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Seminars

Special Colloquium

Strolling through space - missed antibiotic doses and extreme first passage times

2025/12/11 (Thu.) 15:30~16:30
  • Date : 2025/12/11 (Thu.) 15:30~16:30
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Hwai-Ray Tung (University of Utah)
  • Abstract : Randomness is ubiquitous in biology. In this talk, we illustrate how mathematical biology inspires new mathematically interesting probabilistic questions and gives applications for stochastic processes. In the first half, we ask what to do after missing a dose of antibiotic. To do so, 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 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 analytically tractable random walk model and use it to prove when taking a double dose after a missed dose might be advisable. In the second half, we ask how long it takes for searchers to find a target when additional 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 theorems constitute a rare instance in which extreme value statistics can be determined exactly for strongly correlated random variables.
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