Conditions for Bacterial Selection and Extinction Driven by Growth-Kill Trade-Off in Cyclic Antimicrobial Treatments

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.

💡 Research Summary

The paper presents a minimalist population‑dynamics framework to investigate how cyclic antimicrobial regimens shape the evolutionary fate of bacterial subpopulations that differ in susceptibility. Two phenotypic classes are considered: a “sensitive” strain with a high intrinsic growth rate (g₁) but also a high killing rate under drug exposure (k₁), and a “tolerant/resistant” strain with a lower growth rate (g₂) that suffers a reduced killing rate (k₂). The trade‑off between the fitness cost of slower growth and the survival advantage of reduced killing is the central biological premise.

Time is divided into an “antimicrobial phase” of duration τ and a “recovery phase” of duration T − τ, where T is the total cycle length. During the antimicrobial phase the net per‑capita rate for strain i is (gᵢ − kᵢ), while during recovery it is simply gᵢ. By averaging over one full cycle the authors derive effective growth parameters:

 Λᵢ = gᵢ − (τ/T) kᵢ (average net growth)
 Kᵢ = (τ/T) kᵢ (average killing contribution)

Competition between the two strains is governed by the sign of ΔΛ = Λ₂ − Λ₁. If ΔΛ > 0 the tolerant strain will increase in frequency; if ΔΛ < 0 the sensitive strain dominates or the whole population collapses. To make the condition more intuitive the authors introduce a “selection index”

 S = (g₂ − g₁)/(k₁ − k₂)

which quantifies the relative magnitude of the growth penalty versus the killing advantage. A critical threshold S_c emerges from the model: when S > S_c the tolerant strain is expected to be selected, whereas S < S_c predicts eradication of the tolerant subpopulation (or total extinction if the antimicrobial pressure is strong enough).

Two explicit design criteria for successful cyclic therapy are obtained:

1. The antimicrobial exposure must be sufficient to render the sensitive strain’s average net growth negative: (τ/T) k₁ > g₁.
2. The differential killing between strains must outweigh the growth advantage of the sensitive strain: (τ/T)(k₁ − k₂) > (g₁ − g₂).

These inequalities provide concrete, experimentally measurable targets for clinicians or sanitation engineers: adjust the fraction of time under drug (τ/T) and the drug potency (which influences k₁ and k₂) to satisfy both conditions.

Numerical explorations across a broad parameter space confirm the analytical predictions. Short cycles (small T) combined with high killing rates (large k₁) suppress both strains, achieving sterilization. Moderate cycles with low exposure fractions allow the tolerant strain to accumulate gradually, leading to treatment failure. Conversely, long cycles with high exposure fractions favor rapid elimination of the sensitive strain while permitting the tolerant strain to dominate, a scenario reminiscent of sub‑optimal dosing that selects for resistance.

The study’s strengths lie in its clarity and applicability. By reducing the complex genetics of resistance to two measurable traits—growth and kill rates—the model bridges laboratory data (e.g., growth curves, time‑kill assays) with protocol design. The derived formulas can be directly plugged into dosing schedules for antibiotics, disinfectants, or antiseptics, offering a quantitative safeguard against inadvertent selection of low‑susceptibility phenotypes.

Limitations are acknowledged. The binary strain assumption ignores the continuum of susceptibility that typically exists in natural populations. Environmental factors such as biofilm formation, host immune pressure, and spatial heterogeneity are not modeled. Moreover, stochastic mutation events that generate new tolerant variants are omitted, meaning the model captures selection on pre‑existing heterogeneity but not de‑novo resistance emergence. Future extensions could incorporate multi‑strain dynamics, explicit pharmacokinetic/pharmacodynamic (PK/PD) curves, and stochastic mutation processes.

In conclusion, the paper demonstrates that the balance between bacterial growth and antimicrobial killing—captured by simple, experimentally accessible parameters—determines whether cyclic antimicrobial treatments eradicate a population or inadvertently select for tolerant/resistant subpopulations. The analytical conditions and the selection index S provide practical guidance for designing dosing regimens that minimize the risk of resistance development while maintaining therapeutic efficacy across clinical, industrial, and environmental settings.