Modeling of Biological Systems: From Algebra to Calculus and Computer Simulations

Abstract

In this chapter we present a survey of mathematical modeling approaches to biological problems. We approach the modeling efforts through several mathematical techniques: from basic algebra, already studied in middle- and high school, to calculus, at the transition of high school and college. Throughout the chapter, we rely heavily on computer simulation techniques with which we investigate different aspects of these models and their relationships with the studies systems, illustrating the modern approach of computational thinking. We have presented versions of these problems and models in our own courses in mathematics for non-majors, targeted to first- and second-year colleges students who are interested in biology and life sciences. Many students have told us that they found the approach engaging and that it increased their appreciation of mathematics as an applied science. The problems and project that you will see here are selected from areas of population biology (populations of squirrels, insects, flies, and wasps); use of medical sensing and modeling to detect the blood pressure and heartbeat in patients; and epidemiology, modeling the spread of infectious diseases, from Ebola in West Africa, with an option to study the COVID pandemic in 2020–2021.