The impact of mixing on the basic reproduction number in the model without treatment.

<p>The results are for populations with different variances in partner change rates, <i>σ</i>², and the mean rate of partner change kept constant. Mixing is proportionate (assortative) for <i>ω</i> = 1 (<i>ω</i> = 0). The dashed line indicates the threshold value of <i>R</i>₀ = 1 below which HIV cannot spread in the population. <i>R</i>₀ decreases as the mixing becomes proportionate and the variance gets lower. For low variances and high levels of mixing (i.e. low levels of assortativeness) <i>R</i>₀ can be smaller than 1 even in the absence of treatment. For the lowest variance we used in the analysis HIV cannot persist for any level of mixing (the yellow curve).