skip to main content


Title: Stochastic vs. Deterministic Modeling for the Spread of COVID-19 in Small Networks
This paper proposes and analyzes a stochastic Susceptible-Exposed-Infected-Removed (SEIR) spreading model on networks. Imagine a nursing home housing 28 seniors and 7 staff workers, in which one of the staff has tested positive for COVID-19. Unfortunately, the results of this test are 3 days late and the infected person had not been quarantining while waiting for their test results. What is now the individual risk to the different people living in this nursing home? If the home has access to two rapid COVID-19 viral tests, who should they be given to and why? In order to answer questions like this, we need to study stochastic models rather than deterministic ones. Unlike the vast majority of works that analyze various deterministic models, stochastic models are required when analyzing the risk of COVID-19 to individual people rather than tracking aggregate numbers in a given region. More specifically, this paper compares the results provided by analyzing stochastic and deterministic models and investigating when it is suitable to use the different models. In particular, we show why it is not suitable to use deterministic models when analyzing the spread in small communities and how these questions can be better addressed using stochastic ones. Finally, we show the added complications that arise due to the relatively long incubation period of COVID-19, and how it can be addressed. A simulated case study of the spread of COVID-19 in a 35-person nursing home is used to help illustrate our results.  more » « less
Award ID(s):
2028523
NSF-PAR ID:
10274935
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the American Control Conference
ISSN:
0743-1619
Page Range / eLocation ID:
1342-1347
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract This project is funded by the US National Science Foundation (NSF) through their NSF RAPID program under the title “Modeling Corona Spread Using Big Data Analytics.” The project is a joint effort between the Department of Computer & Electrical Engineering and Computer Science at FAU and a research group from LexisNexis Risk Solutions. The novel coronavirus Covid-19 originated in China in early December 2019 and has rapidly spread to many countries around the globe, with the number of confirmed cases increasing every day. Covid-19 is officially a pandemic. It is a novel infection with serious clinical manifestations, including death, and it has reached at least 124 countries and territories. Although the ultimate course and impact of Covid-19 are uncertain, it is not merely possible but likely that the disease will produce enough severe illness to overwhelm the worldwide health care infrastructure. Emerging viral pandemics can place extraordinary and sustained demands on public health and health systems and on providers of essential community services. Modeling the Covid-19 pandemic spread is challenging. But there are data that can be used to project resource demands. Estimates of the reproductive number (R) of SARS-CoV-2 show that at the beginning of the epidemic, each infected person spreads the virus to at least two others, on average (Emanuel et al. in N Engl J Med. 2020, Livingston and Bucher in JAMA 323(14):1335, 2020). A conservatively low estimate is that 5 % of the population could become infected within 3 months. Preliminary data from China and Italy regarding the distribution of case severity and fatality vary widely (Wu and McGoogan in JAMA 323(13):1239–42, 2020). A recent large-scale analysis from China suggests that 80 % of those infected either are asymptomatic or have mild symptoms; a finding that implies that demand for advanced medical services might apply to only 20 % of the total infected. Of patients infected with Covid-19, about 15 % have severe illness and 5 % have critical illness (Emanuel et al. in N Engl J Med. 2020). Overall, mortality ranges from 0.25 % to as high as 3.0 % (Emanuel et al. in N Engl J Med. 2020, Wilson et al. in Emerg Infect Dis 26(6):1339, 2020). Case fatality rates are much higher for vulnerable populations, such as persons over the age of 80 years (> 14 %) and those with coexisting conditions (10 % for those with cardiovascular disease and 7 % for those with diabetes) (Emanuel et al. in N Engl J Med. 2020). Overall, Covid-19 is substantially deadlier than seasonal influenza, which has a mortality of roughly 0.1 %. Public health efforts depend heavily on predicting how diseases such as those caused by Covid-19 spread across the globe. During the early days of a new outbreak, when reliable data are still scarce, researchers turn to mathematical models that can predict where people who could be infected are going and how likely they are to bring the disease with them. These computational methods use known statistical equations that calculate the probability of individuals transmitting the illness. Modern computational power allows these models to quickly incorporate multiple inputs, such as a given disease’s ability to pass from person to person and the movement patterns of potentially infected people traveling by air and land. This process sometimes involves making assumptions about unknown factors, such as an individual’s exact travel pattern. By plugging in different possible versions of each input, however, researchers can update the models as new information becomes available and compare their results to observed patterns for the illness. In this paper we describe the development a model of Corona spread by using innovative big data analytics techniques and tools. We leveraged our experience from research in modeling Ebola spread (Shaw et al. Modeling Ebola Spread and Using HPCC/KEL System. In: Big Data Technologies and Applications 2016 (pp. 347-385). Springer, Cham) to successfully model Corona spread, we will obtain new results, and help in reducing the number of Corona patients. We closely collaborated with LexisNexis, which is a leading US data analytics company and a member of our NSF I/UCRC for Advanced Knowledge Enablement. The lack of a comprehensive view and informative analysis of the status of the pandemic can also cause panic and instability within society. Our work proposes the HPCC Systems Covid-19 tracker, which provides a multi-level view of the pandemic with the informative virus spreading indicators in a timely manner. The system embeds a classical epidemiological model known as SIR and spreading indicators based on causal model. The data solution of the tracker is built on top of the Big Data processing platform HPCC Systems, from ingesting and tracking of various data sources to fast delivery of the data to the public. The HPCC Systems Covid-19 tracker presents the Covid-19 data on a daily, weekly, and cumulative basis up to global-level and down to the county-level. It also provides statistical analysis for each level such as new cases per 100,000 population. The primary analysis such as Contagion Risk and Infection State is based on causal model with a seven-day sliding window. Our work has been released as a publicly available website to the world and attracted a great volume of traffic. The project is open-sourced and available on GitHub. The system was developed on the LexisNexis HPCC Systems, which is briefly described in the paper. 
    more » « less
  2. Ghate, A ; Krishnaiyer, K. ; Paynabar, K. (Ed.)
    Maintaining an appropriate staffing level is essential to providing a healthy workplace environment at nursing homes and ensuring quality care among residents. With the widespread Covid-19 pandemic, staff absenteeism frequently occurs due to mandatory quarantine and providing care to their inflicted family members. Even though some of the staff show up for work, they may have to perform additional pandemic-related protection duties. In combination, these changes lead to an uncertain reduction in the quantity of care each staff member able to provide in a future shift. To alleviate the staff shortage concern and maintain the necessary care quantity, we study the optimal shift scheduling problem for a skilled nursing facility under probabilistic staff shortage in the presence of pandemic-related service provision disruptions. We apply a two-stage stochastic programming approach to our study. Our objective is to assign staff (i.e., certified nursing aids) to shifts to minimize the total staffing cost associated with contract staff workload, the adjusted workload for the changing resident demand, and extra workload due to required sanitization. Thus, the uncertainties considered arise from probabilistic staff shortage in addition to resident service need fluctuation. We model the former source of uncertainty with a geometric random variable for each staffer. In a proof-of-the-concept study, we consider realistic COVID-19 pandemic response measures recommended by the Indiana state government. We extract payment parameter estimates from the COVID-19 Nursing Home Dataset publicly available by the Centers for Medicare and Medicaid Services (CMS). We conclude with our numerical experiments that when a skilled nursing facility is at low risk of the pandemic, the absenteeism rate and staff workload increase slightly, thus maintaining the current staffing level can still handle the service disruptions. On the other hand, under high-risk circumstances, with the sharp increase of the absence rate and workload, a care facility likely needs to hire additional full-time staff as soon as possible. Our research offers insights into staff shift scheduling in the face of uncertain staff shortages and service disruption due to pandemics and prolonged disasters. 
    more » « less
  3. Grilli, Jacopo (Ed.)
    A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, limiting contacts is impractical or impossible for the many disabled people who do not live in care facilities but still require caregivers to assist them with activities of daily living. We seek to determine which interventions can best prevent infections of disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed/recovered individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risk levels of different types of interactions, time-dependent lockdown and reopening measures, and interaction distributions for four different groups (caregivers, disabled people, essential workers, and the general population). Of these groups, we find that the probability of becoming infected is largest for caregivers and second largest for disabled people. Consistent with this finding, our analysis of network structure illustrates that caregivers have the largest modal eigenvector centrality of the four groups. We find that two interventions—contact-limiting by all groups and mask-wearing by disabled people and caregivers—most reduce the number of infections in disabled and caregiver populations. We also test which group of people spreads COVID-19 most readily by seeding infections in a subset of each group and comparing the total number of infections as the disease spreads. We find that caregivers are the most potent spreaders of COVID-19, particularly to other caregivers and to disabled people. We test where to use limited infection-blocking vaccine doses most effectively and find that (1) vaccinating caregivers better protects disabled people from infection than vaccinating the general population or essential workers and that (2) vaccinating caregivers protects disabled people from infection about as effectively as vaccinating disabled people themselves. Our results highlight the potential effectiveness of mask-wearing, contact-limiting throughout society, and strategic vaccination for limiting the exposure of disabled people and their caregivers to COVID-19. 
    more » « less
  4. Background: Nursing home (NH) residents and staff were at high risk for COVID-19 early in the pandemic; several studies estimated seroprevalence of infection in NH staff to be 3-fold higher among CNAs and nurses compared to other staff. Risk mitigation added in Fall 2020 included systematic testing of residents and staff (and furlough if positive) to reduce transmission risk. We estimated risks for SARS-CoV-2 infection among NH staff during the first winter surge before widespread vaccination. Methods: Between February and May 2021, voluntary serologic testing was performed on NH staff who were seronegative for SARS-CoV-2 in late Fall 2020 (during a previous serology study at 14 Georgia NHs). An exposure assessment at the second time point covered prior 3 months of job activities, community exposures, and self-reported COVID-19 vaccination, including very recent vaccination (≤4 weeks). Risk factors for seroconversion were estimated by job type using multivariable logistic regression, accounting for interval community-incidence and interval change in resident infections per bed. Results: Among 203 eligible staff, 72 (35.5%) had evidence of interval seroconversion (Fig. 1). Among 80 unvaccinated staff, interval infection was significantly higher among CNAs and nurses (aOR, 4.9; 95% CI, 1.4–20.7) than other staff, after adjusting for race and interval community incidence and facility infections. This risk persisted but was attenuated when utilizing the full study cohort including those with very recent vaccination (aOR, 1.8; 95% CI, 0.9–3.7). Conclusions : Midway through the first year of the pandemic, NH staff with close or common resident contact continued to be at increased risk for infection despite enhanced infection prevention efforts. Mitigation strategies, prior to vaccination, did not eliminate occupational risk for infection. Vaccine utilization is critical to eliminate occupational risk among frontline healthcare providers. Funding: None Disclosures: None 
    more » « less
  5. null (Ed.)
    The new coronavirus (now named SARS-CoV-2) causing the disease pandemic in 2019 (COVID-19), has so far infected over 35 million people worldwide and killed more than 1 million. Most people with COVID-19 have no symptoms or only mild symptoms. But some become seriously ill and need hospitalization. The sickest are admitted to an Intensive Care Unit (ICU) and may need mechanical ventilation to help them breath. Being able to predict which patients with COVID-19 will become severely ill could help hospitals around the world manage the huge influx of patients caused by the pandemic and save lives. Now, Hao, Sotudian, Wang, Xu et al. show that computer models using artificial intelligence technology can help predict which COVID-19 patients will be hospitalized, admitted to the ICU, or need mechanical ventilation. Using data of 2,566 COVID-19 patients from five Massachusetts hospitals, Hao et al. created three separate models that can predict hospitalization, ICU admission, and the need for mechanical ventilation with more than 86% accuracy, based on patient characteristics, clinical symptoms, laboratory results and chest x-rays. Hao et al. found that the patients’ vital signs, age, obesity, difficulty breathing, and underlying diseases like diabetes, were the strongest predictors of the need for hospitalization. Being male, having diabetes, cloudy chest x-rays, and certain laboratory results were the most important risk factors for intensive care treatment and mechanical ventilation. Laboratory results suggesting tissue damage, severe inflammation or oxygen deprivation in the body's tissues were important warning signs of severe disease. The results provide a more detailed picture of the patients who are likely to suffer from severe forms of COVID-19. Using the predictive models may help physicians identify patients who appear okay but need closer monitoring and more aggressive treatment. The models may also help policy makers decide who needs workplace accommodations such as being allowed to work from home, which individuals may benefit from more frequent testing, and who should be prioritized for vaccination when a vaccine becomes available. 
    more » « less