Mathematical Details S1 - The Emergence of HIV Transmitted Resistance in Botswana: “When Will the WHO Detection Threshold Be Exceeded?”

Here we present technical details that describe mathematical methodologies and analytical derivations used for our results presented in the main text and parameter estimates. In section 1 we present our mathematical model, which describes the dynamics of the emergence of acquired and transmitted drug-resistant HIV in a population. This is followed by a discussion of the parameters used in the model. We formulate the ordinary differential equations (ODEs) describing the mean-field population dynamics and describe the initial conditions for the model. In section 2 we formulate the dynamics of the drug-resistant population using a Markov chain equation and we discuss the approximations required for this formulation to produce acceptably accurate dynamics. We then show how this can be used to obtain expressions for the evolution of the mean, variance and skewness of the cumulative transmitted resistance.
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