SIAM News Blog

Mathematical Modeling for Social Good: COVID-19 in Long-term Care Facilities

By Aditi Ghosh, Carmen Caiseda, and Padmanabhan Seshaiyer

The Workshop Celebrating Diversity (WCD) at the 2022 SIAM Annual Meeting (AN22)—which took place in Pittsburgh, Pa., this July—continues to promote the creation of a diverse community of practice in applied and computational mathematics. SIAM’s Diversity Advisory Committee oversees the WCD, sets general guidelines for the workshop, and appoints a working group to supervise its organization. The many excellent WCD sessions at AN22 included a minisymposium on “Mathematical Modeling for Social Good.” This event was inspired in part by the “Data Science for Social Good” (DSSG) programs that have emerged around the world in recent decades, as well as mathematical applications that address the United Nation’s Sustainable Development Goals. In the same spirit of DSSG, the presenters in our minisymposium contend with problems that impact society, use fair and equitable data practices, and communicate effectively with stakeholders. One specific research talk—presented by Aditi Ghosh of Texas A&M University-Commerce—introduced an epidemiological model with a distinct social context that addressed the dynamics of COVID-19’s spread in long-term care facilities under non-pharmaceutical interventions. Here we explore mathematical modeling’s impact on such a societal application.

Modeling for Social Good 

In order to create positive real-world impacts, mathematical modelers must identify stakeholders and enable conversations about modeling and ethics. Stakeholders in the context of COVID-19 in long-term care facilities include representatives of nursing homes or associations, state survey/data agencies, geriatric individuals, epidemiological directors, academic researchers, and consumers. The classical susceptible-exposed-infectious-recovered (SEIR) compartmental flow diagram and model often serves as a starting graphical communication tool for stakeholders (see Figure 1). Subsequent conversations about SEIR diagrams can improve a model’s reality and the fairness of its assumptions. 

Figure 1. A modified susceptible-exposed-infectious-recovered (SEIR) compartmental model for COVID-19 control in long-term care facilities. Figure courtesy of Aditi Ghosh.

COVID-19 modeling in long-term care facilities involves a complex socio-technological interaction that requires ethical analysis of technology usage and embodiment of fairness and inclusivity. A successful social mathematical model builds a bridge between mathematical modeling and real-world projects. This connection allows stakeholders to inform and respond to societal needs; the U.S. Centers for Disease Control and Prevention’s (CDC) planning scenarios (see Figure 2) and cost-effectiveness analysis are two such examples. 

A Mathematical Model

Close-contact establishments like retirement communities, nursing homes, and even cruise ships pose a high risk of emergent disease outbreaks. In long-term care facilities, chronic underlying health conditions and residents’ advanced age can make occupants especially vulnerable to COVID-19 if the pathogen contaminates the environment. Researchers utilize numerous modeling approaches to study these types of infection risks within a population. The optimal control modeling technique is a powerful method that optimizes dynamic control strategies based on epidemiological models. Here, we aim to identify and quantify the roles of different subpopulations (staff, residents, and visitors) and related infection transmission pathways (within and between subpopulations, between superspreaders and other individuals, and within contaminated environments) to better control COVID-19 in these facilities (see Figure 1). 

In order to implement effective intervention policies and mitigate the impact of infection transmission through multiple pathways one must identify the optimal time, duration, and choice of intervention in real time. We simulated three different cases with superspreading and non-superspreading events, then performed a cost-effectiveness analysis to determine the optimal implementation of two control measures: wearing masks and cleaning surfaces. Doing so reveals the trade-off between disease burden and prevention cost. 

Figure 2. Five planning scenarios provided by the U.S. Centers for Disease Control and Prevention (CDC). Figure courtesy of Aditi Ghosh.

In another modeling framework, we considered two types of social contexts (community and long-term care facilities) and three different groups of interacting populations: non-mobile individuals in the community who do not visit long-term care facilities \((Q)\), mobile individuals in the community who visit long-term care facilities \((T)\), and residents of long-term care facilities \((P)\). We employed an SEIR-type model within each subgroup and defined mixing probabilities to understand the strategies that would work well in these facilities for five different CDC planning scenarios (see Figure 2).


Figure 3. The exposed population of infected healthcare staff as a function of time for different proportions of infected healthcare workers who act as superspreaders. Figure courtesy of Aditi Ghosh.
Our results suggest that the estimates of the basic reproduction number \((R_0)\) for non-superspreading events are significantly lower than the estimates in superspreading cases for the same values of the transmission rate \((\beta)\). The highest \(R_0\) occurs in superspreading events that arise through infected healthcare workers who have high-contact influences both within and outside the facilities. Figure 3 illustrates the exposed population of infected healthcare staff as a function of time for different proportions \((\theta_2)\) of infected healthcare workers who serve as superspreaders. 

Public health policies should focus on continued efforts to rapidly trace and quarantine contacts to avoid the dire consequences of superspreading events. The initial conditions do not heavily influence our numerical simulations — i.e., introducing the first arrival infection in the resident, visitor, or staff populations all have a low impact on the dynamics. Decision-makers should instead pay more attention to the timely application of selective non-pharmaceutical interventions. Cleaning surfaces should be a priority at the onset of a COVID-19 epidemic, while mask wearing becomes crucial as the number of infections significantly increases and eventually establishes. However, one may have to alter the latter situation if the virus has a large concentration in the environment and there is a possibility for infection transmission through surface contamination.

We also found that heterogeneous mixing worsens the epidemic as compared to homogeneous mixing: the epidemic burden is hundreds of times greater for community spread (between visitors and non-visitors) than within the facility population. In both mixing scenarios, CDC strategies 1, 2, and 5 have the similarly best outcomes, followed by strategy 3 (see Figure 2). Strategy 4 is the worst approach (see Figure 4).

Figure 4. Outcomes for the five planning scenarios provided by the U.S. Centers for Disease Control and Prevention (CDC) under different mixing conditions. Figure courtesy of Aditi Ghosh.

The findings of our mathematical model serve as an analytical tool for the healthcare community of stakeholders, including the CDC, to assess the value of the suggested planning scenarios. Our results serve as an opportunity to open doors of conversation around the mathematical representation of social problems and share recommendations that may lead to viable solutions of local and global challenges for the good of society. 

Aditi Ghosh presented this research during a minisymposium presentation that was part of the Workshop Celebrating Diversity at the 2022 SIAM Annual Meeting, which took place in Pittsburgh, Pa., in July 2022.

Further Reading
[1] Ballard, S., Chappell, K.M., & Kennedy, K. (2019). Judgment call the game: Using value sensitive design and design fiction to surface ethical concerns related to technology. In Proceedings of the 2019 on designing interactive systems conference (DIS’19) (pp. 421-433). San Diego, CA: Association for Computing Machinery.

Aditi Ghosh is a tenure-track assistant professor at Texas A&M University-Commerce. Her research interests are in mathematical biology and her critical research work involves projects in hepatology. Ghosh helps prepare undergraduate students for cutting-edge, modeling-based interdisciplinary research projects and model competitions, including the SIMIODE Challenge Using Differential Equations Modeling and COMAP’s international contests in modeling. Carmen Caiseda is a professor and coordinator of the mathematics group at the Inter American University of Puerto Rico (IAUPR) – Bayamon Campus. She is co-principal investigator of the Data Science at IAUPR project, which builds a data science community of practice that impacts faculty, students, and professionals. Caiseda is also an undergraduate research mentor who engages students in science, technology, mathematics, and engineering through mathematical modeling of real-world challenges with pertinent socio-cultural contexts. Padmanabhan Seshaiyer is a professor of mathematical sciences at George Mason University and chair of the SIAM Diversity Advisory Committee. He works in the broad area of computational mathematics, data science, biomechanics, design and systems thinking, and STEM education. Seshaiyer also serves as vice chair of the U.S. National Academies Commission on Mathematics Instruction and as Associate Director for Applied Mathematics of the Math Alliance.

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