Speaker: Hwai-Ray Tung (University of Utah)
Title: Strolling through space - missed antibiotic doses and extreme first passage times
Abstract: In the first half of the talk, we consider the effects of different patient responses after missing an antibiotic dose using a mathematical model that links antibiotic concentration with bacteria 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 being added over time. This quantity is of interest in a variety of biological scenarios, including cell signaling, ant foraging, and finding mates with pheromones. 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.