C) and radiotherapy (R)--should be administered. A system of ordinary differential equations is formulated that captures the various local and systemic effects of the three modes of treatment, as well as the first-order effects of the inter-relationship between the primary tumour and the distant metastatic tumours, including primary tumour shedding and the primary tumour's effect on the rate of angiogenesis in the metastatic tumours. Under a set of stated assumptions on the parameter values, we find the exact cancer cure probability (subject to toxicity constraints) for the six permutation schedules (i.e. SCR, CSR, CRS, SRC, RSC, RCS) and for two novel schedules, SRCR and RSCR, that apply radiotherapy in disjoint, optimally timed portions. We show analytically that SRCR and RSCR are the two best-performing (i.e. highest cure probability) schedules among the eight considered. Further, SRCR is shown to be optimal among all possible schedules, provided a modest condition is satisfied on the delay of initial angiogenesis experienced by the patient's dormant tumours.

Purpose: The linear-quadratic model typically assumes that tumor sensitivity and repopulation are constant over the time course of radiotherapy. However, evidence suggests that the growth fraction increases and the cell-loss factor decreases as the tumor shrinks. We investigate whether this evolution in tumor geometry, as well as the irregular time intervals between fractions in conventional hyperfractionation schemes, can be exploited by fractionation schedules that employ time-varying fraction sizes. Methods: We construct a mathematical model of a spherical tumor with a hypoxic core and a viable rim, which is most appropriate for a prevascular tumor, and is only a caricature of a vascularized tumor. This model is embedded into the traditional linear-quadratic model by assuming instantaneous reoxygenation. Dynamic programming is used to numerically compute the fractionation regimen that maximizes the tumor-control probability (TCP) subject to constraints on the biologically effective dose of the early and late tissues. Results: In several numerical examples that employ five or 10 fractions per week on a 1-cm or 5-cm diameter tumor, optimally varying the fraction sizes increases the TCP significantly. The optimal regimen incorporates large Friday (afternoon, if 10 fractions per week) fractions that are escalated throughout the course of treatment, and larger afternoon fractions than morning fractions. Conclusion: Numerical results suggest that a significant increase in tumor cure can be achieved by allowing the fraction sizes to vary throughout the course of treatment. Several strategies deserve further investigation: using larger fractions before overnight and weekend breaks, and escalating the dose (particularly on Friday afternoons) throughout the course of treatment.

We analyze two joint decisions in the management of HIV-infected patients on antiretroviral therapy: how frequently to measure a patient's virus level, and when to switch therapy. The underlying stochastic model captures the initial suppression and eventual rebound of the virus level in the blood of a typical HIV-infected patient undergoing treatment. We consider two classes of policies: a viral load policy, which triggers a change in therapy when the current virus level divided by the smallest level achieved thus far exceeds a prespecified threshold, and a proactive policy, which is similar to the viral load policy but also switches drugs at a prespecified time if no evidence of viral rebound has been seen. We find approximate analytical expressions for the probability of switching before the virus reaches its nadir (minimum value) and the mean delay in detection of viral rebound (i.e., the time interval from when the viral nadir occurs until the switch in therapy). Numerical results show that the proactive policy outperforms (i.e., a smaller detection delay for a given probability of prenadir switching) the viral load policy and recent recommendations by an expert AIDS panel, and may delay the onset of multidrug resistance in a significant proportion of patients who experience drug failure.

BACKGROUND: There are not enough cadaveric kidneys to meet the demands of transplant candidates. The equity and efficiency of alternative organ allocation strategies have not been rigorously compared. METHODS: We developed a five-compartment Monte Carlo simulation model to compare alternative organ allocation strategies, accommodating dynamic changes in recipient and donor characteristics, patient and graft survival rates, and quality of life. The model simulated the operations of a single organ procurement organization and attempted to predict the evolution of the transplant waiting list for 10 years. Four allocation strategies were compared: a first-come first-transplanted system; a point system currently utilized by the United Network of Organ Sharing; an efficiency-based algorithm that incorporated correlates of patient and graft survival; and a distributive efficiency algorithm, which had an additional goal of promoting equitable allocation among African-American and other candidates. RESULTS: A 10-year computer simulation was performed. The distributive efficiency policy was associated with a 3.5% ± 0.8% (mean ± SD) increase in quality-adjusted life expectancy (33.9 months vs 32.7 months), a decrease in the median waiting time to transplantation among those who were transplanted (6.6 months vs 16.3 months), and an increase in the overall likelihood of transplantation (61% vs 45%), compared with the United Network of Organ Sharing algorithm. Improved equity and efficiency were also seen by race (African-American vs other), sex, and age ( CONCLUSION: Evidence-based organ allocation strategies in cadaveric kidney transplantation would yield improved equity and efficiency measures compared with existing algorithms.

Those who solve more of a given type of problem tend to get better at it—which suggests that problems of any given type should be brought to specialists for a solution. However, in this paper we argue that agency-related costs and information transfer costs (“sticky” local information) will tend drive the locus of problem-solving in the opposite direction—away from problem-solving by specialist suppliers, and towards those who directly benefit from a solution and who have difficult-to-transfer local information about a particular application being solved, such as the direct users of a product or service. We examine the actual location of design activities in two fields in which custom products are produced by “mass-customization” methods: application-specific integrated circuits (ASICs) and computer telephony integration (CTI) systems. In both, we find that users rather than suppliers are the actual designers of the application-specific portion of the product types examined. We offer anecdotal evidence that the pattern of user-based customization we have documented in these two fields is in fact quite general, and we discuss implications for research and practice.

Because of the health and economic costs of childhood obesity, coupled with studies suggesting the benefits of comprehensive (dietary, physical activity, and behavioral counseling) intervention, the U.S. Preventive Services Task Force recently recommended childhood screening and intervention for obesity beginning at age 6. Using a longitudinal data set consisting of the body mass index of 3,164 children up to age 18 and another longitudinal data set containing the body mass index at ages 18 and 40 and the presence or absence of disease (hypertension and diabetes) at age 40 for 747 people, we formulate and numerically solve—separately for boys and girls—a dynamic programming problem for the optimal biennial (i.e., at ages 2,4,…,16) obesity screening thresholds. Unlike most screening problem formulations, we take a societal viewpoint, where the state of the system at each age is the population-wide probability density function of the body mass index. Compared to the biennial version of the task force's recommendation, the screening thresholds derived from the dynamic program achieve a relative reduction in disease prevalence of 3% at the same screening (and treatment) cost, or—because of the flatness of the disease versus screening trade-off curve—achieves the same disease prevalence at a 28% relative reduction in cost. Compared to the task force's policy, which uses the 95th percentile of body mass index (from cross-sectional growth charts tabulated by the Centers for Disease Control and Prevention) as the screening threshold for each age, the dynamic programming policy treats mostly 16-year-olds (including many who are not obese) and very few males under 14 years old. Although our results suggest that adult hypertension and diabetes are minimized by focusing childhood obesity screening and treatment on older adolescents, the shortcomings in the available data and the narrowness of the medical outcomes considered prevent us from making a recommendation about childhood obesity screening policies. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

To address growing concerns over childhood obesity, the United States Preventive Services Task Force (USPSTF) recently recommended that children undergo obesity screening beginning at age 6 [1]. An Expert Committee recommends starting at age 2 [2]. Analysis is needed to assess these recommendations and investigate whether there are better alternatives. We model the age- and sex-specific population-wide distribution of body mass index (BMI) through age 18 using National Longitudinal Survey of Youth data [3]. The impact of treatment on BMI is estimated using the targeted systematic review performed to aid the USPSTF [4]. The prevalence of hypertension and diabetes at age 40 are estimated from the Panel Study of Income Dynamics [5]. We fix the screening interval at 2 years, and derive the age- and sex-dependent BMI thresholds that minimize adult disease prevalence, subject to referring a specified percentage of children for treatment yearly. We compare this optimal biennial policy to biennial versions of the USPSTF and Expert Committee recommendations. Compared to the USPSTF recommendation, the optimal policy reduces adult disease prevalence by 3% in relative terms (the absolute reductions are < 1%) at the same treatment referral rate, or achieves the same disease prevalence at a 28% reduction in treatment referral rate. If compared to the Expert Committee recommendation, the reductions change to 6% and 40%, respectively. The optimal policy treats mostly 16 year olds and few children under age 14. Our results suggest that adult disease is minimized by focusing childhood obesity screening and treatment on older adolescents.

The article of record as published may be found at http://dx.doi.org/10.1080/1057610X.2010.484028 Supporting material can be found in the Online Appendix located at http://faculty- gsb.stanford.edu/wein/personal/documents/terror network-appendix-sct.pdf Motivated by the links between terror and crime and the difficulty in directly detecting terror activity, this article formulates and solves a resource allocation problem on overlapping networks to determine if interdiction efforts may be able to take advantage of these connections. The government, knowing only the general structure and overlap of the networks, allocates its scarce resources to investigate each terror and criminal network. There are two stages to the investigation: an initial investigation of all nodes (i.e., terrorists or criminals) and a secondary investigation of criminals identified during the initial investigation to determine if they are terrorists. Applying the model to data derived from a population of terrorists in the United States between 1971–2003 suggests that the government may be able to exploit the terror connections of crimes that are relatively uncommon, somewhat easy to detect, and are attractive to terrorists. This research was supported by an Abbott Laboratories Stanford Graduate Fellowship and by grants from the John D. and Catherine T. MacArthur Foundation (Award #02-69383-000-GSS) and the Defense Threat Reduction Agency (DTRA) University Strategic Partnership (Award # DTRA01- 03-D0009/0014 to University of New Mexico) in support of a fellowship at the Center for International Security and Cooperation, Stanford University (M.P.A.), and by the Center for Social Innovation, Graduate School of Business, Stanford University (L.M.W.). This research was supported by an Abbott Laboratories Stanford Graduate Fellowship and by grants from the John D. and Catherine T. MacArthur Foundation (Award #02-69383-000-GSS) and the Defense Threat Reduction Agency (DTRA) University Strategic Partnership (Award # DTRA01- 03-D0009/0014 to University of New Mexico) in support of a fellowship at the Center for International Security and Cooperation, Stanford University (M.P.A.), and by the Center for Social Innovation, Graduate School of Business, Stanford University (L.M.W.).

We construct a mathematical model of aerosol (i.e., droplet-nuclei) transmission of influenza within a household containing one infected and embed it into an epidemic households model in which infecteds occasionally infect someone from another household; in a companion paper, we argue that the contribution from contact transmission is trivial for influenza and the contribution from droplet transmission is likely to be small. Our model predicts that the key infection control measure is the use of N95 respirators, and that the combination of respirators, humidifiers, and ventilation reduces the threshold parameter (which dictates whether or not an epidemic breaks out) by approximately 20% if 70% of households comply, and by approximately 40% if 70% of households and workplaces comply (approximately 28% reduction would have been required to control the 1918 pandemic). However, only approximately 30% of the benefits in the household are achieved if these interventions are used only after the infected develops symptoms. It is also important for people to sleep in separate bedrooms throughout the pandemic, space permitting. Surgical masks with a device (e.g., nylon hosiery) to reduce face-seal leakage are a reasonable alternative to N95 respirators if the latter are in short supply.

We derive mathematical expressions for the mean number of casualties resulting from a deliberate release of a biological or chemical agent into a food supply chain. Our analysis first computes the amount of contaminated food as a function of the network topology and vessel sizes in the food processing plant. A probabilistic analysis, in which each potential consumer of contaminated food has his own random purchase time, infectious dose, and incubation period, determines the number of people who consume enough tainted food to get infected or poisoned before the attack is detected and food consumption is halted. These simple formulas can be used by the U.S. government and the food industry to develop a rough-cut prioritization of the threats from food terrorism, which would be a 1st step toward the allocation of appropriate prevention and mitigation resources.

Decision making for bioterror preparedness involves estimating the consequences of different attack scenarios paired with alternative preparedness and response policies, and selecting an appropriate strategy to minimize deaths, disease, and costs to society. Smallpox vaccination policy provides an excellent case study of these concepts in action. We review both the smallpox vaccination policy debate in the United States circa 2002, and the successful use of operations research methods to influence policy in this arena.

We incorporate a previously validated mathematical model of a vascularized tumor into an optimal control problem to determine the temporal scheduling of radiotherapy and angiogenic inhibitors that maximizes the control of a primary tumor. Our results reveal that optimal antiangiogenic monotherapy gives a large initial injection to attain a 20: 1 ratio of tumor cell volume to supporting vasculature volume. It thereafter maintains this 20: 1 ratio via a continuous dose rate that is intensified over time. The optimal radiation monotherapy schedule is characterized by amodest dose intensification over time. The best performance is achieved by our optimal combination regimen, where the antiangiogenic treatment again maintains a constant tumor-to-vasculature ratio, but is administered in a dose-intensified manner only during the latter portion of the radiation fractionation schedule.

We present results from a mathematical analysis that is aimed at finding the best way to sequence the three traditional cancer treatments: surgery (S), chemotherapy (C), and radiotherapy (R). The mathematical model tracks the temporal evolution of the primary tumor and its associated metastases, and incorporates the primary tumor's effect on the dormancy and growth of the metastases. We show that the SCR schedule (i.e., surgery followed by chemotherapy followed by radiotherapy) achieves a higher cure probability than SRC if the primary tumor is sufficiently large or if the metastatic population is sufficiently large relative to the primary tumor. We also show that a novel schedule, SRCR, which splits the radiotherapy regimen into two disjoint portions, is optimal among all schedules, provided that the patient's dormant metastatic tumors do not become vascularized within about 40 days after surgery.

The author derives a relationship between the mean amount of time wafers spend in the fab and the mean production rate of nondefective die, assuming the number of defects per die is a Poisson random variable whose mean varies linearly with the amount of time the wafer spends in the fab. >

A effective way to improve time-sensitive service systems is to reduce the right tail of the customer waiting-time distribution. We have instituted the following process at Operations Research that aims to reduce the right tail of the review-time distribution for submitted papers. 1. After a newly submitted paper has been with an Area Editor for 4 months, the Managing Editor contacts the Area Editor to get a status report. If the paper has not been processed by the 5-month mark, then the Managing Editor contacts the Associate Editor to get a status report. If a referee’s report is still outstanding at 6 months, then the Managing Editor and/or Editor contacts the referee. At this point, the referee has two options: he/she can agree to withdraw from the paper (and a new referee is sought) or can commit to producing a report within 2 months (i.e., by the end of month 8). If the referee chooses the latter option but fails to produce a report by the agreed-upon date, then the referee receives a demerit and a new referee is sought. 2. The process for dealing with revisions is the same as in (1) above, except the time epochs are reduced from 4 to 2, 5 to 3, 6 to 4, and 8 to 6 months, respectively. 3. The Managing Editor maintains an electronic list of the number of times that a referee has kept an original (revised) paper longer than 6 (4) months (i.e., the Managing Editor and/or Editor had to contact the referee) and the number of demerits received by a referee. This list will be distributed to all Area Editors and Associate Editors, but will not be made available to the community at large. 4. Sanctions are imposed on any referee who receives 3 demerits. This referee will be unable to submit any papers to Operations Research for a duration of time that is at least one year but no more than three years. The referee can reduce the sanction duration (but not to less than one year) by successfully completing a referee’s report (on a subsequent paper) for Operations Research. After a referee receives two sanctions, frequent communication between the Managing Editor and the referee will be maintained, so that the referee clearly understands the ramifications of his/her actions. 5. Although the Managing Editor and Editor will also monitor Associate Editors who have received referees’ reports but have not written their own report, at this point we plan to deal with tardy Associate Editors on a case-bycase basis. A few final comments are in order. First, this process will remain flexible enough to accommodate unusually difficult papers, personal issues (e.g., health, divorce) that the reviewers are struggling with, etc. To ensure flexibility in this process, the Area Editor and the Associate Editor have the option of allowing a referee additional time to handle an unusually difficult paper, and no demerits are incurred without the consent of the Area Editor. Second, our goal here is not to punish referees; aside from the authors, they are the Journal’s most valuable resource. Indeed, given that a referee would have to behave irresponsibly (i.e., renege on a committed 8-month lead time after being given the opportunity to withdraw in a penaltyfree manner) three times to earn a sanction, I do not foresee having to sanction anyone during my three-year appointment as Editor. Rather, our goal is to bring closure to papers that appear headed for very lengthy delays. However, we are not in a position to offer an honorarium for reviewing papers. The annual Meritorious Service Award for outstanding referees is our only concrete positive incentive. Our hope is that the presence of the monitoring process will deter referees from generating unsatisfactory delays in the review process. The resulting reductions in the review times should benefit our entire community, particularly our tenure-track faculty.

In their report “Containing bioterrorist smallpox” (15 Nov., p. [1428][1]), M. E. Halloran et al. state that their “structured simulator” does not produce the “two orders of magnitude difference” between the number of deaths under targeted vaccination and the number of deaths under mass

We consider bi-criteria scheduling problems for three queueing systems (a single queue, a two-station closed network, and a two-station network with controllable inputs) populated by various customer types. The objective is to minimize the long run expected average value of a linear combination of the customer sojourn time and the sojourn time inequity. The inequity at time t is the sum of squares of the pairwise differences of the total number of customers in the system at time t of each type divided by their respective arrival rates. Brownian approximations to these three scheduling problems are solved, and the solutions are interpreted in order to obtain scheduling policies. Simulation results show that the second objective criteria tends to equalize the mean sojourn times of the various customer types, and may lead to a reduction in sojourn time variance. The simulation results also show that in the network settings, in contrast to the single queue case, there are priority sequencing policies that significantly reduce the variance of sojourn times relative to the first-come first-served policy.

We consider a queueing network with two single-server stations and two types of customers. Customers of type A require service only at station 1 and customers of type B require service first at station 1 and then at station 2. Each server has a different general service time distribution, and each customer type has a different general interarrival time distribution. The problem is to find a dynamic sequencing policy at station 1 that minimizes the long-run average expected number of customers in the system. The scheduling problem is approximated by a dynamic control problem involving Brownian motion. A reformulation of this control problem is solved, and the solution is interpreted in terms of the queueing system in order to obtain an effective sequencing policy. Also, a pathwise lower bound (for any sequencing policy) is obtained for the total number of customers in the network. We show via simulation that the relative difference between the performance of the proposed policy and the pathwise lower bound becomes small as the load on the network is increased toward the heavy traffic limit.

The impact that scheduling can have on the performance of semi-conductor wafer fabrication facilities is assessed. The performance measure considered is the mean throughput time (sometimes called cycle time, turnaround time or manufacturing interval) for a lot of wafers. A variety of input control and sequencing rules are evaluated using a simulation model of a representative, but fictitious, semiconductor wafer fabrication. Certain of these scheduling rules are derived by restricting attention to the sub-set of stations that are heavily utilized, and by using a Brownian network model, which approximates a multi-class queuing network model with dynamic control capability. Three versions of the wafer fabrication model, which differ only by the number of servers present at particular stations, are studied. The three versions have one, two, and four stations, respectively, that are heavily utilized (near 90% utilization). The simulation results indicate that scheduling has a significant impact on average throughput time, with larger improvements coming from discretionary imput control than from lot sequencing. The effects that specific sequencing rules have are highly dependent on both the type of input control used and the number of bottleneck stations in the fabrication. >

Background Motivated by the observation that children suffering from undernutrition are more likely to experience disease and are more likely to die if they do contract a disease, mathematical modelling is used to explore the ramifications of targeting preventive disease measures to undernutritioned children. Methods A malaria model is constructed with superinfection and heterogeneous susceptibility, where a portion of this susceptibility is due to undernutrition (as measured by weight-for-age z scores); so as to isolate the impact of supplementary food on malaria from the influence of confounding factors, the portion of the total susceptibility that is due to undernutrition is estimated from a large randomized trial of supplementary feeding. Logistic regression is used to estimate mortality given malaria infection as a function of weight-for-age z scores. The clinical malaria morbidity and malaria mortality are analytically computed for a variety of policies involving supplementary food and insecticide-treated bed nets. Results The portion of heterogeneity in susceptibility that is due to undernutrition is estimated to be 90.3 %. Targeting insecticide-treated bed nets to undernutritioned children leads to fewer malaria deaths than the random distribution of bed nets in the hypoendemic and mesoendemic settings. When baseline bed net coverage for children is 20 %, supplementary food given to underweight children is estimated to reduce malaria mortality by 7.2–22.9 % as the entomological inoculation rate ranges from 500 to 1.0. In the hyperendemic setting, supplementary food has a bigger impact than bed nets, particularly when baseline bed net coverage is high. Conclusions Although the results are speculative (e.g., they are based on parameter estimates that do not possess the traditional statistical significance level), the biological plausibility of the modelling assumptions and the high price-sensitivity of demand for bed nets suggest that free bed net distribution targeted to undernutritioned children in areas suffering from both undernutrition and malaria (e.g., sub-Saharan Africa) should be the subject of a randomized trial in a hypoendemic or mesoendemic setting. Electronic supplementary material The online version of this article (doi:10.1186/s12936-015-0894-x) contains supplementary material, which is available to authorized users.