The Process of Resistance Emergence

<div><p>The bars indicate between-host fitness levels of the different strains. Solid curved arrows show conversion events that occur frequently due to large or expanding source populations.</p><p>Dashed arrows show conversion events that occur infrequently due to small source populations.</p><p>(A) Without treatment, all resistant strains are less fit than the sensitive strain. Therefore, resistance emergence is not possible.</p><p>(B) Treatment of a small fraction of the population reduces fitness of the sensitive strain enough to allow for emergence of the fittest resistant strain. For that to happen, one frequent and two rare conversions need to occur.</p><p>(C) Further increase in treatment level allows both the second and third resistant strains to emerge. For the second resistant strain to emerge, one frequent and one rare conversion need to occur. Subsequently, the third resistant strain is rapidly generated and will outcompete all other strains.</p><p>(D) Treatment of a large fraction of the population results in all conversion events being frequent and in rapid emergence of resistance.</p></div

Years until Resistance Emerges—Deterministic Model

<p>The black diamonds show the earliest time at which any one of the resistant strains emerges (reaches a level of 5% of total infecteds), obtained from simulations of the full deterministic system (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020137#pcbi-0020137-e001" target="_blank">Equation 1</a>). The red dashed, green dash-dotted, and blue solid lines show the analytic approximation (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020137#pcbi-0020137-e016" target="_blank">Equation 7</a>) for the time to emergence of the first, second, and third resistant strain. The vertical black lines indicate the level of treatment at which the fitness (<i>R</i>₀) of the respective resistant strain is the same as that of the sensitive. For the top panels, fitness levels of the resistant strains are 75%, 85%, and 95% of the sensitive strain in the absence of treatment, resulting in values for the basic reproductive numbers as indicated. For the bottom panels, fitness levels of the resistant strains are 60%, 75%, and 90% of the sensitive strain. The left panels show results for conversion rates <i>μ_t</i> = <i>μ</i>₁ = <i>μ</i>₂ = 10⁻¹, the right panels show results for <i>μ_t</i> = <i>μ</i>₁ = <i>μ</i>₂ = 10⁻³. Other parameter choices are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020137#pcbi-0020137-t001" target="_blank">Table 1</a>.</p

Model variables.

<p>Model variables.</p

Years until Emergence Occurs as a Function of Treatment

<div><p>(A) All conversion probabilities are <i>μ_i</i> = 10⁻³. The green dashed line shows a situation with two resistant strains with fitness 60% and 90% that of the sensitive strain. The blue dash-dotted line shows three resistant strains with fitness 60%, 75%, and 90%, and the red solid line shows four resistant strains with fitness 60%, 70%, 80%, and 90%.</p><p>(B) Same number of strains and fitness levels as (A) but the product of all conversion probabilities is kept the same. We choose <i>μ_t</i> = 10⁻² for all three cases and <i>μ</i>₁ = 10⁻⁶ for the two-strain scenario (dashed green line), <i>μ</i>₁ = <i>μ</i>₂ = 10⁻³ for the three-strain scenario (dash-dotted blue line), and <i>μ</i>₁ = <i>μ</i>₂ = <i>μ</i>₃ = 10⁻² for the four-strain scenario (solid red line).</p><p>(C) Three resistant strains with fitness of 60%, 75%, and 90%. Conversion rates are <i>μ_i</i> = 10⁻¹ (dashed green line), <i>μ_i</i> = 10⁻² (dash-dotted blue line), and <i>μ_i</i> = 10⁻³ (solid red line).</p><p>(D) Same as (C) but with conversion rates <i>μ_t</i> = 10⁻², <i>μ</i>₁ = <i>μ</i>₂ = 10⁻³ (dashed green line), <i>μ_t</i> = 10⁻⁴, <i>μ</i>₁ = <i>μ</i>₂ = 10⁻² (dash-dotted blue line), and <i>μ_t</i> = <i>μ</i>₂ = 10⁻³, <i>μ</i>₁ = 10⁻² (solid red line).</p></div

as a Function of Treatment Start and Antiviral Efficacy

<p>Unless varied, treatment starts 24 h post-infection, and antiviral efficacy is <i>a</i> = 0.99/0.97. Red = TD model, blue = IR model.</p

Years until Resistance Emerges—Stochastic Model

<p>Boxplots show distribution of times to emergence (resistance at a level of 5% of total infecteds) for 5,000 simulations of the stochastic model. The red dashed, green dash-dotted, and blue solid lines show the analytic approximations for the time to emergence of the first, second, and third resistant strain. The vertical black lines indicate the level of treatment at which the fitness of the respective resistant strain is the same as that of the sensitive. For comparison, the black dashed line shows the deterministic result (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020137#pcbi-0020137-e016" target="_blank">Equation 7</a>). Parameters are chosen as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020137#pcbi-0020137-g004" target="_blank">Figure 4</a>. </p

Schematic of Resistance Generation and Spread

<p>Schematic of Resistance Generation and Spread</p

Nasal Discharge Weight as a Function of Viral Load

<p>Data are from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030240#pcbi-0030240-b042" target="_blank">42</a>] (squares) and [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030240#pcbi-0030240-b043" target="_blank">43</a>] (circles). Also shown is the best fit for the function <i>s</i> (Equation 1). Note that daily discharge is measured in grams; we make the approximation that one gram corresponds to 1 ml in volume.</p

Flow Diagram of the Compartmental Model Describing Gonorrhea Transmission within a Homogenous Core Group

<p>Not shown are the flows out of each compartment at rate <i>λ</i>. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020137#pcbi-0020137-t001" target="_blank">Table 1</a> summarizes the variables and parameters. A detailed explanation of the model is given in the text.</p

Model parameters.

<p>Model parameters.</p