Details of the analysis (Mathematica notebook) from The evolution of antibiotic resistance in a structured host population

The evolution of antibiotic resistance in opportunistic pathogens such as Streptococcus pneumoniae, Escherichia coli or Staphylococcus aureus is a major public health problem, as infection with resistant strains leads to prolonged hospital stay and increased risk of death. Here, we develop a new model of the evolution of antibiotic resistance in a commensal bacterial population adapting to a heterogeneous host population composed of untreated and treated hosts, and structured in different host classes with different antibiotic use. Examples of host classes include age groups and geographic locations. Explicitly modelling the antibiotic treatment reveals that the emergence of a resistant strain is favoured by more frequent but shorter antibiotic courses, and by higher transmission rates. In addition, in a structured host population, localized transmission in host classes promotes both local adaptation of the bacterial population and the global maintenance of coexistence between sensitive and resistant strains. When transmission rates are heterogeneous across host classes, resistant strains evolve more readily in core groups of transmission. These findings have implications for the better management of antibiotic resistance: reducing the rate at which individuals receive antibiotics is more effective to reduce resistance than reducing the duration of treatment. Reducing the rate of treatment in a targeted class of the host population allows greater reduction in resistance, but determining which class to target is difficult in practice.肺炎链球菌(Streptococcus pneumoniae)、大肠杆菌(Escherichia coli)、金黄色葡萄球菌(Staphylococcus aureus)等机会致病菌(opportunistic pathogens)的抗生素耐药性(antibiotic resistance)演化是重大公共卫生问题，耐药菌株感染会导致患者住院时间延长、死亡风险升高。本研究构建了全新模型，用于分析共生细菌种群(commensal bacterial population)的抗生素耐药性演化过程：该共生菌种群适应由未接受抗生素治疗与接受治疗的宿主构成的异质性宿主种群(heterogeneous host population)，且宿主种群依据抗生素使用模式划分为不同宿主类别(host classes)，宿主类别的示例包括年龄组与地理区域。 对抗生素治疗进行显式建模(explicitly modelling)后发现，更频繁但疗程更短的抗生素使用方案，以及更高的传播速率(transmission rates)，会促进耐药菌株的出现。此外，在结构化宿主种群中，宿主类别的局部传播(localized transmission)既能推动细菌种群的局部适应性演化，也能维持敏感菌株与耐药菌株在全球范围内的共存状态。当不同宿主类别的传播速率存在异质性时，耐药菌株更易在传播核心群体(core groups of transmission)中演化形成。 上述研究结果对抗生素耐药性的优化管理具有重要指导意义：降低个体接受抗生素治疗的频率，比缩短单疗程抗生素使用时长更能有效降低耐药性发生风险。针对特定宿主类别降低治疗频率，可进一步降低耐药性水平，但实际操作中难以确定应靶向哪一类宿主。