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We propose a mathematical model of the transmission dynamics of colonization by commensal bacteria within a human community subject to varying levels of antibiotic use designed to control morbidity induced by pathogenic strains of the normally commensal organisms. Colonization is assumed not to induce morbidity in the majority of cases, and antibiotic use is assumed to be related to the arrival and growth of pathogenic strains that give rise to infections including clinical symptoms of disease. In the absence of antibiotic resistance, the model shows how the pattern of antibiotic prescription and use can eliminate the non-pathogenic commensal strains from the host community if the fraction of people taking antibiotics with a defined efficacy exceeds some critical level. The model is extended to take account of the evolution of antibiotic resistance in the commensal population. We assume resistance may be either plasmid-mediated or conferred by selection of low-level pre-existing mutants, and that resistant organisms may experience reduced reproductive fitness. Invasion of the host community by drug-resistant commensals is possible if certain antibiotic prescribing patterns pertain. We calculate these conditions in terms of the transmission parameter of the organism and the level of antibiotic prescription and use. The model is employed to address the issues of how best to use antibiotics in populations harbouring resistant organisms, and when resistant bacteria will out-compete sensitive strains.
Austin et al. (1997) studied this question.