Martin Dindoš

Effect of Periodic Disinfection on Persisters in a One-Dimensional Biofilm Model

It is well known that disinfection methods that successfully kill suspended bacterial populations often fail to eliminate bacterial biofilms. Recent efforts to understand biofilm survival have focused on the existence of small, but very tolerant, subsets of the bacterial population termed persisters. In this investigation, we analyze a mathematical model of disinfection that consists of a susceptible-persister population system embedded within a growing domain. This system is coupled to a reaction-diffusion system governing the antibiotic and nutrient.We analyze the effect of periodic and continuous dosing protocols on persisters in a one-dimensional biofilm model, using both analytic and numerical method. We provide sufficient conditions for the existence of steady-state solutions and show that these solutions may not be unique. Our results also indicate that the dosing ratio (the ratio of dosing time to period) plays an important role. For long periods, large dosing ratios are more effective than similar ratios for short periods. We also compare periodic to continuous dosing and find that the results also depend on the method of distributing the antibiotic within the dosing cycle.

Analysis of Adaptive Response to Dosing Protocols for Biofilm Control

Biofilms are sessile populations of microbes that live within a self-secreted matrix of extracellular polymers. They exhibit high tolerance to antimicrobial agents, and experimental evidence indicates that in many instances repeated doses of antimicrobials further reduce disinfection efficiency due to an adaptive stress response. In this investigation, a mathematical model of bacterial adaptation is presented consisting of an adapted-unadapted population system embedded within a moving boundary problem coupled to a reaction-diffusion equation. The action of antimicrobials on biofilms under different dosing protocols is studied both analytically and numerically. We find the limiting behavior of solutions under periodic and on-off dosing as the period is made very large or very small. High dosages often carry undesirable side effects so we specially consider low dosing regimes. Our results indicate that on-off dosing for small doses of biocide is more effective than constant dosing. Moreover, in a specific ...

LARGE SOLUTIONS FOR YAMABE AND SIMILAR PROBLEMS ON DOMAINS IN RIEMANNIAN MANIFOLDS

We present a unifled approach to study large positive solutions (i.e., u(x) ! 1 as x ! @›) of the equation ¢u + hu i kˆ(u) = if in an arbitrary domain ›. We assume ˆ(u) is convex and grows su‐ciently fast as u ! 1. Equations of this type arise in geometry (Yamabe problem, two dimensional curvature equation), probability (superdifiusion). We prove that both existence and uniqueness are local properties of points of the boundary @›, i.e., they depend only on properties of › in arbitrary small neighborhood of each boundary point. We also flnd several new necessary and su‐cient conditions for existence and uniqueness of large solutions including an existence theorem on domains with fractal boundaries.

Elliptic equations in the plane satisfying a Carleson measure condition

In this paper we settle (in dimension n = 2) the open question whether for a divergence form equation div(A∇u) = 0 with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the Lp Neumann and Dirichlet regularity problems are solvable for some values of p ∈ (1,∞). The related question for the Lp Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].

Stationary Navier{Stokes Equation on Lipschitz Domains in Riemannian Manifolds with Nonvanishing Boundary Conditions

In the previous work, the author and M. Mitrea presented a method of solving the stationary Navier{Stokes equation on Lipschitz do- mains in Riemannian manifolds via the boundary integral technique, where only the vanishing Dirichlet boundary condition was considered. In this pa- per, more sophisticated estimates are developed, which allows us to consider arbitrary large (dim M 6 4) Dirichlet boundary data for this equation.