Modeling local coronavirus outbreaks.

This article presents an overview of methods developed for the modeling and control of local coronavirus outbreaks. The article reviews early transmission dynamics featuring exponential growth in infections, and links this to a renewal epidemic model where the current incidence of infection depends upon the expected value of incidence randomly lagged into the past. This leads directly to simple formulas for the fraction of the population infected in an unmitigated outbreak, and reveals herd immunity as the solution to an optimization problem. The model also leads to direct and easy-to-understand formulas for aligning observable epidemic indicators such as cases, hospitalizations and deaths with the unobservable incidence of infection, and as a byproduct leads to a simple first-order approach for estimating the effective reproduction number R t . The model also leads naturally to direct assessments of the effectiveness of isolation in preventing the spread of infection. This is illustrated with application to repeat asymptomatic screening programs of the sort utilized by universities, sports teams and businesses to prevent the spread of infection.

Scaling SARS-CoV-2 wastewater concentrations to population estimates of infection.

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.

Predicting daily COVID-19 case rates from SARS-CoV-2 RNA concentrations across a diversity of wastewater catchments.

We assessed the relationship between municipality COVID-19 case rates and SARS-CoV-2 concentrations in the primary sludge of corresponding wastewater treatment facilities. Over 1700 daily primary sludge samples were collected from six wastewater treatment facilities with catchments serving 18 cities and towns in the State of Connecticut, USA. Samples were analyzed for SARS-CoV-2 RNA concentrations during a 10 month time period that overlapped with October 2020 and winter/spring 2021 COVID-19 outbreaks in each municipality. We fit lagged regression models to estimate reported case rates in the six municipalities from SARS-CoV-2 RNA concentrations collected daily from corresponding wastewater treatment facilities. Results demonstrate the ability of SARS-CoV-2 RNA concentrations in primary sludge to estimate COVID-19 reported case rates across treatment facilities and wastewater catchments, with coverage probabilities ranging from 0.94 to 0.96. Lags of 0 to 1 days resulted in the greatest predictive power for the model. Leave-one-out cross validation suggests that the model can be broadly applied to wastewater catchments that range in more than one order of magnitude in population served. The close relationship between case rates and SARS-CoV-2 concentrations demonstrates the utility of using primary sludge samples for monitoring COVID-19 outbreak dynamics. Estimating case rates from wastewater data can be useful in locations with limited testing availability, testing disparities, or delays in individual COVID-19 testing programs.

Aligning SARS-CoV-2 indicators via an epidemic model: application to hospital admissions and RNA detection in sewage sludge.

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.

Repeat SARS-CoV-2 testing models for residential college populations.

Residential colleges are considering re-opening under uncertain futures regarding the COVID-19 pandemic. We consider repeat SARS-CoV-2 testing models for the purpose of containing outbreaks in the residential campus community. The goal of repeat testing is to detect and isolate new infections rapidly to block transmission that would otherwise occur both on and off campus. The models allow for specification of aspects including scheduled on-campus resident screening at a given frequency, test sensitivity that can depend on the time since infection, imported infections from off campus throughout the school term, and a lag from testing until student isolation due to laboratory turnaround and student relocation delay. For early- (late-) transmission of SARS-CoV-2 by age of infection, we find that weekly screening cannot reliably contain outbreaks with reproductive numbers above 1.4 (1.6) if more than one imported exposure per 10,000 students occurs daily. Screening every three days can contain outbreaks providing the reproductive number remains below 1.75 (2.3) if transmission happens earlier (later) with time from infection, but at the cost of increased false positive rates requiring more isolation quarters for students testing positive. Testing frequently while minimizing the delay from testing until isolation for those found positive are the most controllable levers for preventing large residential college outbreaks. A web app that implements model calculations is available to facilitate exploration and consideration of a variety of scenarios.

Snapshot Models of Undocumented Immigration.

Accurately estimating the size of the undocumented immigrant population is a critical component of assessing the health and security risks of undocumented immigration to the United States. To provide one such estimate, we use data from the Mexican Migration Project (MMP), a study that includes samples of undocumented Mexican immigrants to the United States after their return to Mexico. Of particular interest are the departure and return dates of a sampled migrant's most recent sojourn in the United States, and the total number of such journeys undertaken by that migrant household, for these data enable the construction of data-driven undocumented immigration models. However, such data are subject to an extreme physical bias, for to be included in such a sample, a migrant must have returned to Mexico by the time of the survey, excluding those undocumented immigrants still in the United States. In our analysis, we account for this bias by jointly modeling trip timing and duration to produce the likelihood of observing the data in such a "snapshot" sample. Our analysis characterizes undocumented migration flows including single-visit migrants, repeat visitors, and "retirement" from circular migration. Starting with 1987, we apply our models to 30 annual random snapshot surveys of returned undocumented Mexican migrants accounting for undocumented Mexican migration from 1980 to 2016. Scaling to population quantities and supplementing our analysis of southern border crossings with estimates of visa overstays, we produce lower bounds on the total number of undocumented immigrants that are much larger than conventional estimates based on U.S.-based census-linked surveys, and broadly consistent with the more recent estimates reported by Fazel-Zarandi, Feinstein, and Kaplan.

Measurement of SARS-CoV-2 RNA in wastewater tracks community infection dynamics.

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.

Containing 2019-nCoV (Wuhan) coronavirus.

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.

The number of undocumented immigrants in the United States: Estimates based on demographic modeling with data from 1990 to 2016.

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.

An Adaptive Approach to Locating Mobile HIV Testing Services.

BACKGROUND: Public health agencies suggest targeting "hotspots" to identify individuals with undetected HIV infection. However, definitions of hotspots vary. Little is known about how best to target mobile HIV testing resources. METHODS: We conducted a computer-based tournament to compare the yield of 4 algorithms for mobile HIV testing. Over 180 rounds of play, the algorithms selected 1 of 3 hypothetical zones, each with unknown prevalence of undiagnosed HIV, in which to conduct a fixed number of HIV tests. The algorithms were: 1) Thompson Sampling, an adaptive Bayesian search strategy; 2) Explore-then-Exploit, a strategy that initially draws comparable samples from all zones and then devotes all remaining rounds of play to HIV testing in whichever zone produced the highest observed yield; 3) Retrospection, a strategy using only base prevalence information; and; 4) Clairvoyance, a benchmarking strategy that employs perfect information about HIV prevalence in each zone. RESULTS: Over 250 tournament runs, Thompson Sampling outperformed Explore-then-Exploit 66% of the time, identifying 15% more cases. Thompson Sampling's superiority persisted in a variety of circumstances examined in the sensitivity analysis. Case detection rates using Thompson Sampling were, on average, within 90% of the benchmark established by Clairvoyance. Retrospection was consistently the poorest performer. LIMITATIONS: We did not consider either selection bias (i.e., the correlation between infection status and the decision to obtain an HIV test) or the costs of relocation to another zone from one round of play to the next. CONCLUSIONS: Adaptive methods like Thompson Sampling for mobile HIV testing are practical and effective, and may have advantages over other commonly used strategies.

A Randomized, Open-Label, Safety and Exploratory Efficacy Study of Kanglaite Injection (KLTi) plus Gemcitabine versus Gemcitabine in Patients with Advanced Pancreatic Cancer.

Background: This study was designed to assess the safety and preliminary efficacy of KLTi plus gemcitabine in patients with locally advanced or metastatic pancreatic cancer. Methods: In a randomized, open-label study, patients with locally advanced or metastatic pancreatic cancer were randomized 2:1 to receive KLTi plus gemcitabine or gemcitabine monotherapy. Three sequential cohorts were tested at 30 g/day, 50 g/day, and 30 g/day. Gemcitabine was administered at 1000 mg/m2 on days 1, 8 and 15 of each 28 day cycle. KLTi was administered on days 1-5, 8-12, and 15-19 of each 28 day cycle. Patients received study treatment until disease progression. The primary endpoint was progression-free survival in the ITT population. Safety evaluation was based on patients who received any study treatment. ClinicalTrials.gov identifier NCT00733850. Results: Eighty-five patients were randomized including 41 (28:13) in Cohort 1, 18 (12:6) in Cohort 2, and 26 (17:9) in Cohort 3. Due to a different dose and/or shift in patient populations in Cohort 2 and 3, efficacy data for the 30 gm dose are presented in this manuscript for Cohort 1 alone, and for the combination of Cohort 1+3. The 30 gm KLTi + gemcitabine group had a statistically significant improvement in progression-free survival (PFS) as assessed by blinded independent radiology review in the ITT population, with a median of 112 days, versus 58 days in the gemcitabine group (HR 0.50; 95% CI: 0.27, 0.92), p = 0.0240. The incidence rates of TEAEs, CTCAE Grade 3 or higher TEAEs, and SAEs were similar between the two arms. There were no deaths related to KLTi + gemcitabine treatment. Conclusion: Kanglaite Injection (30 g/day) plus a standard regimen of gemcitabine demonstrated encouraging clinical evidence of anti-neoplastic activity and a well-tolerated safety profile.

A Flow-Based Model of the HIV Care Continuum in the United States.

BACKGROUND: Understanding the flow of patients through the continuum of HIV care is critical to determine how best to intervene so that the proportion of HIV-infected persons who are on antiretroviral treatment and virally suppressed is as large as possible. METHODS: Using immunological and virological data from the Centers for Disease Control and Prevention and the North American AIDS Cohort Collaboration on Research and Design from 2009 to 2012, we estimated the distribution of time spent in and dropout probability from each stage in the continuum of HIV care. We used these estimates to develop a queueing model for the expected number of patients found in each stage of the cascade. RESULTS: HIV-infected individuals spend an average of about 3.1 months after HIV diagnosis before being linked to care, or dropping out of that stage of the continuum with a probability of 8%. Those who link to care wait an additional 3.7 months on average before getting their second set of laboratory results (indicating engagement in care) or dropping out of care with probability of almost 6%. Those engaged in care spent an average of almost 1 year before achieving viral suppression on antiretroviral therapy or dropping out with average probability 13%. For patients who achieved viral suppression, the average time suppressed on antiretroviral therapy was an average of 4.5 years. CONCLUSIONS: Interventions should be targeted to more rapidly identifying newly infected individuals, and increasing the fraction of those engaged in care that achieves viral suppression.

Reducing sexual violence by increasing the supply of toilets in Khayelitsha, South Africa: a mathematical model.

BACKGROUND: 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. METHODS: 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. FINDINGS: 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. INTERPRETATION: 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.

Importance and relevance of pulmonary symptoms among patients receiving second- and third-line treatment for advanced non-small-cell lung cancer: support for the content validity of the 4-item Pulmonary Symptom Index.

BACKGROUND: In advanced non-small-cell lung cancer (NSCLC), reducing symptoms can be a meaningful treatment outcome. This study characterizes the pulmonary symptoms of patients receiving second- and third-line systemic therapies for NSCLC and assesses the content validity of the 4-item Pulmonary Symptom Index (PSI) of the Functional Assessment of Cancer Therapy-Lung (FACT-L). METHODS: Twenty patients with advanced NSCLC undergoing second- and third-line treatment ("qualitative sample") completed semistructured interviews regarding their NSCLC symptoms and the importance of pulmonary symptoms. Results were mapped to the PSI. In addition, existing PSI data from 912 patients with cancer ("validation sample") was analyzed to evaluate the scalability of the 4 PSI items. RESULTS: In the qualitative sample, mean age was 62 years (range 30-79 years); 80% had nonsquamous histologic type, and 25% had comorbid chronic obstructive pulmonary disease (COPD). A core set of pulmonary symptoms emerged in the data-shortness of breath, cough, and chest tightness. These mapped to 3 PSI items. A quarter of the patients reported an absence of pulmonary symptoms, which supports the inclusion of the final PSI item, "breathing is easy." In the validation sample, for the shortness of breath/breathing ease item pair, weighted kappa representing chance-adjusted agreement ranged from 0.39 to 0.54 and percent agreement from 44% to 49% (both considered moderate), supporting a distinct contribution of each item. CONCLUSION: The PSI captures the most important and relevant symptoms reported by patients with NSCLC receiving second- and third-line treatment. Our results suggest that the PSI may provide a clinically useful method to measure patient benefit from lung cancer therapies.

Estimating HIV incidence in the United States from HIV/AIDS surveillance data and biomarker HIV test results.

The development of an human immunodeficiency virus (HIV) test that detects recent infection has enabled the U.S. Centers for Disease Control and Prevention (CDC) to estimate annual HIV incidence (number of new infections per year, not per person at risk) in the United States from data on new HIV and acquired immunodeficiency syndrome (AIDS) diagnoses reported to HIV/AIDS surveillance. We developed statistical procedures to estimate the probability that an infected person will be detected as recently infected, accounting for individuals choosing whether and how frequently to seek HIV testing, variation of testing frequency, the reporting of test results only for infected persons, and infected persons who never had an HIV-negative test. The incidence estimate is the number of persons detected as recently infected divided by the estimated probability of detection. We used simulation to show that, under the assumptions we make, our procedures have acceptable bias and correct confidence interval coverage. Because data on the biomarker for recent infection or on testing history were missing for many persons, we used multiple imputation to apply our models to surveillance data. CDC has used these procedures to estimate HIV incidence in the United States.

Estimation of HIV incidence in the United States.

CONTEXT: Incidence of human immunodeficiency virus (HIV) in the United States has not been directly measured. New assays that differentiate recent vs long-standing HIV infections allow improved estimation of HIV incidence. OBJECTIVE: To estimate HIV incidence in the United States. DESIGN, SETTING, AND PATIENTS: Remnant diagnostic serum specimens from patients 13 years or older and newly diagnosed with HIV during 2006 in 22 states were tested with the BED HIV-1 capture enzyme immunoassay to classify infections as recent or long-standing. Information on HIV cases was reported to the Centers for Disease Control and Prevention through June 2007. Incidence of HIV in the 22 states during 2006 was estimated using a statistical approach with adjustment for testing frequency and extrapolated to the United States. Results were corroborated with back-calculation of HIV incidence for 1977-2006 based on HIV diagnoses from 40 states and AIDS incidence from 50 states and the District of Columbia. MAIN OUTCOME MEASURE: Estimated HIV incidence. RESULTS: An estimated 39,400 persons were diagnosed with HIV in 2006 in the 22 states. Of 6864 diagnostic specimens tested using the BED assay, 2133 (31%) were classified as recent infections. Based on extrapolations from these data, the estimated number of new infections for the United States in 2006 was 56,300 (95% confidence interval [CI], 48,200-64,500); the estimated incidence rate was 22.8 per 100,000 population (95% CI, 19.5-26.1). Forty-five percent of infections were among black individuals and 53% among men who have sex with men. The back-calculation (n = 1.230 million HIV/AIDS cases reported by the end of 2006) yielded an estimate of 55,400 (95% CI, 50,000-60,800) new infections per year for 2003-2006 and indicated that HIV incidence increased in the mid-1990s, then slightly declined after 1999 and has been stable thereafter. CONCLUSIONS: This study provides the first direct estimates of HIV incidence in the United States using laboratory technologies previously implemented only in clinic-based settings. New HIV infections in the United States remain concentrated among men who have sex with men and among black individuals.