The aim of this paper is the mathematical study of the interactions between bacterial populations, materials they colonize, and drugs delivered from surfaces where they adhere. Bacteria can cause infections, which are common events in different types of medical implants as, for example, orthopedic prosthesis, and are often responsible for rejection. A controlled drug delivery to fight bacterial adhesion is crucial in reducing infection rates. A strategy recently adopted to address the problem is to deliver therapeutic agents locally by dispersing them into polymeric implant coatings. The mathematical model is composed of a system of three partial differential equations that describe the drug release from a biodegradable polymeric coating and by an ordinary differential equation that governs the density of a bacterial population. The link between the system of partial differential equations and the ordinary differential equation is defined by an integral that represents the mass of drug that is released by the polymeric coating at time t. Quasi-sharp estimates for the bacterial density that give insight into its dependence on the polymeric properties and the drug characteristics are established. Numerical experiments illustrating the behavior of the density of bacteria, depending on the characteristics of the drug-polymeric coating system, are included.
