Tracking Covid-19 cases and deaths in the United States: metrics of pandemic progression derived from a queueing framework
Randolph Hall, Andrew Moore and Mingdong Lyu
Health Care Manag Sci 26, 79–92 (2023).
We analyze the progression of COVID-19 in the United States over a nearly one-year period beginning March 1, 2020 with a novel metric motivated by queueing models, tracking partial-average day-of-event and cumulative probability distributions for events, where events are points in time when new cases and new deaths are reported. The partial average represents the average day of all events preceding a point of time, and is an indicator as to whether the pandemic is accelerating or decelerating in the context of the entire history of the pandemic. The measure supplements traditional metrics, and also enables direct comparisons of case and death histories on a common scale. We also compare methods for estimating actual infections and deaths to assess the timing and dynamics of the pandemic by location. Three example states are graphically compared as functions of date, as well as Hong Kong as an example that experienced a pronounced recent wave of the pandemic. In addition, statistics are compared for all 50 states. Over the period studied, average case day and average death day varied by two to five months among the 50 states, depending on data source, with the earliest averages in New York and surrounding states, as well as Louisiana.
Pandemic Prediction and Control with Integrated Dynamic Modeling of Disease Transmission and Healthcare Resource Optimization
Dr. Mingdong Lyu Ph.D. Thesis, 2023
To mitigate the impact of future pandemics on social and economic life, research focuses on enhancing surveillance, developing targeted interventions, and optimizing vaccine distribution. In the initial stages of a novel infectious disease, the lack of biological and medical knowledge makes it difficult to estimate the extent and rapidity of its spread. A primary job is ascertaining the case and fatality patterns of the disease based on which we could evaluate the transmissibility and severity of the diseases. Moreover, the spread of an epidemic hinges on the probability of infection and the nature of individual interactions. Mobility networks are instrumental in shaping the temporal and spatial 3 dynamics of disease transmission within populations. The rising global mobility of humans and increased trade volumes facilitate the introduction of infectious diseases to new regions. Consequently, our research will employ mathematical modeling that incorporates time-varying transmission and fatality rates, as well as spatial interactions, to create a comprehensive representation of transmission dynamics. This modeling approach will generate quantitative predictions to inform health policies, enabling evaluation of epidemiological outcomes and the effectiveness of intervention strategies.
Optimizing the Selection of COVID-19 Vaccine Distribution Centers and Allocation Quantities: A Case Study for the County of Los Angeles
Basim Aljohani, Masters Thesis, 2023
This thesis aims to provide a tool to help policy and decision-makers establish well-informed plans about the selection and distribution of locations and quantities of vaccines. Optimization of vaccine distribution centers’ locations plays a crucial role in providing communities with easy access to vaccines, which will help in controlling global pandemics, such as the recent COVID-19, and mitigate the risks of losing lives and economic losses. As studies have proven, strategic planning of the vaccine site locations and the allocated quantities of the vaccines could help boost the amount of vaccine uptake. This thesis utilizes mathematical modeling techniques to develop a mixed integer program that aims to minimize travel time, distance, and associated costs in one of the largest counties in the United States, Los Angeles County. The developed model takes into account the diverse demographics and socioeconomic factors of the County and plans for the selection and allocations accordingly. The model explores 277 zip codes within Los Angeles and analyzes them as potential vaccine distribution centers. It also incorporates the two different and most common means of transportation, cars, and public transit, to account for all users. Three scenarios are explored where each zip code of the 277 is assigned priority based on the following factors: population, Healthy Places Index, and a Vulnerability to COVID-19 index. The output showed significant improvements in reducing average travel times and distances as well as savings in costs when compared to the actual selected sites within the County.
Dynamic Vaccine Allocation for Control of Human Transmissible Disease (preprint)
Mingdong Lyu, Cici Chang , Kuofu Liu and Randolph Hall
During pandemics, such as COVID-19, supplies of vaccines can be insufficient to meet all needs, particularly when vaccines first become available. Our study develops a dynamic methodology for vaccine allocation, segmented by region, age, and timeframe, using a time-sensitive, age-structured compartmental model. Based on the objective of minimizing a weighted sum of deaths and cases, we used the Sequential Least Squares Quadratic Programming method to search for a locally optimal COVID-19 vaccine allocation for the United States, for the period from December 16, 2020, to June 30, 2021, where regions corresponded to the 50 states in the United States (US). We also compared our solution to actual allocations of vaccines. From our model, we estimate that approximately 1.8 million cases and 9 thousand deaths could have been averted in the US with an improved allocation. When case reduction is prioritized over death reduction, we found that young people (17 and younger) should receive priority over old people due to their potential to expose others. However, if death reduction is prioritized over case reduction, we found that more vaccines should be allocated to older people, due to their propensity for severe disease. While we have applied our methodology to COVID-19, our approach generalizes to other human transmissible diseases, with potential application to future epidemics.
Optimizing the Selection of Mass Vaccination Sites: Access and Equity Consideration (preprint)
Basim Aljohani and Randolph Hall
Access to vaccines was severely limited by capacity when they first became available for COVID-19 in 2021. For example, just nine locations in Los Angeles County, with a population of more than 10 million people, were initially used. As a consequence, people experienced long travel times to obtain vaccines, sometimes exceeding one hour in each direction. We develop and optimize a mixed integer-linear model to select a constrained number of vaccination sites and apply the model to analyze outcomes for multiple objective functions, accounting for equitable access to vulnerable populations. Using Los Angeles County as an example, we model 277 zip codes, accounting for car ownership at the household level, disease vulnerability by ethnic group, and the Healthy Places Index (a measure of localized health outcome disparity) as well as travel times by automobile and public transit. We found that the optimized model showed significant improvements over the actual sites for all ethnic groups. We also found that Whites generally had longer travel times to vaccination sites than other ethnic groups, which can be attributed to their larger concentrations in more remote and lower density zip codes, which tended to be more distant from vaccination sites. From the perspective of equity, optimized solutions tend to favor vaccination sites in densely populated areas toward the city center. Because these areas in LA County have higher concentrations of Latinos and Black people, they tended to have shorter travel times, even after factoring in access to automobiles at the household level. On the other hand, people who do not have access to automobiles, regardless of race, are seriously disadvantaged, with much longer travel times. While having many vaccination sites might improve access for those dependent on public transit, that advantage diminished if people must search among many sites to find a location with available vaccines.
Spatial Interaction Analysis of Infectious Disease Import and Export Between Regions (preprint)
Mingdong Lyu, Kuofu Liu, Randolph W. Hall
Human travel plays a crucial role in the spread of infectious disease between regions. Travel of infected individuals from one region to another can transport a virus to places that were previously unaffected or may accelerate the spread of disease in places where the disease is not yet well established. We develop and apply models and metrics to analyze the role of inter-regional travel relative to the spread of disease, drawing from data on Covid-19 in the United States. To better understand how transportation affects disease transmission, we established a multi-regional time-varying compartmental disease model with spatial interaction. The compartmental model was integrated with statistical estimates of travel between regions. From the integrated model, we derived a transmission import index to assess the risk of Covid-19 transmission between states. Based on the index, we determined states with high risk for disease spreading to other states at months scale, and we analyzed how the index changed over time during 2020. Our model provides a tool for policymakers to evaluate the influence of travel between regions on disease transmission in support of strategies for epidemic control.
Dynamic Modeling of Reported Covid-19 Cases and Deaths with Continuously Varying Case Fatality and Transmission Rate Functions (preprint)
Mingdong Lyu, Andrew Moore, and Randolph Hall
This paper develops and applies an enhanced SEIRD (Susceptible-Exposed-Infectious- Recovered-Death) model with time-varying case fatality and transmission rates for the COVID-19 pandemic. Our aim is to accurately characterize time-variations in transmission and fatality rates relative to reported cases and deaths with a function that utilizes a small set of parameters. The time-varying functions, when integrated into the SEIRD model, efficiently characterize dynamic changes in fatality and transmission rates, which result from public health interventions, changes in medical care, changing human behavior, and potential changes in the virus itself.
Efficiency and Equity in Covid-19 Vaccine Allocation and Administration in the United States (in progress)
Randolph Hall, Cici Chang (research in progress)
We empirically investigate the patterns of vaccine delivery and administration among the 50 United States between December 2020 to March 2022, with a focus on efficiency and disparities. Efficiency entails minimizing the gap between vaccine delivery and vaccine administration and allocating vaccines to locations with greatest need. Disparity entails minimizing unwarranted variations in per capita allocations of vaccines. We focus on answering these questions:
- To what degree were deliveries and administration of vaccines with states correlated with
- Number of people eligible (by age) to receive vaccines?
- Recorded inventories of vaccines within states?
- Prevalence of disease, measured in cases and deaths, within states?
- To what degree were delivery and administration of vaccines within states correlated with:
- State level distribution of population by ethnicity?
- State level social vulnerability index?
We recognize that vaccine inventories and rates of vaccine administration and delivery were not static. In particular, in early 2021, vaccines were in short supply relative to both eligible population and relative to total population desiring vaccination. Thus, during this time period, rates of vaccination were highly dependent on vaccine deliveries.
Toward the middle of 2021 vaccine eligibility expanded to all adults along with older children. Soon after, vaccines were no longer in short supply. When this occurred, rates of vaccination became highly dependent on the willingness of people to be vaccinated.
Finally, toward the end of 2021, individuals began receiving vaccine booster shots, creating a secondary demand. Around the same time, emergence of the Omicron variant led to both a new wave of Covid-19 and additional demand for vaccination. Taking these factors into consideration, our analysis considers three phases:
- Limited Supply: January 2021 until April 2021
- Expanded Eligibility and Supply: May 2021 until November 2021
- Boosters and Omicron: December 2021 until March 2022