A kinetic model is proposed to assess the feasibility of strategies for the removal of biofilms by using substances that induce detachment by affecting the cohesiveness of the matrix of extracellular polymeric substances (EPSs). The model uses a two-state description of the EPS (natural EPS and compromised EPS) to provide a unified representation of diverse mechanisms of action of detachment-promoting agents (DPAs), which include enzymes that degrade the EPS and other agents described in the literature. A biofilm-cohesiveness factor describes local increases in detachment rates resultant from losses in cohesive strength. The kinetic model was implemented in an individual-based biofilm-modelling framework, including detachment rates dependent on local cohesiveness. The efficacy of treatments with DPAs was assessed by three-dimensional model simulations. Changes in treatment efficacy were evaluated quantitatively by using a Thiele modulus, which quantifies the relationship between diffusion of the DPA through the biofilm matrix and DPA decay rate, and a Damköhler number relating the rate of EPS reaction with a DPA and the rate of EPS production by the micro-organisms in the biofilm. This study demonstrates the feasibility and limits of implementing biofilm-control strategies based on attacking the EPS.