Does limiting population movement during a pandemic really help to minimize the spread of disease? Ph.D. candidate Keoni Castellano is using math to tackle that question.

His research under mentor Rachidi Salako, an assistant professor in the Department of Mathematical Sciences, explores epidemic models through analysis using mathematical, statistical, and computational tools to study the spread of disease. He specifically looks at the effects of population movement — or limiting movement — on disease persistence. 

“It is cool to be able to translate mathematical results, which can often be very abstract, into more tangible outcomes related to the universe around us,” says Castellano. “Mathematics can be used in all sorts of ways to solve different problems.”

Castellano is already the lead author on a major publication in a Q1 journal, which refers to the most prestigious and highly cited journals, and has presented at Auburn and Virginia Tech universities. He is co-founder of the UNLV student chapter of the Society for Applied and Industrial Mathematics. Clearly, Castellano already is making a mark in the world of mathematics early in his career.

What excites you about the research you are doing?

I find it amazing that math can be used in all sorts of different places and solve all sorts of different problems. I know there are a lot of people that like mathematics for the pure enjoyment of the subject, but I have always been intrigued about the way math can be used to give more information about the world that we live in.

In the case of my research, I like how we can use mathematical analysis to poke and prod at a mathematical infectious disease model to gain insight into how infectious diseases behave. 

How could your research help provide insight into public health policy in a future pandemic?

The statistician George Box once said, “All models are wrong, but some are useful.” The idea behind this quote is that models are built on assumptions that often have to be justified. Because of these assumptions, the models don’t always give the complete picture over how the real world operates. This is especially true with epidemic models, such as the ones that I study.

Our mathematical results will never be able to predict how a disease will spread with 100% accuracy. However, we do assist in gaining deeper insight into the factors that play a role in how epidemics start and how we can end them once they start. In the future, I would like to be able to incorporate real-world data with our math models to demonstrate if what we see mathematically is also seen in actual epidemics.

What’s next for you researchwise and beyond?

Researchwise, we are trying to extend our results to more complicated infectious disease models, some that even take into consideration multiple strains of a disease. Careerwise, I am currently in the process of applying to postdocs. I would like to take the knowledge that I learned during my Ph.D. and develop my skills further so that I can become an independent researcher in mathematical biology.

What inspired you to get into your field?

I have always been fascinated with seeing the way mathematics is used in real-world applications. I was drawn to the research of Dr. Salako because he was looking at math that had interpretations in biology. He gave a talk on chemotaxis (movement of an organism in response to a chemical signal) models that I happened to attend. I was fascinated by the reach and versatility of mathematics in understanding things as intricate as chemotaxis.

After asking him to become my advisor, Dr. Salako and I started doing research on infectious disease models. This was another step in pushing me toward mathematical biology as the mathematics behind our models is universal to all sorts of different biological models. When I attended the annual conference of the Society for Mathematical Biology, I was in awe of the variety of different problems that others were doing research in. It was then and there that I knew I belonged with the mathematical biologists. 

What made you want to pursue your Ph.D. at UNLV?

I actually went to UNLV for my undergraduate degree in mathematics. I have lived in Las Vegas for the past 13-14 years. I ultimately decided to stay here for my Ph.D. since this is where my family and my support system is. I am happy I stayed as I was fortunate to already be with my family during the COVID-19 pandemic, which made things easier.

I am also grateful for the opportunities I have had here at UNLV. If I hadn’t stayed, I wouldn’t have been able to work with Dr. Salako, who has introduced me to the wide world of mathematical biology.

Dr. Salako is a remarkably intelligent mathematician who has keen insight into all sorts of mathematical concepts. I have learned a great deal from him and I am grateful for the opportunity to work with him. Having him as a mentor has really opened my eyes as to what type of mentor I want to be in the future.

What inspired you to co-found the UNLV student chapter of the Society for Industrial and Applied Mathematics?

It was actually my friend, Jorge Reyes, who first brought the idea up. He was entering his last year as a Ph.D. student, and I knew that he would not be able to spend a lot of time doing things for the chapter. I stepped up and took on the share of the work in creating the chapter, making it a registered student organization, and getting it up and running. 

I wanted to be a part of the creation of the chapter, and serve as its first president because I noticed that there wasn’t really a community for math majors to be part of at UNLV. I wanted to fix that issue by providing more opportunities for math students to come together and learn from each other. I also wanted to provide more professional development opportunities specific to mathematics that would help other graduate students prepare for whatever career path they chose.

What highlights from your academic career stand out for you?

I am proud I got second place in my podium session at the Graduate & Professional Student Association Research Forum and that I made it to the semi-finals of Rebel Grad Slam. It can be really difficult to talk about mathematics to a general audience, and I am happy I was able to do well.

I am proud that I was able to help jumpstart the Society for Industrial and Applied Mathematics (SIAM) student chapter to provide a new avenue of professional development opportunities to our math department.

I am also proud that I was given the opportunity to present at the Joint Mathematics Meetings, the Society for Mathematical Biology annual meeting, a workshop at Auburn University, and at Virginia Tech as part of the Future Faculty Diversity Program.

Castellano was lead author on a publication in April 2022 titled “On the effect of lowering a population’s movement to control the spread of an infectious disease, in the Journal of Differential Equations. He has two more papers submitted.