O ne key factor contributing to emergency department (ED) overcrowding is prolonged waiting time for admission to inpatient wards, also known as ED boarding time. To gain insights into reducing this waiting time, we study operations in the inpatient wards and their interface with the ED. We focus on understanding the effect of inpatient discharge policies and other operational policies on the time-of-day waiting time performance, such as the fraction of patients waiting longer than six hours in the ED before being admitted. Based on an empirical study at a Singaporean hospital, we propose a novel stochastic processing network with the following characteristics to model inpatient operations: (1) A patient's service time in the inpatient wards depends on that patient's admission and discharge times and length of stay. The service times capture a two-time-scale phenomenon and are not independent and identically distributed.(2) Pre-and post-allocation delays model the extra amount of waiting caused by secondary bottlenecks other than bed unavailability, such as nurse shortage.(3) Patients waiting for a bed can overflow to a nonprimary ward when the waiting time reaches a threshold, where the threshold is time dependent. We show, via simulation studies, that our model is able to capture the inpatient flow dynamics at hourly resolution and can evaluate the impact of operational policies on both the daily and time-of-day waiting time performance. In particular, our model predicts that implementing a hypothetical policy can eliminate excessive waiting for those patients who request beds in mornings. This policy incorporates the following components: a discharge distribution with the first discharge peak between 8 a.m. and 9 a.m. and 26% of patients discharging before noon, and constant-mean allocation delays throughout the day. The insights gained from our model can help hospital managers to choose among different policies to implement depending on the choice of objective, such as to reduce the peak waiting in the morning or to reduce daily waiting time statistics.

BackgroundDuring the 2009 H1N1 influenza pandemic, concerns arose about the potential negative effects of mass public gatherings and travel on the course of the pandemic. Better understanding the potential effects of temporal changes in social mixing patterns could help public officials determine if and when to cancel large public gatherings or enforce regional travel restrictions, advisories, or surveillance during an epidemic.MethodsWe develop a computer simulation model using detailed data from the state of Georgia to explore how various changes in social mixing and contact patterns, representing mass gatherings and holiday traveling, may affect the course of an influenza pandemic. Various scenarios with different combinations of the length of the mass gatherings or traveling period (range: 0.5 to 5 days), the proportion of the population attending the mass gathering events or on travel (range: 1% to 50%), and the initial reproduction numbers R0 (1.3, 1.5, 1.8) are explored.ResultsMass gatherings that occur within 10 days before the epidemic peak can result in as high as a 10% relative increase in the peak prevalence and the total attack rate, and may have even worse impacts on local communities and travelers' families. Holiday traveling can lead to a second epidemic peak under certain scenarios. Conversely, mass traveling or gatherings may have little effect when occurring much earlier or later than the epidemic peak, e.g., more than 40 days earlier or 20 days later than the peak when the initial R0 = 1.5.ConclusionsOur results suggest that monitoring, postponing, or cancelling large public gatherings may be warranted close to the epidemic peak but not earlier or later during the epidemic. Influenza activity should also be closely monitored for a potential second peak if holiday traveling occurs when prevalence is high.

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SUMMARY As the 2009 H1N1 influenza pandemic (H1N1) has shown, public health decision-makers may have to predict the subsequent course and severity of a pandemic. We developed an agent-based simulation model and used data from the state of Georgia to explore the influence of viral mutation and seasonal effects on the course of an influenza pandemic. We showed that when a pandemic begins in April certain conditions can lead to a second wave in autumn (e.g. the degree of seasonality exceeding 0·30, or the daily rate of immunity loss exceeding 1% per day). Moreover, certain combinations of seasonality and mutation variables reproduced three-wave epidemic curves. Our results may offer insights to public health officials on how to predict the subsequent course of an epidemic or pandemic based on early and emerging viral and epidemic characteristics and what data may be important to gather.

We analyze a time-varying Mperi/Geo2timeScale/N queueing system. The arrival process is periodic Poisson. The service time of a customer has components in different time scales: length of stay (LOS) in days and departure time (hdis) in hours. This queueing system has been used to study patient flows from the emergency department (ED) to hospital inpatient wards. In that setting, the LOS of a patient is simply the number of days she spends in a ward, and her departure time hdis is the discharge hour on the day of her discharge. We develop a new analytical framework that can perform exact analysis on this novel queueing system. This framework has two steps: first analyze the midnight customer count process and obtain its stationary distribution, then analyze the time-dependent customer count process to compute various performance measures. We also develop approximation tools that can significantly reduce the computational time. In particular, via Stein’s method, we derive explicit expressions to approximate the stationary distribution of the midnight count. We provide error bounds for these approximations and numerically demonstrate that they are remarkably accurate for systems with various sizes and load conditions. Our theoretical and numerical analysis have produced a number of insights that can be used to improve hospital inpatient flow management. We find that the LOS term affects the overnight wait caused by the mismatch between daily arrivals and discharges, whereas the hdis term affects the intraday wait caused by the nonsynchronization between the arrival and discharge time patterns. Thus, reducing LOS or increasing capacity can impact the daily average performance significantly; shifting the discharge timing to earlier times of a day can alleviate the peak congestion in the morning and mainly affects the time-dependent performance. The e-companion is available at https://doi.org/10.1287/opre.2016.1566 .