Conditions for Bacterial Selection and Extinction Driven by Growth-Kill Trade-Off in Cyclic Antimicrobial Treatments
Nerea Martínez-López, Niclas Nordholt, Frank Schreiber, Míriam R. García
TL;DR
This work tackles how cyclic antimicrobial protocols shape the fate of multi-strain bacterial populations by introducing a minimal deterministic model where strains differ only in growth rates $\mu_i$ and kill rates $k_i(C)$. The framework combines growth during recovery and a first-order kill during treatment, constrained by a carrying capacity $K$ and dilution $D$, and yields analytic expressions for cycle-wide dynamics via initial conditions $X_{i,c}^0$. It derives necessary and sufficient extinction conditions for the total population and for individual strains, as well as selection criteria based on equilibrium times $t_{eq,i}$, revealing a trade-off between fitness costs and survival advantages that governs which strains persist or are eliminated. The results provide actionable criteria to design cyclic protocols that prevent resistance or tolerance spread and to estimate the number of cycles needed for extinction, with extensions to variable dosing and more complex kill dynamics discussed for future work.
Abstract
Antimicrobial protocols - using substances such as antibiotics or disinfectants - remain the preferred option for preventing the spread of pathogenic bacteria. However, bacteria can develop mechanisms to reduce their antimicrobial susceptibility, which can lead to treatment failure and the selection of resistance or tolerance. In this work, we propose a minimal population dynamics model to study bacterial selection during cyclic antimicrobial application, a commonly used protocol. Selection in bacterial populations with heterogeneous antimicrobial susceptibility is modelled here as a trade-off between survival advantage (reduction in antimicrobial killing) and potential fitness costs (reduction in growth rate) of the less susceptible strains. The proposed model allows us to derive useful expressions for determining the success of cyclic antimicrobial treatments based on two bacterial traits: growth and kill rates. The results obtained here are directly applicable to preventing the selection and spread of resistant and tolerant bacterial strains in real-life protocols.