Mathematical Biology Seminar Hawi-Ray Tung, University of Utah, Wednesday, October 22, 2025 12:30 pm in LCB 222 Strolling through space - missed antibiotic doses and extreme first passage times Abstract: Randomness is ubiquitous in biology. In this talk, we illustrate how mathematical biology provides a fertile source of inspiration for new mathematically interesting probabilistic questions and of applications for stochastic processes. In the first half, we explore the effects of different patient responses after randomly missing an antibiotic dose using a mathematical model that links antibiotic concentration with bacterial dynamics. We show using simulations that, in some circumstances, (a) missing just a few doses can cause treatment failure, and (b) this failure can be remedied by simply taking a double dose after a missed dose. We then develop an approximate random walk model that is analytically tractable and use it to understand when it might be advisable to take a double dose after a missed dose. In the second half, we ask how long it takes for a searcher to find a target when searchers are continuously added over time. This quantity is of interest in a variety of biological scenarios, including cell signaling, ant foraging, and bacterial migration between hydrothermal vents. Our rigorous theory applies to many models of stochastic motion, including random walks on discrete networks and diffusion on continuous state spaces, and our results constitute a rare instance in which extreme value statistics can be determined exactly for strongly correlated random variables.