Comparison of classical and adaptive regimes, for variable dose and treatment delay.

<p>Different treatment scenarios are simulated up to <i>T</i> = 30 days post-infection. Classical treatment assumes a fixed duration of 7 days, while in the adaptive regime, drug uptake is related to bacterial density above the threshold Ω = <i>B</i>(<i>τ</i>₁). Parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>. <b>A)</b> Clearance of infection by 30 days can be obtained: via classical treatment only (red), via adaptive treatment only (green) or using either regime (blue). <b>B)-C)</b> The amount of drug deployed in each treatment and the associated time to clearance. Longer time to clearance in the classical regime at low doses corresponds to relapsing infection after treatment cessation, and delayed clearance by host immunity. <b>D)</b> Treatment outcomes in those cases where both regimes, classical/C, and adaptive/A, can yield infection clearance (mean ± sd), with: , ; , ; , . <b>E)</b> Treatment outcomes in those cases where clearance can be achieved exclusively via one or the other regime (mean ± sd), with: , ; , ; , .</p

The critical antibiotic dose range, for bacterial behaviour immediately after treatment onset.

<p>As the treatment onset is postponed, and more immunity accumulates in the host, smaller doses can be used to interrupt the growth of each bacterial sub-population (blue line for <i>B</i>_<i>s</i>, and red line for <i>B</i>_<i>r</i>). Depending on how the actual dose, <i>A</i>_<i>m</i>, that is deployed, sits in this range, different dynamic scenarios may ensue during treatment, with specific consequences for immune dynamics. In the lower dose range, immunity can still increase during treatment and assist in infection clearance. In the higher dose range, immune build-up is disrupted by treatment, and clearance can be achieved only by prolonged antibiotic pressure. Parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>. The time it takes the pathogen load to trigger immune activation (i.e. reach the immunity threshold <i>k</i>), in the absence of treatment, denoted by <i>t</i>_<i>k</i>, is given by the gray vertical line. The time it takes the host immunity to trigger bacterial decline (i.e. time for <i>B</i>(<i>t</i>) to reach its peak), in the absence of treatment, denoted by <i>t</i>_<i>peak</i> is given by the black vertical line. An optimal delay usually sits in the middle of this range.</p

Aggressive treatment guaranteeing infection clearance using a classical regime, without relying on host immunity.

<p>Antibiotic dose and treatment duration can be traded-off against one another, at any treatment onset (lines depict <i>τ</i>₁ varying between 2 days and 5 days), to achieve the same final result: infection clearance by the end of therapy. We apply <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.e024" target="_blank">Eq 19</a> to two infection scenarios: <b>A)</b> <i>a</i> = 0.1, very high resistance; and <b>B)</b> <i>a</i> = 0.3 lower resistance of the drug-resistant bacterial sub-population. Parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>.</p

Adaptive treatment dynamics depends on dose <i>A</i>_<i>m</i> and the symptom threshold Ω.

<p><b>A)</b> High cost of resistance (<i>c</i> = 2.2) where . <b>B)</b> Low cost of resistance (<i>c</i> = 0.1) where . All other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a> (<i>r</i>₀ = 3.3, <i>k</i> = 10⁵). Drug-sensitive pathogen dynamics are plotted in blue solid lines, and drug-resistant pathogen dynamics are given by the red dashed lines. In adaptive treatment, doses below allow bacterial growth during treatment thus co-stimulation of immunity. Higher doses are scaled according to pathogen density <i>B</i>(<i>t</i>) ≥ Ω, which maintains the total infection load at Ω, until sufficient host immunity has been mounted. Doses above can be scaled down if necessary (A top right panel), or used in full (B top panel) guaranteeing the no-growth condition. Under <i>σ</i> = 2 as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>, at too low symptom thresholds (Ω < <i>k</i>), the treatment starts too early, and immunity does not reach the critical level. When coupled with high dosage of treatment, this results in chronic infection being maintained indefinitely, unless other killing mechanisms or non-specific immune defenses are present at such low bacterial densities and can assist in clearance.</p

Illustration of model dynamics.

<p><b>A)</b> Untreated infection. <b>B)</b> Classical treatment with: <i>A</i>_<i>m</i> = 6, <i>τ</i>₁ = 3.5, <i>τ</i>₂ = 7. <b>C)</b> Adaptive treatment with parameters Ω = 10⁶, <i>A</i>_<i>m</i> = 6. Other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>. The resulting duration of adaptive treatment is 2.7 days. From the coupling to pathogen load, the effective rate of antibiotic uptake in adaptive treatment within such interval is 0.44, which implies a reduction in the effective dose from the prescribed <i>A</i>_<i>m</i> = 6 to about 3, sufficient to restrict growth of the drug-sensitive sub-population. The treatment onset <i>τ</i>₁ = 3.5 days corresponds to Ω = 10⁶ (adaptive regime), where Ω > <i>k</i>.</p

Illustration of adaptive treatment above the immunity threshold (Ω > <i>k</i>).

<p><b>A)</b> Clearance dynamics when Ω is sufficiently high (Ω = 10<i>k</i>), i.e. satisfies <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.e044" target="_blank">Eq 22</a>. <b>B)</b> No clearance dynamics, when Ω is too close to <i>k</i> (Ω = 5.6<i>k</i>), and adaptive treatment induces oscillatory dynamics. <b>C)</b> High rate of effector cell conversion into memory <i>f</i> = 0.1. <b>D)</b> Lower rate of conversion into memory <i>f</i> = 0.05. When persistent immunity accumulates faster, the range of symptom thresholds where adaptive treatment works, approaches the host immunity threshold, enabling treatment success at lower pathogen densities. Parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>, with <i>k</i> = 10⁵.</p

Resistance selection over treated infections, for different combinations of dose <i>A</i>_<i>m</i> and delay <i>τ</i>₁ in the classical regime.

<p>The simulated values of <i>A</i>_<i>m</i> correspond to 30 doses in the range . We plot the proportional change in the resistance burden over treated infection <i>R</i>_<i>tot</i>, relative to the same measure in untreated infection, as a function of antibiotic dose and timing of treatment onset for a range of infection scenarios. In the subpanels, the benefit and cost of resistance, and treatment duration vary as: A) <i>a</i> = 0.1, <i>c</i> = 2.2, <i>τ</i>₂ = 7; B) <i>a</i> = 0.2, <i>c</i> = 2.2, <i>τ</i>₂ = 7; C) <i>a</i> = 0.1, <i>c</i> = 2.2, <i>τ</i>₂ = 15; D) <i>a</i> = 0.1, <i>c</i> = 1, <i>τ</i>₂ = 7; E) <i>a</i> = 0.2, <i>c</i> = 1, <i>τ</i>₂ = 7; F) <i>a</i> = 0.1, <i>c</i> = 1, <i>τ</i>₂ = 15; G) <i>a</i> = 0.1, <i>c</i> = 0.1, <i>τ</i>₂ = 7; H) <i>a</i> = 0.2, <i>c</i> = 0.1, <i>τ</i>₂ = 7; I) <i>a</i> = 0.1, <i>c</i> = 0.1, <i>τ</i>₂ = 15. The resistance selection window is defined by the dashed white line (contour line corresponding to a proportional change of 1). Superimposed are treatment combinations that maintain infection duration within a factor of 1.1 relative to no treatment (yellow dots), and those that, in addition, satisfy a reduction in immunopathology by at least 2-logs order of magnitude (red dots). All parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004857#pcbi.1004857.t001" target="_blank">Table 1</a>, unless otherwise stated. The growth rate of the resistant bacteria <i>B</i>_<i>r</i> is varied as <i>r</i>₁ = <i>r</i>₀ − <i>c</i> (different rows). Moderate dose-delay combinations, applied below the resistance selection window at each infection, can be effective in clearing the pathogen, in synergy with host immune responses. The aggressive high doses instead are effective without relying on the contribution by the immune system.</p

Model parameters and interpretation.

<p>Model parameters and interpretation.</p

Dose-response curves and susceptibility distributions inferred from survival curves.

<p>A, Curves represent the estimated dose-response relationships from fitting the model described in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003773#s2" target="_blank">Methods</a> to survival over time, for Wolb⁻ (black) and Wolb⁺ (blue). Shaded areas represent the 95% CI. B, Distribution of susceptibility to infection in Wolb⁺. The posterior median distribution is the curve and the shaded area is the 95% CI. C, Posterior samples of the Beta-distribution shape parameters describing Wolb⁺ susceptibility in blue. Red dot marks the median of distribution.</p

Selection of optimal days to collect mortality measurements for traditional dose-response models.

<p>The red line traces a score for how well mortality at any given day represents infection estimated by the time-dependent model (refer to axis on the right). The score is given by , where Δ denotes the number of doses in the dataset, () represents the proportion infected in the Wolb⁻ (Wolb⁺) group subject to <i>D</i>CV dose <i>j</i>, and () the observed mortality proportion over time in the Wolb⁻ (Wolb⁺) group subject to <i>D</i>CV dose <i>j</i>. Gray vertical lines mark the optimal day to measure mortality for dose-response models (day 30, dash-dotted line) and the limits of the acceptable range (days 17 and 46). Dashed lines represent the Gamma distributions that describe old-age mortality, and black (blue) full curves refer to the Gamma distributions that describe infection-induced mortality in Wolb⁻ (Wolb⁺) (refer to axis on the left). Curves are the mean posterior probabilities and shaded areas represent the 95% CI.</p