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.
Antimicrobial protocols are used daily to eliminate bacteria and prevent the spread of pathogens in home [1], industrial or clinical settings. However, bacteria from the same population can respond to treatment very differently, as a result of genetic or phenotypic changes altering antimicrobial susceptibility, among other bacterial characteristics. That is the case of antimicrobial resistance (AMR) or tolerance, which can seriously compromise antimicrobial treatment. In these scenarios, even a small subpopulation of bacteria with reduced antimicrobial susceptibility can survive treatment, making evolutionary processes-mutation, selection, and competition-highly relevant for understanding treatment failure and development of AMR and tolerance [2]. Then, accurately predicting the dynamics of AMR and tolerance selection under biocidal stress is essential for systematic optimisation of antimicrobial protocols [3].
Although the evolutionary process is fundamentally stochastic, especially in small populations [4], outcomes become more predictable and often repeatable under strong and recurrent selective pressures, such as those imposed by cyclic biocide treatments [5]. Mutation itself is random; however, in practice only a few mutant lineages tend to expand and dominate the population even at antimicrobial concentrations far below the minimum inhibitory concentration [6]. In other words, evolution is highly repeatable when the efficiency of selection is high relative to the stochasticity of arXiv:2602.14645v1 [q-bio.PE] 16 Feb 2026 genetic drift, mutation, recombination and unpredictable environmental changes. Consequently, most mathematical models of antimicrobial resistance (AMR) require deterministic equations [7], typically systems of Ordinary Differential Equations (ODEs) [8].
If the process can be assumed to be deterministic under strong selective pressures, as is often observed in cyclic treatments or in treatments that are highly bactericidal, then it becomes necessary to identify a useful and experimentally applicable theory that will allow us to determine the conditions under which bacterial populations will go extinct during these treatment regimens. When a population is driven to extinction, it is also important to estimate the time to extinction so that unnecessary additional treatment cycles can be avoided. Conversely, when survival occurs, it becomes essential to characterise the conditions under which resistant or tolerant subpopulations gain a selective advantage, enabling treatment protocols to be adjusted to minimise their enrichment.
The establishment of this theoretical framework constitutes the main unresolved challenge, and overcoming it is indispensable for the optimisation of effective disinfection or sanitation protocols [7,9]. Recent research has derived extinction conditions for bacterial populations exposed to antimicrobials, although this work assumes a constant antimicrobial stress without cyclic or time-varying concentration dynamics, and accounts for variability through stochastic fluctuations in growth rather than through the explicit coexistence of strains with different traits [10]. Other studies use the birth-death stochastic process to investigate population dynamics under sequential therapies, capturing complex evolutionary phenomena such as collateral sensitivity but without providing explicit analytical conditions for selection or extinction [11]. As a consequence, these approaches require numerical solution through dedicated in silico tools that must be recalibrated for each specific scenario and that usually depended on large parameter sets [12]. Collectively, these studies motivate simple, analytically tractable models of strain competition and extinction under cyclic antimicrobial killing, with minimal population dynamics models appearing most useful. However existing results provide selection conditions only for growth trait evolution under serial dilution without antimicrobial treatment [13].
In this work, we study selection during cyclic antimicrobial application for bacterial populations formed by multiple strains. First, we propose a mathematical model to describe the population dynamics under cyclic treatment, consisting of successive growth and antimicrobial-killing periods. The model formulation is kept simple to study selection as a function of the minimum bacterial characteristics (traits) to describe the dynamics of the different strains, namely, growth rates during recovery and kill rates in response to antimicrobial killing. Then, the mathematical model is used to derive conditions for determining extinction or selection of the different strains based on the bacterial traits and the setup parameters for cyclic treatment. We also provide important measures to quantify selection and compare the selective ability of the strains, such as the extinction cycles and the selection coefficients. The resulting approach provides directly applicable criteria for
This content is AI-processed based on open access ArXiv data.