SIAM News Blog

Preparing Future Generations to Address Global Pandemics with Innovative Mathematical Thinking

By Padmanabhan Seshaiyer

While researchers continue to apply mathematics to increasingly complex real-world problems, sustainability challenges—as posed by the United Nations’ Sustainable Development Goals (UN SDGs)—remain of the utmost importance, especially in the context of COVID-19 (see Figure 1). For example, Goal 3: Good Health and Well-being aims to “Ensure healthy lives and promote well-being for all at all ages.” This goal presents a major opportunity for mathematicians who wish to study the impact of COVID-19 and use their findings to tackle global challenges that relate to food production, health security, clean water, affordable and clean energy, climate change and ocean health, peace and justice, and so forth. To do so, they must utilize innovative approaches that integrate knowledge from various science, technology, engineering, and mathematics disciplines [4].

Figure 1. Examples of several of the United Nations’ Sustainable Development Goals that are directly affected by the COVID-19 pandemic, including (i) Goal 3: Good Health and Well-being, (ii) Goal 4: Quality Education, and (iii) Goal 16: Peace, Justice, and Strong Institutions. Figure courtesy of Padmanabhan Seshaiyer.
Goal 4: Quality Education seeks to “Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all.” As we know, COVID-19 has affected education at all levels. By March 23, 2020, roughly 80 percent of learners around the world—from pre-primary to post-tertiary levels—faced the physical closures of their educational institutions. While the pandemic created numerous challenges, including the forced adoption of online learning for most educational establishments, it also offered creative opportunities for educators to exchange lessons and insights.

Here I share an example from a problem-solving course at George Mason University that transitioned to online instruction in 2020. The course, which was open to undergraduate students from multiple disciplines with a dual enrollment option for high school students, required participants to work in multidisciplinary teams and generate potential solutions for the UN SDGs. Students selected specific targets from the goals, applied global problem-solving principles, and considered future implications for research and development.

The course’s design initially centered on face-to-face meetings, during which students worked on semester-long team projects that comprised the backbone of the class experience. This format introduced students to various skills and competencies, such as problem-solving, mathematical modeling, computational thinking, and communication techniques. During the course’s second phase—which commenced in early March 2020 before pandemic-forced closures—self-assigned student teams chose global design challenges from the UN SDGs to pursue for the remainder of the course. However, COVID-19 constraints in mid-March forced us to rapidly contrive and implement novel, meaningful online team project experiences that allowed students to apply knowledge from previous exercises.

Many students were stressed by the unfolding situation and wanted to work on projects that pertained to COVID-19 and Goal 4: Quality Education. We thus devised assignments that encouraged creative thinking and required students to utilize previously learned skills and techniques. These assignments asked participants to employ data-driven decision-making tools that use simple mathematical ideas—like weighted means through a decision matrix framework—to identify the best vendor for delivering face masks. Students also utilized computational thinking via a Fermi approach to estimate the number of required ventilators given the daily growth of COVID-19 cases. The latter technique, which was difficult to solve with specific methods, could inspire similar approaches that estimate the necessary number of beds to support acute cases of COVID-19. In addition, students learned to apply a human-centered design thinking approach to develop ideas that addressed quality education and COVID-19.

An exposition of simple yet powerful mathematical approaches provides students with an uncomplicated introduction to a complex topic and prepares them for similar grand challenges. One way to continue this excitement is to engage students in research that fosters their own sense of agency [3]. Several course participants wanted to delve deeper into the mathematical research, so we exposed them to graph-theoretic approaches for understanding contact tracing, epidemiological modeling with differential equations, and machine learning techniques via physics-informed neural networks [2]. Students also learned about the importance of data collection, interpretation, visualization, analysis, and prediction, and discovered how to create user-friendly visualizations—such as dashboards—to understand disease spread. In response, they made connections between mathematical research and its capability to address specific challenges from the UN SDGs.

Figure 2. A typical susceptible-exposed-infected-quarantined-hospitalized-recovered (modified SEIR) model. A confinement compartment accounts for domestic violence and further incorporates the dynamics of members who are susceptible to domestic violence, victims (V), abusers (A), and those who are removed. Figure courtesy of Padmanabhan Seshaiyer.
A sample project builds upon the analysis of Comfort Ohajunwa, a current high school senior who has been working with me since July 2020 on a mentored research project to develop a new mathematical model that tracks the impact of social behavior during COVID-19 [1]. Ohajunwa’s efforts have already led to four peer-reviewed journal publications; her most recent work helped generate novel models and ideas that pertained to Goal 16: Peace, Justice, and Strong Institutions of the UN SDGs, which intends to “Promote peaceful and inclusive societies for sustainable development, provide access to justice for all and build effective, accountable, and inclusive institutions at all levels.”

Specifically, Ohajunwa identified a relevant global challenge that emerged due to the various lockdowns and confinement strategies throughout the world. While these interventions were implemented to save lives and mitigate the spread of COVID-19, multiple unfortunate consequences affected the economy, education, health, and even the basic blocks of society: homes. Pandemic-related fears, financial stress, and isolation all detrimentally affect mental health, thereby disrupting peace in one’s place of living. If a home is susceptible to domestic violence, confinement under a deteriorating mental health climate and abnormally high levels of home interaction can create a perfect storm — particularly for intimate partner violence. While most mathematical models focus on the nature of COVID-19’s spread, Ohajunwa’s model provides deeper insights into other adverse impacts of COVID-19 of which many people are not aware. Figure 2 illustrates a typical susceptible-exposed-infected-quarantined-hospitalized-recovered (a modified SEIR) model with additional complexities in a confinement compartment that further incorporates the dynamics of members who are susceptible to domestic violence, victims (V), abusers (A), and those who are removed. These types of models and tools can allow researchers to study the relationship between lockdowns, confinement strategies, COVID-19, and domestic violence to ultimately mitigate the social problems that accompany such drastic measures.

Although students initially struggled when they switched to virtual learning in the middle of the semester, they still developed a sense of ownership and produced solutions that addressed grand challenges with design thinking principles and mathematical problem-solving. They tackled real-world societal problems that were inspired by the UN SDGs and applied mathematics in a meaningful and impactful way. I encourage other instructors and institutions to implement similar projects to encourage critical thinking and mathematical modeling applications. These projects can provide students like Ohajunwa with opportunities to not only make significant contributions to science and engineering, but also develop a system that will change lives and positively impact society.

[1] Ohajunwa, C., Kumar, K., & Seshaiyer, P. (2020). Mathematical modeling, analysis, and simulation of the COVID-19 pandemic with explicit and implicit behavioral changes. Comput. Math. Biophys., 8(1), 216-232.
[2] Raissi, M., Ramezani, N., & Seshaiyer, P. (2019). On parameter estimation approaches for predicting disease transmission through optimization, deep learning and statistical inference methods. Lett. Biomath., 6(2), 1-26.
[3] Seshaiyer, P. (2017). Leading undergraduate research projects in mathematical modeling. PRIMUS, 27(4-5), 476-493.
[4] Seshaiyer, P., & McNeely, C.L. (2020). Challenges and opportunities from COVID-19 for global sustainable development. World Med. Health Policy, 12(4), 443-453.

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. In 2021, he was appointed to the Virginia STEM Advisory Board to the Governor of Virginia.

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