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Mathematical models are presented and analyzed to facilitate a food bank's equitable and effective distribution of donated food among the population at risk for hunger. Typically exceeding the donated supply, demand is proportional to the poverty population within the food bank's service area. The food bank seeks to ensure a perfectly equitable distribution of food, i.e., each county in the service area should receive a food allocation that is exactly proportional to the county's demand such that no county is at a disadvantage compared to any other county. This objective often conflicts with the goal of maximizing effectiveness by minimizing the amount of undistributed food. Deterministic network-flow models are developed to minimize the amount of undistributed food while maintaining a user-specified upper bound on the absolute deviation of each county from a perfectly equitable distribution. An extension of this model identifies optimal policies for the allocation of additional receiving capacity to counties in the service area. A numerical study using data from a large North Carolina food bank illustrates the uses of the models.A probabilistic sensitivity analysis reveals the effect on the models' optimal solutions arising from uncertainty in the receiving capacities of the counties in the service area.

Female pelvic floor dysfunction is integral to the woman's role in the reproductive process, largely because of the unique anatomic features that facilitate vaginal birth and also because of the trauma that can occur during that event. Interventions such as primary elective cesarean delivery have been discussed for the primary prevention of pelvic floor dysfunction; however, existing data about potentially causal factors limit our ability to evaluate such strategies critically. Here we consider the conceptual principles of epidemiologic function and the availability of data that are necessary to make informed recommendations about prevention opportunities for pelvic floor dysfunction at delivery. Available epidemiologic data on pelvic floor dysfunction suggest that there may be substantial opportunities for the primary prevention of pelvic organ prolapse at delivery. Although definitive recommendations await further epidemiologic studies of the potential risk and benefits of obstetric practice change, it is hoped that this discussion will provide a novel, quantitative framework for the assessment of pelvic floor dysfunction prevention opportunities.

Questions regarding the relative value and frequency of mammography screening for premenopausal women versus postmenopausal women remain open due to the conflicting age-based dynamics of both the disease (increasing incidence, decreasing aggression) and the accuracy of the test results (increasing sensitivity and specificity). To investigate these questions, we formulate a partially observed Markov chain model that captures several of these age-based dynamics not previously considered simultaneously. Using sample-path enumeration, we evaluate a broad range of policies to generate the set of “efficient” policies, as measured by a lifetime breast cancer mortality risk metric and an expected mammogram count, from which a patient may select a policy based on individual circumstance. We demonstrate robustness with respect to small changes in the input data and conclude that, in general, to efficiently achieve a lifetime risk comparable to the current risk among U.S. women, screening should start relatively early in life and continue relatively late in life regardless of the screening interval(s) adopted. The frontier also exhibits interesting patterns with respect to policy type, where policy type is defined by the relationship between the screening interval prescribed in younger years and that prescribed later in life.

Key Points Question What is the association of COVID-19 vaccine efficacy and coverage scenarios with and without nonpharmaceutical interventions (NPIs) with SARS-CoV-2 infections, hospitalizations, and deaths? Findings A decision analytical model of North Carolina found that removing NPIs while vaccines were distributed resulted in substantial increases in infections, hospitalizations, and deaths. Furthermore, as NPIs were removed, higher vaccination coverage with less efficacious vaccines contributed to a larger reduction in risk of infection compared with more efficacious vaccines at lower coverage. Meaning These findings highlight the need for high COVID-19 vaccine coverage and continued adherence to NPIs before safely resuming many prepandemic activities.

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