Abstract
Acquired bacterial resistance is currently one of the causes of mortality and morbidity from infectious diseases. Mathematical modeling allows us to predict the further spread of resistance and to some extent to control its dynamics. The purpose of this review is to find and analyze the existing mathematical models in order to understand all the pros and cons of current approaches to collecting and processing the data. During the analysis, 7 articles about mathematical approaches to the studying of resistance that satisfy the inclusion / exclusion criteria were selected. All models were classified according to the approach used to studying resistance in the presence of the antibiotic. Three main classes and one additional class were allocated. Class #1 consists of two models which include the parameter responsible for the effect of the antibiotic as the defined daily dosage (DDD). These models are characterized by similar mathematical approaches (time series analysis and regression). Class #2 consists of one model where the effect of the antibiotic is presented as the fraction of patients treated with this antibiotic and the process is described with differential equations. Class #3 consists of two models: the effect of the antibiotic is estimated via the antibiotic dose as the degree of growth inhibition. The process is described in detail with differential equations from a biological standpoint. Class #4 is optional and consists of models that are interesting not so much in terms of mathematical approaches but in terms of the obtained results. All models are analyzed within classes and their pros and cons in terms of our research are identified. Each of the described models can be used on our data, though some models require certain modifications due to the specifics of the research.
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