Flattening the curve: Insights from queueing theory

Abstract

The worldwide outbreak of the coronavirus was first identified in 2019 in Wuhan, China. Since then, the disease has spread worldwide. As it is currently spreading in the United States, policy makers, public health officials and citizens are racing to understand the impact of this virus on the United States healthcare system. They fear a rapid influx of patients overwhelming the healthcare system and leading to unnecessary fatalities. Most countries and states in America have introduced mitigation strategies, such as using social distancing to decrease the rate of newly infected people. This is what is usually meant by flattening the curve. In this paper, we use queueing theoretic methods to analyze the time evolution of the number of people hospitalized due to the coronavirus. Given that the rate of new infections varies over time as the pandemic evolves, we model the number of coronavirus patients as a dynamical system based on the theory of infinite server queues with time inhomogeneous Poisson arrival rates. With this model we are able to quantify how flattening the curve affects the peak demand for hospital resources. This allows us to characterize how aggressive societal policy needs to be to avoid overwhelming the capacity of healthcare system. We also demonstrate how curve flattening impacts the elapsed lag between the times of the peak rate of hospitalizations and the peak demand for the hospital resources. Finally, we present empirical evidence from Italy and the United States that supports the insights from our model analysis.

Influence of the Effective Reproduction Number on the SIR Model with a Dynamic Transmission Rate

“…Finally, by making substitutions R e = (B/γ)(S/N) and f = (B/γ)(I/N), there follows, via factorization by R e on the right-hand side, the first Equation (2).…”

“…At the beginning of the COVID-19 pandemic, when no vaccines were available, one of the natural concerns in almost all countries was to flatten the epidemic curve to avoid the collapse of the healthcare sector [1][2][3]. Through the ordinance and implementation of nonpharmaceutical mitigation measures recommended by experienced or specialized agencies, such as WHO, the urgent task was not to exceed the maximum healthcare capacity [4,5], thus saving the lives of critically ill patients and avoiding having to make difficult decisions about who should receive care [6,7].…”

A queueing‐theoretic framework for evaluating transmission risks in service facilities during a pandemic

“…(2018) borrow standard queueing‐theoretic notions such M/M/1, M/G/1, and busy‐period analysis to investigate the efficiency of interventions pertaining to quarantine centers and vaccination. The COVID‐19 pandemic has spurred renewed interest in this topic (Alban et al., 2020; Cui et al., 2020; Long et al., 2020; Meares & Jones, 2020; Palomo et al., 2020). We use queueing theory differently than the works cited above.…”

HGSOXGB: Hunger-Games-Search-Optimization-Based Framework to Predict the Need for ICU Admission for COVID-19 Patients Using eXtreme Gradient Boosting

“…Age, dyspnea, sex, initial body temperature, history of kidney disease, hemoptysis, and the ADL scale were criteria for the scoring system. A study by Palomo et al [14] adopted a slightly different approach and emphasized the bed demand for COVID-19 patients utilizing queuing models to show occupancy scenarios based on various patient arrival patterns.…”