Quantifying the therapeutic requirements and potential for combination therapy to prevent bacterial coinfection during influenza

Abstract

Secondary bacterial infections (SBIs) exacerbate influenza-associated disease and mortality. Antimicrobial agents can reduce the severity of SBIs, but many have limited efficacy or cause adverse effects. Thus, new treatment strategies are needed. Kinetic models describing the infection process can help determine optimal therapeutic targets, the time scale on which a drug will be most effective, and how infection dynamics will change under therapy. To understand how different therapies perturb the dynamics of influenza infection and bacterial coinfection and to quantify the benefit of increasing a drug's efficacy or targeting a different infection process, I analyzed data from mice treated with an antiviral, an antibiotic, or an immune modulatory agent with kinetic models. The results suggest that antivirals targeting the viral life cycle are most efficacious in the first 2 days of infection, potentially because of an improved immune response, and that increasing the clearance of infected cells is important for treatment later in the infection. For a coinfection, immunotherapy could control low bacterial loads with as little as 20 % efficacy, but more effective drugs would be necessary for high bacterial loads. Antibiotics targeting bacterial replication and administered 10 h after infection would require 100 % efficacy, which could be reduced to 40 % with prophylaxis. Combining immunotherapy with antibiotics could substantially increase treatment success. Taken together, the results suggest when and why some therapies fail, determine the efficacy needed for successful treatment, identify potential immune effects, and show how the regulation of underlying mechanisms can be used to design new therapeutic strategies.

Keywords: Antibiotics; Antivirals; Coinfection; Combination therapy; Immunotherapy; Influenza; Kinetic modeling; Pneumococcus.

Fig. 1

Breakdown of viral kinetics and effects of antiviral therapy. a Fit (black line) of Eqs. (1–4) to viral titers in the lungs of mice infected with 100 TCID${}_{50}$ PR8 (black squares) [41]. The equations and time scale that characterize the phases of exponential growth (shaded in gray), the transition from growth to clearance (shaded in white), and the exponential decay (shaded in blue) [40] are shown along with the most effective antiviral target. b–d Simulation of Eqs. (1–4) against viral load data under NAI therapy given prophylactically (Panels b–c) or at 5 days pii (Panel d) [21] for no therapy (black line) and for different antiviral targets [virus infection ($\mathit{\beta }$, cyan line), eclipse phase (k, magenta line), virus production (p, blue line), virus clearance (c, green line), or infected cell clearance ($\mathit{\delta }$, orange line)] with efficacy ${\mathit{\epsilon }}_v$ = 60 %. e Simulation of Eqs. (1–4) against viral load data under NAI therapy given prophylactically (green bars) or at 5 days pii (black bars) [21] assuming that NAIs inhibit virus production ($p(1-{\mathit{\epsilon }}_v)$) with efficacy ${\mathit{\epsilon }}_v$ = 10 % and protect target cells from being infected (Eq. (14)) at rate ${\mathit{\epsilon }}_t$ = 0.68 day${}^{-1}$. The parameters values used for all simulations are provided in Table 1 (Color figure online)

Fig. 2

Effect of rGM-CSF therapy. a Therapeutic schedule used to evaluate rGM-CSF therapy in mice infected with PR8 (“Flu”) followed by 200 CFU A66.1 (“Spn”) [8]. b Simulation of Eq. (10) with the parameters in Table 1 and various values of $\widehat{\mathit{\varphi }}$. Dose-AM depletion pairing and distance from the threshold are illustrated for no therapy (black) and rGM-CSF therapy (green). c Simulation of Eqs. (5–9) against bacterial load data under no therapy (black) or rGM-CSF therapy (green). The parameters used are those in Table 1 with the indicated range of AM depletion ($\widehat{\mathit{\varphi }}$) (Color figure online)

Fig. 3

Differential therapeutic benefit of decreasing AM depletion. a Minimum percentage of AMs ($1-\widehat{\mathit{\varphi }}$) needed to achieve resolution ($P=0{log}_{10}$ CFU) by 3 h pbi for coinfections at 3 days pii (black) or 7 days pii (blue) and for bacterial doses of 200 CFU, 1000 CFU, or 5000 CFU. b Percent efficacy (${\mathit{\epsilon }}_g$) needed to achieve resolution by 3 h pbi for a coinfection at 3 days pii or 7 days pii and for a bacterial dose of 200 CFU (black), 1000 CFU (cyan), or 5000 CFU (magenta). c–d Simulation of Eqs. (5–9) for different percentage increases in AMs calculated from baseline for a coinfection at 3 days pii (Panel c) or 7 days pii (Panel d). e–f Calculated therapeutic benefit (change in AUC) for different percentage increases in the AM population ($\widehat{\mathit{\varphi }}$) (Panel e) or for different dose increases (Panel f) for a coinfection at 3 days pii (squares) or 7 days pii (circles). Green indicates a positive therapeutic benefit and red indicates a negative therapeutic benefit (Panel e). g Schematic showing how the slope of the threshold and, thus, the therapeutic benefit increases more rapidly for higher degrees of AM depletion. Baseline values of AM depletion at 3 days pii (square) and 7 days pii (circle) are shown for a dose of 200 CFU. Unless otherwise noted, the numerical solution to Eqs. (5–9) with the parameters in Table 1 was used. Baseline is $\widehat{\mathit{\varphi }}=64.6$ % for a coinfection at 3 days pii and $\widehat{\mathit{\varphi }}=87$ % for a coinfection at 7 days pii (Color figure online)

Fig. 4

Effect of antibiotic therapy and potential for combination therapy. a Simulation of Eqs. (5–8) and (15) against bacterial load data (obtained by bioluminescent imaging, RLU) under mock therapy (magenta) or antibiotics [ampicillin (green) or clindamycin (cyan)] [12]. The parameters used are those in Table 1 with ${\mathit{\epsilon }}_{a,c,i}=0$ (for no therapy and mock therapy), r = 6.5 d⁻¹ (for mock (PBS) and antibiotic therapy), ${\mathit{\epsilon }}_a=11.35{\text{d}}^{-1}$ (for ampicillin), and ${\mathit{\epsilon }}_c=1$ and ${\mathit{\epsilon }}_i=3{\text{d}}^{-1}$ until $\sim$8 days pii and ${\mathit{\epsilon }}_{c,i}=0$ thereafter (for clindamycin). The model output was adjusted to RLU with Eq. (13). b–c Simulation of Eqs. (5–8) and (15) for various values of antibiotic efficacy (${\mathit{\epsilon }}_c$) for prophylactic treatment (beginning at 0d pbi, Panel b) or delayed treatment (beginning at 5 h pbi, Panel b). d Minimum efficacy (${\mathit{\epsilon }}_c$) needed to achieve a clearance phenotype found by simulating Eqs. (5–8) and (15) for treatment beginning at various times pbi. e–f Simulation of the threshold solution (Eq. (10)) with various values of the bacterial growth rate (r) alone (Panel e) or in addition to the degree of AM depletion ($\widehat{\mathit{\varphi }}$) (Panel f) (Color figure online)

Fig. 5

Summary of therapeutic strategies to combat SBIs during influenza. Schematic of the regulating mechanism driving SBIs during influenza virus infections and various therapeutic strategies targeted at each process. Influenza virus infection results in the depletion of alveolar macrophages (AMs), which in turn allows for bacteria to invade and grow. This bacterial growth then increases the viral load. Antiviral therapy (AV) can reduce virus growth, which may in turn decrease AM depletion. AM depletion can be reduced by immunotherapy (IM), which improves bacterial clearance. Antibiotics (Abx) can reduce the bacterial loads and/or the bacterial growth rate, which may reduce the post-bacterial viral load rebound. The figure in the center shows the relationship between AM depletion (x-axis), bacteria load (y-axis), and bacterial growth rate (colored lines), as defined by Eq. (10). Values above/below the threshold lines support growth/clearance phenotypes. Also depicted are the ways in which each therapy can be used alone or in combination (i.e., by using Abx to slow bacterial growth (from the black line to the blue line) or to reduce bacterial loads, and by using IM or AV to reduce AM loss) (Color figure online)