Well-Posedness and Stability Analysis of a PDE-ODE Model for the Evolution of Bacterial Persisters

ChongmingLi

Queen's University Department of Mathematics and Statistics

"Well-Posedness and Stability Analysis of a PDE-ODE Model for the Evolution of Bacterial Persisters"

Most antibiotics kill bacteria by disrupting cell wall formation during mitosis. Bacterial persisters are individuals within a population that avoid this fate by not replicating. We use a parabolic PDE to model the phenotypic switch between normal, active bacteria and persisters along with a nonlocal birth-jump process that captures epigenetic inheritance. In addition, we relate bacterial population development to resource dynamics in order to depict a more realistic bacterial growth limit. Mathematically, the model consists of a non-local PDE coupled to an ODE. We prove the well-posedness of the model using semi-group theory and the Banach fixed point theorem. We then examine the evolutionarily stable strategies of persister cells by conducting a global invasion analysis with an appropriately chosen Lyapunov functional.
Additional authors:

---