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We measured severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA concentrations in primary sewage sludge in the New Haven, Connecticut, USA, metropolitan area during the Coronavirus Disease 2019 (COVID-19) outbreak in Spring 2020. SARS-CoV-2 RNA was detected throughout the more than 10-week study and, when adjusted for time lags, tracked the rise and fall of cases seen in SARS-CoV-2 clinical test results and local COVID-19 hospital admissions. Relative to these indicators, SARS-CoV-2 RNA concentrations in sludge were 0–2 d ahead of SARS-CoV-2 positive test results by date of specimen collection, 0–2 d ahead of the percentage of positive tests by date of specimen collection, 1–4 d ahead of local hospital admissions and 6–8 d ahead of SARS-CoV-2 positive test results by reporting date. Our data show the utility of viral RNA monitoring in municipal wastewater for SARS-CoV-2 infection surveillance at a population-wide level. In communities facing a delay between specimen collection and the reporting of test results, immediate wastewater results can provide considerable advance notice of infection dynamics. Testing sewage for the novel coronavirus reveals epidemiological trends.

We apply standard demographic principles of inflows and outflows to estimate the number of undocumented immigrants in the United States, using the best available data, including some that have only recently become available. Our analysis covers the years 1990 to 2016. We develop an estimate of the number of undocumented immigrants based on parameter values that tend to underestimate undocumented immigrant inflows and overstate outflows; we also show the probability distribution for the number of undocumented immigrants based on simulating our model over parameter value ranges. Our conservative estimate is 16.7 million for 2016, nearly fifty percent higher than the most prominent current estimate of 11.3 million, which is based on survey data and thus different sources and methods. The mean estimate based on our simulation analysis is 22.1 million, essentially double the current widely accepted estimate. Our model predicts a similar trajectory of growth in the number of undocumented immigrants over the years of our analysis, but at a higher level. While our analysis delivers different results, we note that it is based on many assumptions. The most critical of these concern border apprehension rates and voluntary emigration rates of undocumented immigrants in the U.S. These rates are uncertain, especially in the 1990's and early 2000's, which is when-both based on our modeling and the very different survey data approach-the number of undocumented immigrants increases most significantly. Our results, while based on a number of assumptions and uncertainties, could help frame debates about policies whose consequences depend on the number of undocumented immigrants in the United States.

Ascertaining the state of coronavirus outbreaks is crucial for public health decision-making. Absent repeated representative viral test samples in the population, public health officials and researchers alike have relied on lagging indicators of infection to make inferences about the direction of the outbreak and attendant policy decisions. Recently researchers have shown that SARS-CoV-2 RNA can be detected in municipal sewage sludge with measured RNA concentrations rising and falling suggestively in the shape of an epidemic curve while providing an earlier signal of infection than hospital admissions data. The present paper presents a SARS-CoV-2 epidemic model to serve as a basis for estimating the incidence of infection, and shows mathematically how modeled transmission dynamics translate into infection indicators by incorporating probability distributions for indicator-specific time lags from infection. Hospital admissions and SARS-CoV-2 RNA in municipal sewage sludge are simultaneously modeled via maximum likelihood scaling to the underlying transmission model. The results demonstrate that both data series plausibly follow from the transmission model specified and provide a 95% confidence interval estimate of the reproductive number R0 ≈ 2.4 ± 0.2. Sensitivity analysis accounting for alternative lag distributions from infection until hospitalization and sludge RNA concentration respectively suggests that the detection of viral RNA in sewage sludge leads hospital admissions by 3 to 5 days on average. The analysis suggests that stay-at-home restrictions plausibly removed 89% of the population from the risk of infection with the remaining 11% exposed to an unmitigated outbreak that infected 9.3% of the total population.

Monitoring the progression of SARS-CoV-2 outbreaks requires accurate estimation of the unobservable fraction of the population infected over time in addition to the observed numbers of COVID-19 cases, as the latter present a distorted view of the pandemic due to changes in test frequency and coverage over time. The objective of this report is to describe and illustrate an approach that produces representative estimates of the unobservable cumulative incidence of infection by scaling the daily concentrations of SARS-CoV-2 RNA in wastewater from the consistent population contribution of fecal material to the sewage collection system.

The novel coronavirus 2019-nCoV first appeared in December 2019 in Wuhan, China. While most of the initial cases were linked to the Huanan Seafood Wholesale Market, person-to-person transmission has been verified. Given that a vaccine cannot be developed and deployed for at least a year, preventing further transmission relies upon standard principles of containment, two of which are the isolation of known cases and the quarantine of persons believed at high risk of exposure. This note presents probability models for assessing the effectiveness of case isolation and quarantine within a community during the initial phase of an outbreak with illustrations based on early observations from Wuhan.

Sexual violence is a major public health issue, affecting 35% of women worldwide. Major risk factors for sexual assault include inadequate indoor sanitation and the need to travel to outdoor toilet facilities. We estimated how increasing the number of toilets in an urban township (Khayelitsha, South Africa) might reduce both economic costs and the incidence and social burden of sexual assault. We developed a mathematical model that links risk of sexual assault to the number of sanitation facilities and the time a woman must spend walking to a toilet. We defined a composite societal cost function, comprising both the burden of sexual assault and the costs of installing and maintaining public chemical toilets. By expressing total social costs as a function of the number of available toilets, we were able to identify an optimal (i.e., cost-minimizing) social investment in toilet facilities. There are currently an estimated 5600 toilets in Khayelitsha. This results in 635 sexual assaults and US$40 million in combined social costs each year. Increasing the number of toilets to 11300 would minimize total costs ($35 million) and reduce sexual assaults to 446. Higher toilet installation and maintenance costs would be more than offset by lower sexual assault costs. Probabilistic sensitivity analysis shows that the optimal number of toilets exceeds the original allocation of toilets in the township in over 80% of the 5000 iterations of the model. Improving access to sanitation facilities in urban settlements will simultaneously reduce the incidence of sexual assaults and overall cost to society. Since our analysis ignores the many additional health benefits of improving sanitation in resource-constrained urban areas (e.g., potential reductions in waterborne infectious diseases), the optimal number of toilets identified here should be interpreted as conservative.

We consider an infinite sequence of customers of types and an infinite sequence of servers of types where a server of type j can serve a subset of customer types C(j) and where a customer of type i can be served by a subset of server types S(i). We assume that the types of customers and servers in the infinite sequences are random, independent, and identically distributed, and that customers and servers are matched according to their order in the sequence, on a first-come–first-served (FCFS) basis. We investigate this process of infinite bipartite matching. In particular, we are interested in the rate r i,j that customers of type i are assigned to servers of type j. We present a countable state Markov chain to describe this process, and for some previously unsolved instances, we prove ergodicity and existence of limiting rates, and calculate r i,j .

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.

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.

The first-come, first-served (FCFS) stochastic matching model, where each server in an infinite sequence is matched to the first eligible customer from a second infinite sequence, developed from queueing problems addressed by Kaplan (1984) in the context of public housing assignments. The goal of this model is to determine the matching rates between eligible customer types and server types, that is, the fraction of all matches that occur between type- i customers and type- j servers. This model was solved in a beautiful paper by Adan and Weiss, but the resulting equation for the matching rates is quite complicated, involving the sum of permutation-specific terms over all permutations of the server types. Here, we develop an approximation for the matching rates based on Ohm’s Law that in some cases reduces to exact results, and via analytical, numerical, and simulation examples is shown to be highly accurate. As our approximation only requires solving a system of linear equations, it provides an accurate and tractable alternative to the exact solution.