Exploiting ecology in drug pulse sequences in favour of population reduction

A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment.Author summary: The possibilities of lower antibiotic dosages and treatment times, as demanded by antibiotic stewardship programmes have been investigated with complex mathematical models to account for, for example, the presence of an immune host. At the same time, microbial experiments are getting better at mimicking real setups, such as those where the drug gradually permeates in and out of the region with the infectious population. Our work systematically discusses an extremely simple and thus conceptually easy model for an infectious two species system (one wild-type and one more resistant population), interacting via logistic growth, subject to low and high stress environments. In this model, well-defined timescales exist during which the low stress environment is as efficient in reducing the population as the high stress environment. We explain which temporal patterns of low and high stress, corresponding to sequences of drug treatments, lead to the best population reduction for a variety of durations of high stress within a constant long low stress environment. The complexity of the spectrum of best treatments merits further experimental investigation, which could help clarify the relevant timescales. This could then give useful feedback towards the more complex models of the medical community.