Models for the spread of resistant pathogens

I consider three mathematical models of the epidemiology of antibiotic treatment and the evolution of resistance. All of these models explore the relationship between the volume of antibiotic use and the frequency and rate of ascent (or descent) of resistance. The first model is in the population genetics tradition and assumes that in the absence of treatment the frequency of resistance wanes at a rate proportional to the fitness costs associated with resistance, but precipitously ascends to high frequencies in treated patients. The second two models are in the compartment, or SIR, model tradition of infectious disease epidemiology. The first of these considers the relationship between resistance and rates of antibiotic treatment in open communities. The second explores the factors contributing to the frequency of resistance in the closed settings of hospitals and nursing homes. While I give some consideration to the epidemiological and medical implications of the results of the analysis of the properties of these models, for the most part the models are the message. I end with a harangue about the utility of simple mathematics for these considerations and a plea to obtain realistic estimates of the parameters of these models and test the validity of the predictions generated from the analysis of these models.