Phage Therapy and Antibiotics for Biofilm Eradication: A Predictive Model

Abstract

Bacteria that make up the complex physical structures known as biofilms can be 10–1000 fold more resistant to antibiotics than planktonic (free-living) bacteria. In this study we develop a mathematical model to analyze therapeutic techniques that have been proposed to reduce and/or eradicate biofilms, specifically, antibiotics and phage therapy. In this context, the biofilm can be understood as a group defense mechanism, such that the functional response of phages to the biofilm bacterial density is reduced as the biofilm approaches carrying capacity. To capture this mechanism we introduce the function $f(x)=\left( \kappa -\frac{x}{K}\right) x,$ where x is the biofilm density, K is the biofilm carrying capacity and $1<\kappa <2$ is the group defense parameter. The model predicts that two therapeutic strategies of recent experimental interest (phage therapy followed by antibiotics, or antibiotics followed by phage therapy) can reduce but not eradicate the biofilm. In contrast, we predict that complete elimination of biofilm bacteria can be achieved by mechanisms that block the attachment of planktonic bacteria to the biofilm.