Host‐pathogen kinetics during influenza infection and coinfection: insights from predictive modeling

Summary Influenza virus infections are a leading cause of morbidity and mortality worldwide. This is due in part to the continual emergence of new viral variants and to synergistic interactions with other viruses and bacteria. There is a lack of understanding about how host responses work to control the infection and how other pathogens capitalize on the altered immune state. The complexity of multi‐pathogen infections makes dissecting contributing mechanisms, which may be non‐linear and occur on different time scales, challenging. Fortunately, mathematical models have been able to uncover infection control mechanisms, establish regulatory feedbacks, connect mechanisms across time scales, and determine the processes that dictate different disease outcomes. These models have tested existing hypotheses and generated new hypotheses, some of which have been subsequently tested and validated in the laboratory. They have been particularly a key in studying influenza‐bacteria coinfections and will be undoubtedly be useful in examining the interplay between influenza virus and other viruses. Here, I review recent advances in modeling influenza‐related infections, the novel biological insight that has been gained through modeling, the importance of model‐driven experimental design, and future directions of the field.

have made it possible to dissect critical mechanisms that drive the infection. The models have successfully quantified and predicted the viral load kinetics from clinical and experimental infections, [12][13][14][15][16][17][18][19][20][21][22][23][24][25] the symptoms that arise during infection, 12,13 the dynamics and efficiency of different host immune responses, 14,17,18,[25][26][27][28][29][30][31][32][33][34] the effect of different viral and host factors, 15,16,[20][21][22]35 the efficacy and design of vaccines and antiviral therapies, 14,[19][20][21][22][36][37][38][39][40] and the mechanisms of coinfection between influenza viruses and other viruses or bacteria. [41][42][43][44][45] Remarkably, influenza viral load dynamics can be described using as few as 3-4 equations for populations of uninfected cells, infected cells, and virus. 14 The kinetics of host immune responses and/or coinfection with other pathogens can be accurately described by adding only 1-2 more equations. 41 Simple models like these are optimal because they readily allow for mathematical and statistical analyses that extract information about the underlying biology. Although models are typically first calibrated to data to ensure a robust recapitulation of the infection kinetics and to estimate the rates of growth and decay, this is not the only goal. The underlying model structure (eg, non-linear feedbacks between different cell populations), the behavior of the resulting parameter estimates (eg, when two parameters are correlated), and in silico experiments that predict the response under perturbation (eg, with antivirals) can all reveal hidden regulatory mechanisms that may not be readily apparent from the data itself and/or cannot be tested in the clinic or laboratory. A schematic of this model-experiment exchange is shown in Figure 1.
Improvements in the availability of quantitative data in recent years has led to more robust models being developed and to the predictions of some of these models being validated in the laboratory.
One collection of studies, which are described here, illuminate the accuracy and predictive capability of mathematical models and the importance of designing confirmatory experiments to define new biology and improve the models. Here, I review current approaches in modeling influenza virus kinetics and host-pathogen interplay, recent advances in modeling viral-bacterial and viral-viral coinfections, the techniques used to identify controlling mechanisms, biological interpretations of the model results, and the benefits of model-driven experimental design.

| MODELING INFLUENZ A VIRUS INFEC TI ON S: THE G OLD S TANDARD
Influenza A viruses infect the upper and lower respiratory tracts to cause acute, self-limiting infections. The dynamics of the infection are rapid with the virus establishing quickly and replicating exponentially to high titers within 1-2 days. In the majority of cases, the infection resolves within 7-10 days, but viral loads can remain elevated in children and immunocompromised individuals.
The mechanisms that drive these kinetics and how they might be altered by therapy or other pathogens are not well understood even though many of the contributory cytokines, chemokines, and cells are known. Mathematical models have accurately described viral load kinetics without including equations for specific host responses. [46][47][48] The models assume that susceptible epithelial cells ("target cells") are limited and that virus declines once the majority of cells are infected. 14 Accurate predictions have been made under this assumption, which does not specify the mechanisms by which target cells are limited.
Nevertheless, several studies have challenged whether the approximation is accurate and how it relates to different host responses, such as type I interferons (IFNα and IFN-β) 17,25 (A.M. Smith, unpublished data). Some studies have attempted to establish a comprehensive view of the host response 15,35,49,50 while others have taken a more focused approach. 14,17,26,28,34 One benefit of models with reduced complexity is the availability of analytical tools that can facilitate a robust interpretation of the dynamics.
Until recently, progress in the field was plagued by a lack of sufficient data to parameterize/calibrate mathematical models, particularly those that included arms of the immune response. 46 While viral load data remains the most prevalent type of data available, various immune factors have been measured on frequent enough time scales to be utilized in modeling studies, 15,18,51,52 (A.M. Smith, unpublished data). With these data, even the larger, more comprehensive models can be calibrated to data. 15,35,49 In addition, efforts to improve parameter estimation algorithms and employ analytical techniques have significantly advanced our ability to generate robust predictions about the underlying biology. 16,24,49,53 Model results are now undergoing rigorous testing in the laboratory, which has confirmed their predictive capability and importance in identifying regulatory mechanisms driving influenza virus infections.

| Viral kinetic model
The majority of influenza virus infection models developed thus far have utilized a common model core, that is, the standard viral kinetic model 14   The assumption could be interpreted as (i) all cells within the respiratory tract become infected, which is possible but not generally observed 17,25,54 (A.M. Smith, unpublished data), or (ii) there is a predefined number of cells that will become infected (ie, where the initial number of target cells, T 0 , essentially defines the final number of infected cells). The lack of complete destruction of the respiratory tract, suggests that virus spread is regulated by host defense mechanisms. However, omitting specific immune control in the viral dynamics model does not invalidate the target cell limitation hypothesis, but may lead to disparate parameter values. Regardless of the underlying mechanism, influenza models with or without target cell limitation match much of the available viral titer data. [46][47][48] In addition, the predicted dynamics of the infected cells (I 2 ) agree well with the spatial spread, as measured by histomorphometry, even when only ~50%-60% of the lung becomes infected (A.M. Smith, unpublished data). However, another study utilized GFP-reporter virus data, 55 which can also be used to track infected cells, and demonstrated that the target cell limited model breaks down for low dose infections. 25 Simply reducing the number of initial target cells (T 0 ) was insufficient to replicate the dose-dependent dynamics. 25 This may indicate a deficiency in the model or that some host responses are more functional with low dose infection, which has been proposed in other studies using low doses. 41

| Quantifying the rates of infection and the response to perturbation
Understanding time-dependent mechanisms that control viral infection dynamics requires that mathematical models be calibrated to experimental or clinical data and thoroughly analyzed. Fitting a model to data ensures that the equations accurately describe the infection dynamics and provides estimates of the rates of infection, production, and clearance. It also begins to reveal the relationship between these rates and the strength needed to induce a change in the dynamics (eg, with drug therapy or coinfection). Further F I G U R E 1 Data-Driven Mathematical Modeling and Model-Driven Experimental Design. Data-driven mathematical modeling studies are iterative and entail developing a model to describe the underlying biology, calibrating the model to experimental or clinical data, analyzing the model with mathematical techniques, using the model to make predictions and design experiments, and validating the predictions in the laboratory or clinic investigating how changing the rates affects outcome, for example, through sensitivity analysis, has generated predictions about the response to therapy 14,[19][20][21]36,56 or coinfection with other pathogens. [41][42][43]45 Collectively, these types of analyses reveal aspects of influenza biology that are not immediately available from the experimental or clinical data alone.
With appropriate parameter estimation techniques, defining accurate and meaningful parameter values is possible. During model fitting, the log 10 infectious viral load, which is typically in units of 50% tissue culture infectious dose (TCID 50 ) or plaque forming units (PFU), is compared to the log 10 output of the model. A variety of data fitting algorithms have been used, including adaptive simulated annealing (ASA), 24 Monte Carlo Markov Chain (MCMC), 13,15,22,35,49 Gaussian processes (GP), 53 and maximum likelihood estimation (MLE). 16,26,41 Until recently, it was relatively well accepted that the choice of estimation scheme is not critical. However, contrasting parameter estimates may result and some evidence suggests that ASA or GP methods can outperform MCMC and MLE methods in terms of accuracy, convergence, and run time. 24,53 Further investigation is needed to ensure robust results, particularly because MCMC methods are popular.
Uniquely identifying each parameter in a model has been challenging 57,58 but has not limited the predictive capability. 41,44 The standard viral kinetic model has seven unknown parameters (β, p, k, c, δ, V 0 , and T 0 (see Figure 2)). In most studies, the values of the eclipse phase parameter (k) and initial target cells (T 0 ) are fixed because their values can be calculated. 14 However, these can be left free 24,53 without compromising the predictive capability. One problematic parameter has been the virus clearance rate (c), which often estimates to large values that may not be biologically relevant. 16,24 This is because the model attempts to capture the rapid decrease in free virus shortly after the infection is initiated as virus infects cells (~0-4 hours). However, this challenge can be overcome by setting the initial free virus (V 0 ) to zero (ie, V 0 = 0) and assuming that the initial number of infected cells is positive (ie, I 1 > 0). 24 Using this assumption recovers virus clearance rates (c) that are more reliable. 24 Ensuring robust predictions requires more than estimation of the model parameters. A thorough investigation into the uncertainty of the estimates and the corresponding model solution is also required.
This has been particularly true when attempting to determine significant differences in parameter estimates generated by fitting a model to data obtained under varied experimental conditions, such as during F I G U R E 2 Viral Kinetic Model and Dynamics. A schematic of the standard viral kinetic model, 14 associated equations, fit to data from mice infected with influenza A/Puerto Rico/34/8 (PR8), 24 and timeline of major host responses are shown. The model tracks susceptible "target" cells (T), two classes of infected cells (I 1 and I 2 ), and virus (V). Target cells are infected by virus at rate βV. Once infected, the cells undergo an eclipse phase, which accounts for the time between infection and virus production. To account for these dynamics, infected cells are split into two classes, where k is the transition rate from unproductive to productive. Infected cells are lost at rate δ I 2 per day. Virus is produced at rate p per infected cell and is cleared at rate c per day. The resulting model dynamics are shown for a saturating infected cell death rate, that is, I 2 = δ d ∕ K δ + I 2 , where δ d ∕K δ is the maximum rate of clearance and K δ is the half-saturation constant. Viral kinetics generally split into ~5 phases: initial infection of cells, exponential growth, peak, a slow decay, and a fast decay/clearance. Major host responses influencing these phases include, type I interferons (IFN), natural killer (NK) cells, T cells, and antibody (Ab) infection with different virus strains, 16,41 with different doses, 15,59 in different host genetic backgrounds, 60 or in different aged individuals. 59,61 For this, ensemble-style methods have been particularly useful.
Plotting the resulting parameters within a 95% confidence interval (CI) as histograms and as two-dimensional (2D) or 3D projections of the parameter space is critical to effective interpretation of the model results.
Unsurprisingly, parameters are often correlated (eg, virus infection and production, 17 virus production and clearance, 24 or virus clearance and infected cell clearance 16 ), which suggests that the data is insufficient to distinguish between these processes. For example, similar viral load dynamics may be possible with slow virus growth and clearance and with fast virus production and clearance. If the goal was to distinguish between these possibilities, additional data would be necessary.
Utilizing multi-variable data, such as infectious virus and viral RNA copies, can reduce uncertainty, 62

| Insight from analytical solutions: timedependent mechanisms
The predictive capability of influenza models goes beyond data fitting, parameter estimation, and sensitivity analysis. The simplicity of the model is beneficial because additional mathematical analyses are feasible. 65 It can be easily observed that viral load dynamics split into two log-linear (ie, exponential) phases: growth and decay. During the initial growth period, few target cells are infected and their population remains relatively constant (A.M. Smith, unpublished data). This information was used to obtain an equation that describes exponential virus growth 65 : is the slope of the viral growth and α 1 is a constant. 23 Prior to virus decay, there is a short, non-linear period (~12 hours) between virus growth and decay where the growth slows prior to the peak. 65 During the resolution period, most available cells have become infected and there are few target cells remaining (T ≈0).This information was used to obtain an equation that describes exponential virus decay 65 : constants. This solution is less complex than V 1 (t) and defines the peak and infection resolution. Here, the peak shape is dictated by the rates of eclipse transition (k), virus clearance (c), and infected cell clearance (δ). After the peak, the infected cell death rate (δ) controls the rate of decay (ie, where V p is the peak viral load).
Having solutions like these that detail the time-dependent contribution of each infection process to the viral dynamics has been beneficial in establishing robust interpretations of the data and models.

| The antiviral type I interferon response
The type I IFN response has potent antiviral activity and is important for control of influenza virus infections. 67  and IFNα has anti-inflammatory properties. 80,81 However, influenza viruses can antagonize the IFN response within infected epithelial cells, which is primarily mediated by its non-structural protein, NS1. 82,83 The majority of models developed thus far have focused on the effect of IFN (F) in limiting virus production from infected cells: where F is the efficiency of IFN in reducing virus production. 14

| CD8 + T cell-mediated virus control and waning immunity
CD8 + T cells are responsible for clearing virus infected cells and resolving the infection. 51,91,92 The infiltration of these cells into the respiratory tract is concurrent with rapid virus decay and the con-  Only recently was a mathematical model developed to begin examining respiratory virus coinfections. 42  The model replicated in vitro data from coinfection with IAV and RSV, where IAV inhibits RSV growth, 104 and with IAV and PIV, where PIV enhances IAV growth. 103 A key result was that varied infection kinetics and outcomes could manifest from changing the virus dose or the intrinsic virus growth rate. Although RSV dose may not affect the interaction during IAV-RSV coinfection, 106 the finding is relevant for RV-IAV coinfection. 105 However, interference in the infection of epithelial cells is not the proposed mechanism for these viruses. 105 The model prediction could be interpreted in another way. That is, when the interaction between viruses is competitive, target cells be-

| Host control of pneumococcal pneumonia
Pneumococci readily colonize the nasopharynx of healthy adults and children [114][115][116] and occasionally migrate to other tissues to cause severe disease, such as otitis media, pneumonia, meningitis, and septicemia. 117  for which a clearance phenotype can be attained. 64 Indeed, this has been observed in several data sets 44,[120][121][122] and recently shown for varying combinations of aMΦs and bacteria. 44 The subsequent neutrophil response further dictates bacterial growth kinetics and outcome. 60,64,119 Sensitivity of the system revealed that neutrophilmediated damage of the epithelium is an important predictor of outcome. 64 Understanding the role of tissue damage during infections is important and often more closely related to the probability of survival than to pathogen levels. Modeling immune-mediated lung damage has not been attempted for influenza but will undoubtedly prove useful, particularly because tissue damage and defects in tissue repair affect influenza-bacteria related mortality. 123  Figure 4). 41 In the model, bacteria increase the rate of virus production from infected epithelial cells (pI 2 ) according to the saturating function â(P) = aP z (Figure 4). This term drives the viral rebound.

| Host-pathogen regulation during influenzapneumococcal coinfection
There was no pre-defined hypothesis or evidence for this increase, but its inclusion in the model was critical. This novel hypothesis subsequently guided several in vitro experimental studies, [125][126][127] where at least two potential underlying mechanisms were discovered.
First, S. aureus, another common coinfecting bacteria, was shown to inhibit IFN signaling in influenza-infected cells, which resulted in increased virus production. 125 Although it is unknown if pneumococci have this same ability and to what extent this occurs in vivo, particularly considering the enhanced IFN levels during coinfection, [86][87][88] it is an intriguing finding and validates the model-generated hypothesis. Second, pneumococcal neuraminidases, NanA and NanB, have been shown to promote virus replication 126,128 presumably through cleavage of viral NA. Unsurprisingly, increased viral loads were not observed when the two pathogens were simultaneously administered to cell cultures. 127 This reduced synergism is consistent with in vivo results indicating that the order and timing between pathogens is important. 112 The model also predicted that virus infection decreases the rate of bacterial clearance by aMΦs according to the saturating func- Figure 4). This term drives bacterial invasion and was initially included to assess previous reports that aMΦs became dysfunctional during influenza. 120 Although the model could not distinguish whether these cells were functionally impaired or were lost during infection, the changes to the aMΦ population were sufficient to drive the bacterial load dynamics. 41 In addition, the resulting parameter estimate indicated that the strength of this reduction was significant (ie, (V) = 85 − 90%). A follow-up experimental study that tracked the aMΦ population with a labeling dye and employed a novel and robust flow cytometry gating strategy better defined the aMΦ dynamics during IAV infection. 113 This study showed a profound depletion of aMΦs over the course of influenza, 113 which may be specific to BALB/cJ mice. 129 In C57BL/6 mice, aMΦs may be functionally inhibited. 129 Fortunately, the model remains accurate because the underlying mechanism is not defined by the model.
Remarkably, the experimental data showed that aMΦs were reduced at 7 days post-influenza by the exact value that the model predicted, that is, 85%-90%. 113 This study effectively validated the model and the estimate of ̂( V). In addition, the data and model to- Parameter estimation played a key role in identifying these mechanisms and in determining that they are independent. 41 The lack of correlation between the parameters involved in the two functions, â(V) and ̂( V), suggested that they described distinct processes.
Unsurprisingly, there were correlations within each function (ie, a is correlated to z, and is correlated to K PV ). 41 Notably, these correlations did not inhibit accurate parameter values from being obtained. 41,113 These studies illuminate the critical nature of validating a model's predictions to expand its capabilities through correcting any inaccuracies (eg, altering functional forms or adding new equations) and completing new analyses (eg, as in 36,44 ). It remains unclear if the function describing the increase in virus production (â(P) = aP z ) is accurate. However, the new aMΦ data suggested that the effect on these cells does not saturate (ie, ̂( V) ≠ V∕(K PV + V)).
A more mechanistic model for aMΦ interactions with influenza virus is likely required. Nevertheless, approximating aMΦ depletion ̂( V) through produced robust predictions. 41,44

| The non-linear threshold regulating phenotype and heterogeneity
The new knowledge about aMΦ dynamics and the connection of these data to ̂( V) allowed for another iteration of the modelexperiment exchange. 44 By simulating the model with values for ̂( V) between 0 (0% depletion) and 1 (100% depletion), it was observed that this parameter is a bifurcation parameter that regulates bacterial growth trajectories. 44 Mathematical analyses were used to derive the non-linear threshold that defines the dynamical switch between growth and clearance phenotypes ( Figure 4). That is, bacteria-aMΦ pairs that fall below the threshold will result in bacterial clearance while pairings above the threshold will lead to bacterial growth. The threshold can be used to identify the dose needed for successful bacterial invasion during influenza. It also suggests that there is a critical point where any dose will initiate the secondary infection (dot on threshold curve in Figure 4). This is defined by a relation between the rates of bacterial growth (r) and clearance ( M M A ), that is, ̂c rit = 1 − r∕( M M A ). This information was used to design confirmatory experiments, which examined bacterial kinetics for over 20 different combinations of bacteria and aMΦs. 44 The data showed that the threshold was accurate, the rate of bacterial growth/clearance increases with distance above/below the threshold, the phenotype switches if complete clearance is not attained within ~4 hours, and pairings below the threshold result in heterogeneous bacterial titers. 44 This information suggests that the behavior can be predicted for any bacteria-aMΦ pairing, which is ideal. It also aids in the interpretation of bacterial load data and allows for exploration of therapies that manipulate bacterial loads (eg, antibiotics) and aMΦs (eg, immunotherapy or antivirals). 36

| Defining the contribution of other mechanisms
In addition to identifying the mechanisms described above, the model also defined the time scales on which they act. For high-dose infection, the slope in the bacterial dynamics changes at ~10 hours postbacterial infection. 41 This indicates that the contribution of aMΦs to clearance is short lived, which has been observed experimentally. 44,[120][121][122] However, bacteria grow exponentially after this time, which suggests that neutrophils have little contribution to controlling bacterial kinetics when the dose is sufficiently high. 41 This is consistent with experimental evidence that these cells become dysfunctional throughout influenza. [133][134][135][136][137] The contribution from neutrophils may be higher during low-dose infection, 41

| Connecting mathematically derived mechanisms to omics data
The focus of many infectious disease studies has recently switched from collecting qualitative data to collecting large, quantitative 'omics' data sets that simultaneously measures multiple variables (eg, proteins, metabolic factors, and viral and host transcripts).
Omics studies require computational approaches that assess correlations between different measurements. The computational methods for this type of data are frequently network-based and take into account known interactions (eg, protein-protein) or predicted interactions (ie, correlations) between biological variables.
However, one limitation of this analysis is that it cannot readily assess the dynamic feedback of variables (eg, non-linearities like saturating effects), which often occur on distinct time scales. In contrast, mathematical descriptions of infection processes quantitate the intricate host-pathogen feedbacks and link causation and correlation. Kinetic models determine the time scales of various mechanisms, the rate, magnitude, and effectiveness of immune responses, and whether bifurcating behavior is possible. As more omics data become available, it will be valuable to relate this information to the network analyses because each approach may have related and distinct conclusions. For instance, an omics study that profiled gene expression patterns during influenza-pneumococcal coinfection found that lethality is correlated with an early increase in bacterial replication. 123 Interestingly, the kinetic studies described above made the same conclusion but also identified the regulatory mechanism that governs this behavior. 41,44 Likewise, the omics study identified a defect in lung repair mechanisms, 123 which the model did not address. Making these types of connections could be significant, particularly because tissue level changes are correlated with disease outcome.

| MODELING THE P OTENTIAL FOR UNIVER SAL VACCINE S
Preventing influenza virus infections through vaccination is ideal.
However, vaccines often lack efficacy because the virus mutates rapidly and novel viruses emerge through recombination. In addition, initiating a robust and long-lasting response to the vaccine is challenging. Even when immunity is generated by a natural infection, long-term protection may not be guaranteed. 138 Furthermore, some evidence from mathematical and experimental studies suggests that viral epitopes may be masked from recognition by B cells, 29,30 which inhibits the generation of new antibodies during subsequent vaccinations or infections. The model and data were in agreement that the fold increase in antibody titer from baseline declines with repeated vaccination. This was due to an antigen dose threshold that depends on the level of pre-existing antibodies and dictates the level of antibody boosting that can be attained. Sufficiently high antigen doses may be able to reduce the masking of antibodies. 30 However, this could be difficult and may complicate protection by a universal vaccine, which aims to broadly protect against infection with any influenza virus subtype.

| ANTIVIR AL THER APY: THE C A S E FOR IMMUNOMODUL ATORY DRUG S
Without effective vaccines, antivirals remain the primary measure for combatting influenza virus infections. The two major antivirals used to treat influenza are M2 inhibitors (M2Is) and NA inhibitors (NAIs). 66 While M2Is disrupt ion-channel activity of the M2 protein to limit virion uncoating inside the cell, 139,140 NAIs limit virus spread within the lung by preventing virions from being cleaved from infected cells and infecting new host cells. 139 This reduces symptoms and slows disease progression, but does not significantly reduce the viral burden. 140 Antiviral efficacy is greatest when the drug is administered prophylactically or within the first 24-48 hours of symptom onset. 141 Prophylaxis with NAIs has the most profound effect with a 2.5-3.0 log 10 reduction in viral loads. 66,139,142 As discussed above, model analysis of viral kinetic models revealed that this is because the processes that the drugs target (ie, the viral life cycle) dominate only in the early stages of infection. 65 Reduced efficacy and less than 1 log 10 lower viral load are achieved if the drug is given in latter stages of infection (>3 days pi) 143 when viral load kinetics are influenced predominantly by clearance mechanisms (eg, infected cell clearance (δ) and, to a lesser extent, virus clearance (c)). 65 Estimates of antiviral efficacy can be obtained from simulating the model and altering the rate of virus production, p(1 − V ), where V is the efficacy of the antiviral. 14 Drug effectiveness is equal to 1 when the drug is 100% effective and 0 when the drug is inactive or absent. Model simulations suggest that targeting virus infection (β) would yield similar results as targeting virus production and that increased efficacy would be needed for an antiviral that improves clearance of free virus (c). 36 Unsurprisingly, a therapy designed to improve the timing and/or rate of infected cell clearance (δ) could result in faster resolution. 36

| Detecting off target immune effects
A secondary effect of NAI therapy was detected in one study that assessed viral load kinetics when therapy was initiated either early or late in the infection. 36 An extra term (− T T) in the target cell equation together with the reduction in the rate of virus production (p(1 − v )) was needed in the model to simultaneously capture the data 36 : dT∕dt = − TV − T T, where T is the efficacy of the antiviral in reducing the number of cells susceptible to infection. The requirement of the − T T term in the model suggests that the antiviral limits the number of cells that can be infected. Indeed, this was independently observed in an experiment that assessed the area of the lung infected during therapy. 54 Neither the model nor the viral load data identify the underlying mechanism. Interestingly, the predicted efficiency of this off-target effect was significantly greater than the predicted efficacy of the antiviral inhibiting virus production (70% vs 10%). 36 The lack of reduced viral loads even when fewer cells are infected 36

| Potential adverse consequences of antiviral therapy during virus coinfection
Although antivirals exist for treatment of influenza virus infection, antivirals targeting other coinfecting viruses (eg, RV, RSV, and PIV) have not been approved for use or are currently in development. 144 Given that different virus pairings result in different outcomes (ie, infection enhancement or reduction), use of anti-influenza therapy could result in beneficial or adverse consequences. 42 In the case of IAV-RSV coinfection, where influenza viruses reduce RSV growth, 104

| A role for antivirals and combination therapy in limiting bacterial coinfection
Because antivirals restrict viral growth and influenza disease severity, morbidity and mortality from invading bacterial pathogens can also be reduced. 143 (1 − a ), where a is the efficacy of the therapy). 36 As expected, bacterial burden and pneumonia were reduced. 113 Although antibiotics have diminished efficacy during coinfection, 145 analytical results suggest that combination therapy could increase the chances of successful immunotherapy or antiviral treatment by over 200%. 36 This is because changes in the bacterial growth rate (r) also facilitates different outcomes of influenza-bacterial coinfection. 36 Similar to the degree of aMΦ depletion (̂(V)), the bacterial growth rate (r) is a bifurcation parameter and, thus, a drug target (eg, with protein synthesis inhibitors). 36 However, the efficacy needed to sufficiently reduce bacteria through this class of drugs may be higher than immunomodulatory drugs. 36

| CON CLUD ING REMARK S AND PER S PEC TIVE S
Influenza viruses continue to infect millions each year. Increased severity and case fatality rates due to secondary bacterial pneumonia have been emphasized by studies of the 1918, 1957, 1968, and 2009 influenza pandemics. 107,109,110,146 Influenza viruses that cause severe disease support higher incidence of bacterial coinfection, yet only a proportion of infections result in a coinfection. [94][95][96] Furthermore, other respiratory viruses may also coinfect and enhance influenzarelated disease. 103  nological advances continue to improve data quality and quantity and more data on viral-bacterial and viral-viral coinfections materializes, mathematical analyses like those described here will be critical.

ACK N OWLED G EM ENTS
This work was supported by NIH grant AI125324 .

CO N FLI C T O F I NTE R E S T
The author has no conflict of interest.