# Linda J. S. Allen

 What I enjoy most is working with students. Whether it's a research project for undergraduates or a particular dissertation for a graduate student, I really enjoy working with students because they get excited when they learn how to use mathematics to solve problems in biology. I think that my purpose as a researcher and a teacher is to get the next generation excited about mathematics and learn tools that help us to cross disciplinary boundaries. Mathematics is the link . . . that ties all sorts of fields together.

### Horn Professor of Mathematics and Statistics, Department of Mathematics and Statistics, College of Arts and Sciences

What are your research objectives and interests?

In collaboration with colleagues in mathematics, ecology, and microbiology, we are working on problems in infectious diseases. In particular, we are interested in how viral or bacterial infections are spread within an individual host or in a population. We use a variety of mathematical tools, deterministic and stochastic techniques, to model the changing dynamics of the infection as it spreads from person-to-person or within an individual. For example, one viral agent we have studied is hantavirus which is carried by wild rodents and spread to humans from infectious excreta of rodents. The disease in humans is known as hantavirus pulmonary syndrome and is referred to as a zoonotic disease. A zoonotic disease is a disease spread from an animal reservoir to humans. For this and other zoonotic diseases, we are interested in how the diseases are maintained in nature so that they cause little or no ill effect to the natural reservoir but when they spill over from animals to humans (nonreservoirs), the effect is catastrophic, resulting in high mortality. We would like to understand the differences in the immune response in reservoir versus nonreservoir hosts. In a mathematical model for spread of an infectious disease in a population, certain assumptions are made about interactions, transmission, and recovery. Based on these assumptions, the model gives us information about the number of infec- tious individuals over time, the final epidemic size and the time until the epidemic ends. In addition, the models can be used to test the effectiveness of various control methods such as vaccination or culling of wildlife without actually implementing these control methods in the field.

How do you feel your research impacts the globe?

Because of the emergence of new and resurgence of old infectious diseases across the world, there is an urgent need to understand their spread. Through collaborative efforts with experts in immunology, virology, bacteriology, ecology, geography, mammalogy, mathematics and statistics, we help to unravel some of the complexities of disease spread at many levels and how to manage and to control the spread. Mathematics is a scientific language that crosses interdisciplinary boundaries and provides a link between these diverse areas.

What types of service projects have you been involved with?

With colleagues from Texas Tech and other institutions, I lecture and help organize workshops and short courses on mathematical modeling techniques in biology. My emphasis is usually on modeling infectious diseases. These workshops and courses have been offered at universities and institutes in the United States and Canada and are open to students, scientists, and other professionals from around the world. In addition to the lectures, we provide problems and short research projects with the goal that, during the workshop or short course, participants form small interdisciplinary groups to work on and solve some of the problems. For example, this summer, I gave a series of lectures on stochastic epidemic models at a workshop for graduate students held at the Mathematical Biosciences Institute at Ohio State University. Also, this summer, I am serving as a research mentor to several high school and freshmen TTU students on a biomathematics project as part of the STEM Education & Outreach program at TTU.

What are you currently working on?

Currently, in a joint research project with a colleague, our goal is to relate deterministic and stochastic threshold levels for disease outbreaks. The most common disease threshold is known as the basic reproduction number, the average number of secondary infections caused by one infectious individual. The basic reproduction number depends on model parameters such as transmission rate and average length of infectivity and is unique for a particular disease. In deterministic theory, if this threshold exceeds one, there is an outbreak, but in stochastic theory this is not the case. Whether there is an outbreak depends on the initial number of infectious individuals. Relating the various thresholds provides new insight into factors that are important in disease outbreaks. In other research projects, my students and I are developing and analyzing models of the immune response in individual hosts and models of lytic bacteriophage, that is, viruses that infect and kill bacteria. Bacteriophage therapy is being considered as an alternative to antibiotic treatment for bacterial infections. Our department offers undergraduate courses in Calculus I for Life Sciences and an Honors Biomath- ematics course. In addition, we offer graduate courses in Biomathematics. In these courses, we incorporate realistic examples from biology and medicine that apply differential and integral calcu- lus, linear algebra, differential equations, probability and statistics. I will be teaching several of these courses in the near future.

Where do you find your inspiration?

Inspiration to work on problems comes from many sources, including reading the scientific literature, listening and talking to colleagues in mathematics and biology, and attending workshops and research conferences.

What advice do you have for new faculty members about balancing the components of Integrated Scholarshipâ€”teaching, research, and serviceâ€”in their careers?

First, I would advise new faculty to establish a firm research foundation in their area of expertise. From this foundation, new faculty can engage students and colleagues in their research. Second, I would advise new faculty to look for opportunities for themselves and for their students to attend and participate in workshops or conferences to help them build up a network of connections.

Scholar Background

I have always enjoyed solving and thinking about mathematical problems. Also, growing up in the country, I enjoyed hiking and nature. So, during my undergraduate education, I took many courses in mathematics and biology. At the University of Tennessee, I pursued an advanced degree in mathematics. In addition to mathematics courses, there were courses offered in mathematical ecology, where I could apply mathematics to study problems in ecology. My interests and background led me to write a PhD dissertation on spatial models of competition and predation. This is how I got into the field of mathematical biology.

1975, B.A., Mathematics, College of St. Scholastica, Duluth, Minnesota;
1978, M.S., Mathematics, University of Tennessee, Knoxville;
1981, Ph.D., Mathematics, University of Tennessee, Knoxville.

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