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.
BackgroundSchool closure is considered as an effective measure to prevent pandemic influenza. Although Japan has implemented many class, grade, and whole school closures during the early stage of the pandemic 2009, the effectiveness of such a school closure has not been analysed appropriately. In addition, analysis based on evidence or data from a large population has yet to be performed. We evaluated the preventive effect of school closure against the pandemic (H1N1) 2009 and examined efficient strategies of reactive school closure.Materials and MethodsData included daily reports of reactive school closures and the number of infected students in the pandemic in Oita City, Japan. We used a regression model that incorporated a time delay to analyse the daily data of school closure based on a time continuous susceptible-exposed-infected-removed model of infectious disease spread. The delay was due to the time-lag from transmission to case reporting. We simulated the number of students infected daily with and without school closure and evaluated the effectiveness.ResultsThe model with a 3-day delay from transmission to reporting yielded the best fit using R
2 (the coefficient of determination). This result suggests that the recommended period of school closure is more than 4 days. Moreover, the effect of school closure in the simulation of school closure showed the following: the number of infected students decreased by about 24% at its peak, and the number of cumulative infected students decreased by about 8.0%.ConclusionsSchool closure was an effective intervention for mitigating the spread of influenza and should be implemented for more than 4 days. School closure has a remarkable impact on decreasing the number of infected students at the peak, but it does not substantially decrease the total number of infected students.
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