Abstract. The open pit mine block sequencing problem (OPBS) seeks a discrete-time production schedule that maximizes the net present value of the orebody extracted from an open-pit mine. This integer program (IP) discretizes the mine's volume into blocks, imposes precedence constraints between blocks, and limits resource consumption in each time period. We develop a "sliding time window heuristic" to solve this IP approximately. The heuristic recursively defines, solves and partially fixes an approximating model having: (i) fixed variables in early time periods, (ii) an exact submodel defined over a "window" of middle time periods, and (iii) a relaxed submodel in later time periods. The heuristic produces near-optimal solutions (typically within 2% of optimality) for model instances that standard optimization software fails to solve. Furthermore, it produces these solutions quickly, even though our OPBS model enforces standard upper-bounding constraints on resource consumption along with less standard, but important, lower-bounding constraints.
Robust surveillance testing is a key strategic plan to prevent COVID-19 outbreaks and slow the spread of the SARS-CoV-2 pandemic; however, limited resources, facilities and time often impair the implementation of a widespread surveillance effort. To mitigate these resource limitations, we employed a strategy of pooling samples, reducing reagent cost and processing time. Through utilizing academic faculty and labs, successful pooled surveillance testing was conducted throughout Fall 2020 semester to detect positive SARS-CoV-2 infections in a population of 4400 students. During the semester, over 25,000 individual COVID status evaluations were made by pooling eight individual samples into one quantitative reverse transcription polymerase chain reaction. This pooled surveillance strategy was highly effective at detecting infection and significantly reduced financial burden and cost by $3.6 million.
A closed-form equation, the Fizzle Equation, was derived from a mathematical model predicting Severe Acute Respiratory Virus-2 dynamics, optimized for a 4000-student university cohort. This equation sought to determine the frequency and percentage of random surveillance testing required to prevent an outbreak, enabling an institution to develop scientifically sound public health policies to bring the effective reproduction number of the virus below one, halting virus progression. Model permutations evaluated the potential spread of the virus based on the level of random surveillance testing, increased viral infectivity and implementing additional safety measures. The model outcomes included: required level of surveillance testing, the number of infected individuals, and the number of quarantined individuals. Using the derived equations, this study illustrates expected infection load and how testing policy can prevent outbreaks in an institution. Furthermore, this process is iterative, making it possible to develop responsive policies scaling the amount of surveillance testing based on prior testing results, further conserving resources.
Beginning in early March 2021 and continuing through May 2021, the USAF Academy began vaccinating cadets for protection against the SARS-CoV-2 virus with the BNT162b2 (Pfizer-BioNTech) mRNA vaccine. During this period, vaccination of the almost 4200 cadet population increased from 3% to 85% and prevalence of COVID-19 in the cadet population was constant at approximately 0.4% as indicated by weekly surveillance testing. In this study, vaccine effectiveness at preventing infection is estimated by comparing infection risk as a function of time since vaccination. A statistically significant four-fold reduction in infection risk was observed 14 days after the first vaccine dose and an eleven-fold reduction in infection risk was observed in fully vaccinated cadets. Overall, the Pfizer-BioNTech vaccine was 91% (95% confidence interval = 55-99%) effective at preventing infection in healthy young adults (17-26 years of age) in a university setting and military training environment.
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