Influenza A virus (IAV) leads to acute respiratory disease and significant morbidity and mortality around the world each year; the World Health Organization estimates three to five million cases of severe illness and 300,000–650,000 deaths worldwide every year are caused by IAV [1
]. Generally, severe outcomes are limited to high-risk patient groups, namely, infants, aged adults, or individuals with compromised immune systems. Occasionally, however, new strains emerge with pandemic potential that can induce severe disease across a broad portion of the population. For example, the 1918 Spanish influenza pandemic is estimated to have been responsible for the death of 2% of the world’s population between 1918 and 1920 [2
]. Several pandemics have occurred since, including outbreaks in 1957, 1968, and 2009 [3
]. Experts believe that avian H5N1 influenza viruses pose the greatest risk to public health. H5N1 infections have demonstrated the ability to cause severe disease in humans, including symptoms such as fever, respiratory symptoms, lymphopenia, and cytokine storm (hypercytokinemia) [5
]. Cytokine storm occurs when the host experiences out-of-control pro-inflammatory responses and insufficient anti-inflammatory responses to infection. This is often a result of severe influenza infection and causes acute respiratory distress syndrome (ARDS) and multiple organ failure in many patients [7
Often, IAV infections are treated with neuraminidase inhibitors, such as oseltamivir (i.e., TamiFlu), which can be highly effective if administered during the early infection phase. However, IAV-infected hosts often do not seek treatment until late in their infection when the virus is already present at high levels and it may be too late for an effective treatment. Especially in the case of H5N1, neuraminidase inhibitors are often ineffective at containing cytokine storm and do not prevent the excess morbidity and mortality seen in these infections [8
]. Moreover, oseltamivir-resistant strains can quickly evolve, as observed during the 2009 H1N1 pandemic [8
1.1. Immune Modulation for the Treatment of IAV Infection
Modulating the immune response post infection to control inflammation or pre-infection to provide increased protection for high risk groups has been a major theme in severe influenza infection research [10
]. Corticosteroids have been suggested as a potential treatment option for patients undergoing severe IAV infection with accompanied cytokine storm [21
], while pre-stimulating interferon-associated pathways have been suggested to protect high-risk groups [7
Interferon (IFN) is a key regulator of the innate immune system, and pre-stimulation of interferon regulating pathways has provided a preventative advantage in mice infected with deadly influenza viruses [26
]. IFN is essential for viral clearance, has been heavily studied since its discovery in 1957 [29
], and has a complicated role in immunopathology (See [30
] for a review). In recent mouse studies, animals, prior to infection, were exposed to synthetic or natural agonists of the Toll-Like Receptor pathways (specifically TLR3 and TLR4) that activate IFN production [27
]. This pre-stimulation induced higher concentrations of IFN in lung epithelial cells, reduced virus titers and significantly improved infection outcomes in animals infected with highly pathogenic viruses. Interestingly, some studies have shown that select bacterial strains in yogurt provide protection against influenza infection by increasing IFN production [33
]. The suggested mechanism is that exopolysaccharides produced by the bacteria exert immunostimulatory effects via the TLR pathways. These evidences combined with the several studies demonstrating dysregulation of the immune response during deadly influenza infections [13
] suggests that immunomodulation prior to infection may be an option for protecting high risk groups. Moreover, as IFN is a common component of mathematical models of influenza-induced immune responses, the ability to replicate the effects of pre-stimulating IFN-regulating pathways provides a valuable measure of model applicability.
1.2. Mathematical Models of the Lung Host Response to IAV Infection
Mathematical models of the immune response in IAV-infected lungs have previously been used as a computational platform for treatment optimization [37
]. Modeling can be an invaluable tool for ascertaining kinetic parameters of an influenza infection which are difficult to measure in traditional experiments. Many experimental data sources, particularly murine (mouse) models of influenza, are generated from a pool of measures collected from hosts subjected to identical experimental conditions. Multiple hosts are sacrificed at pre-determined intervals and measured for variables of interest. Because these animals need to be sacrificed to measure cell and cytokine levels, hosts cannot be tracked for the full duration of the infection, making true longitudinal data impossible to obtain. These experiments assume that the all animals will react nearly identically to the infection, but inter-individual variability in hosts can invalidate this assumption. Mathematical modeling can be used to help fill in gaps in knowledge created by the deficiencies in experimental data. Models can vary substantially in complexity, depending on the facets of the immune response they contain and the number of interactions represented.
Models generally fall into one of two categories: target cell-limited models, in which the healthy epithelial cells, which act as a target for the virus, are unable to replicate themselves [38
], or models in which healthy cells are able to regenerate [37
]. These models all feature three basic components: healthy epithelial cells, infected epithelial cells, and the virus. More components, such as cytokines, immune cells, or antibodies, can be added to the model with additional equations and parameters. Larger models can provide a more comprehensive understanding of the immune response but may also require a larger pool of data from which to calibrate the model. Smaller models do not need as much data for training the model, but they may also make more simplifying assumptions that can be difficult to support biologically.
In this work, we review three recently published models that contain similar components of the immune response. We consider two points of comparison. The “systems” perspective being which components of the model most strongly regulate virus replication. And the “treatment” perspective being how well do the models recapitulate the observations in IAV-infected animals whose immune system has been stimulated prior to infection. Pre-stimulation is simulated by increased concentration of IFN prior to infection. We find that virus concentration is largely influenced by the proportion of cells in the model that can become infected or virus-resistant; therefore, controlling these populations is paramount to controlling viral replication. We also find that current models do not capture the effect of increased IFN concentrations on suppressing virus replication.
2. Description of IAV Immune Response Models
To provide a review of current models of IAV-induced immune responses, we selected recent models which contain common elements of the innate immune response. This allowed for easier comparisons between model analyses. The models analyzed are as follows: Saenz et al., 2010 [38
], Pawelek et al., 2012 [37
], and Hancioglu et al., 2007 [39
]. Figure 1
depicts the interactions represented within each of the models. The Saenz and Pawelek models are trained to experimental data (e.g., cytokine concentrations and immune cell counts) measured in pony lungs infected with H3N8 virus, while the Hancioglu model was fit to certain qualitative behaviors selected from a study of the human response to IAV infection by Bocharov and Romanyukha [44
Five elements of the intrahost immune response are conserved across each model: healthy epithelial cells (H), infected cells (I), virus (V), type I interferon (F), and “resistant cells”, that is, epithelial cells with interferon-induced virus resistance (R). While each model has these five features in common, the inflammatory response to viral infection is represented differently, depending largely on model complexity. These differences are particularly apparent in the model-specific incorporation of the production, activity, and depletion of IFN. In the Pawelek model (Figure 1
a), interferon has two functions: creating virus-resistant cells when interacting with healthy epithelial cells, and increasing infected cell death when interacting with infected epithelial cells. In the Saenz model (Figure 1
b), interferon leads to the creation of virus-resistant cells but does not impact the infected cells directly. Instead, the infected cells produce more interferon. The Hancioglu model (Figure 1
c) uses interferon to create resistant cells (as in the other two models) while interferon is produced by infected cells and antigen-presenting cells. In all models, a decrease in interferon levels is caused by a combination of natural decay and absorption into epithelial cells.
3. Materials and Methods
Three ordinary differential equation (ODE) models of the intrahost immune response to IAV infection that explicitly included type I interferon were chosen from literature. These three published models were selected for their significant variance in complexity; specifically, in the interactions of IFN with other model components. For each model, the immune response is simulated in MATLAB (version R2017a, Natick, MA, USA) using the parameter values and initial conditions published in the original papers. Integration was performed with ode23s.
We performed two main assessments on the three featured models: a local sensitivity analysis and an interferon pre-stimulation study. Sensitivity analysis was performed using a MATLAB package previously published by Nagaraja et al. [45
]. The Param_var_local.m function performed a local sensitivity analysis on the virus equation in each model to all parameters over a ten-day simulation. The function increases and decreases each parameter in the model by 1% and recalculates the solution to the system of ODEs. Sensitivity is then calculated with the central finite difference formula to generate logarithmic sensitivities of each equation to each parameter in the model. The sensitivity of each parameter was ranked by the area under the curve (AUC). Parameters which yield the highest AUC over the full ten-day simulation are judged to be the most sensitive.
Two tests were used to evaluate each model’s reaction to simulated interferon pre-stimulation. First, four values of the initial level of the IFN present in the system (F0) were tested to assess whether increased initial IFN levels will inhibit viral growth, peak, or clearance. In each case, while the initial condition on the IFN equation changed, all other initial conditions and parameters remain constant. Additionally, the amount of time between the initial IFN induction and the start of the infection was varied by delaying the onset of the virus infection with respect to the IFN. In all cases, induction of IFN via IFN-regulating pathways is modeled as a step change in IFN concentration. The 6 possible delays in the virus administration included 0, 2, 4, 6, 8, and 10 days (equivalent to pre-stimulating IFN 0, 2, 4, 6, 8, and 10 days prior to infection). The initial level of IFN is kept at 1 in these simulations, though the published initial condition of the fold change of IFN in the Saenz model is 0. To simulate a true pre-stimulation, there must be a nonzero initial level of IFN to observe the impact of IFN on the remainder of the system.
Interferon is known to have several antiviral effects in an IAV-infected host, including activating an antiviral state in epithelial cells, sensitizing cells to apoptosis, activating NK cells, and initiating the differentiation of cytotoxic T cells [50
]. Each analyzed model represents a distinct subset of these interactions, including the creation and depletion of virus-resistant cells. In the Pawelek model, IFN is only produced by infected cells, and healthy cells can become resistant through an interaction with IFN. This resistance fades over time and cells return to a susceptible state. Resistant cells in the Hancioglu model also become susceptible, but IFN can be produced by either infected cells or antigen presenting cells. Conversely, the Saenz model features epithelial cells that are either partially or fully resistant to infection, and cells do not lose resistance over time.
Each of the three models shows a sensitivity of the virus to the creation and loss of infected epithelial cells. The virus equation of the Pawelek model is most sensitive to the loss of resistance in epithelial cells and the death rate of infected cells. If the infected cells die off too quickly, the virus cannot replicate at a rate high enough to sustain the infection. Similarly, if cells are becoming virus-resistant too quickly, there will not be a sufficient number of cells remaining to become infected and keep the viral titers elevated. In this way, the presence of the virus in the system is predominantly driven by the number of cells currently infected or able to become infected. The Saenz model also emphasizes a low death rate of infected cells, as well as a short eclipse phase for infected cells. The duration of the eclipse phase determines the delay in time between the infection of the cell and the subsequent release of virion by the infected cell. The shorter the eclipse phase, the more readily the cells can begin producing virus. As in the Pawelek model, the Saenz model shows that the availability of productively infected cells is vital to the continuation of the infection.
The Hancioglu model also emphasizes the importance of maintaining a large pool of infected cells, but through a different set of parameters than the Pawelek or Saenz models. The infectivity of the virus and the replication rate of the virus are the most sensitive parameters in the model. The Hancioglu model is thus controlling the virus by a high rate of production of infected cells, and not through a diminished rate of decay of these cells, as in the other two models. Interestingly, none of the three models shows a strong sensitivity of virus to the concentration of IFN in the system.
All models must make some simplifying assumptions, and thus, no models are fully accurate in their representation of the host response to pre-stimulating IFN-regulating pathways. While these models had been analyzed in previous reviews [54
], previous work had only shown how these models respond to knockouts of various immune components. Here, we perform a complementary study to test early stimulation as well as increased initial levels of IFN to determine if altering IFN levels can improve patient outcomes. Of the three models studied, only one showed significant impact after early IFN induction. The Saenz model predicts a lower viral peak with increased initial interferon levels and a monotonic decay of the virus over time if interferon is stimulated early. Early available interferon creates a large pool of resistant cells in a short period of time and, because the Saenz model does not allow for loss of resistance in cells over time, resistant cells remain resistant for the rest of the simulation. Thus, the system cannot replenish the source of target cells for the virus to infect and the virus concentration decreases steadily. However, this is not a realistic way to represent immune dynamics, as epithelial cells certainly lose their viral resistance over time.
The other two models do not demonstrate this effect of IFN on viral clearance. The Pawelek model is structured such that early administration of interferon-inducing compounds worsens the impact of the virus by creating a secondary rebound of virus in later stages of infection, essentially leading to chronic infection (which is unlikely to be realistic). The Hancioglu model shows no sensitivity to the initial interferon concentration or to the relative timing of infection. Changing the time of the virus infection simply shifts the curves in time but does not change their shape. This model implies that interferon has minimal impact on the host, which does not agree with decades of experimental evidence [29
By stimulating an early IFN response in the model, we simulate a host receiving a preventative treatment for IAV infection (e.g., a TLR agonist [27
]). Dobrovolny et al. [54
] previously investigated how these models react to IFN suppression post-infection, which may suffice to simulate a steroid treatment for influenza as steroids are known to downregulate IFN signaling [20
]. The Hancioglu and Pawelek models predict that IFN has a significant impact on viral clearance when completely removed from the system because no resistant cells are created and the population of susceptible cells remains high for a longer period of time [54
]. In the Saenz model, however, removing IFN does not yield this effect, as cells in this model cannot lose resistance. Therefore, these models may not accurately represent the effect of IFN pre-stimulation for influenza, as they make many simplifying assumptions about the role of IFN in the host immune response to IAV infection.
Currently, we do not have sufficient experimental or computational evidence to support a recommendation for IFN pre-stimulation or corticosteroid treatment post-infection. Few references exist showing steroid treatment of IAV-infected humans [6
], and those few have not shown significant impacts on mortality rate [60
]. For many years, physicians turned toward high doses of steroids, though recent research suggests that lower doses are more effective [60
]. It is quite possible that steroid treatment could be effective in humans, but the timing and magnitude of the drug has not yet been optimized. Tan et al. [47
] have shown Pam2Cys, a TLR-2 agonist, can instigate an inflammatory response even in the absence of an antigen. Mice pre-treated with Pam2Cys were protected from the H1N1 virus for up to seven days post-treatment. Pre-stimulation of TLR-3 by polyinosinic:polycytidylic acid (poly IC) has also shown promise in protecting mice against H5N1 and H3N2 [48
]. TLR-3 pre-stimulation has been effective in protecting rhesus monkeys from yellow fever [62
]. While IFN-prestimulating compounds have been very promising in animal models, they are still in the early phases of drug development [46
]. Nonetheless, the effects of IFN pre-stimulation has been well established and the dynamics induced by pre-stimulation are highly valuable for mathematical model discrimination.
While the models presented do capture many aspects of the immune response to IAV infection, more experimental data is needed to improve the characterization of IFN-regulated immune dynamics. Shinya et al. [26
] demonstrated the IFN pre-stimulation from 12 h to three days pre-infection improved survival to IAV-infected mice, but a more thorough dosing range and high temporal resolution of the data are needed to improve model development and validation.
This review has shown that simply creating a population of virus-resistant cells is not sufficient to model the impact of IFN on control of virus replication. This is the mechanism by which many current published models, including the three covered in this paper, incorporate the effect of IFN on the immune response. For a truly accurate mathematical model, the model structure should be able to simulate known qualitative behaviors as well as reproduce the quantitative data used to tune the model parameters. The models used in this review do not include a mechanism by which IFN levels can be sustained if the virus is not present in the system (see Figure 5
b, Figure 6
b and Figure 7
b). The pre-stimulation is thus ineffective because IFN decays monotonically until the virus is administered days later. Additional cellular sources of IFN production, such as monocytes, may be necessary for a biologically accurate ODE model. The Hancioglu model does include a term for macrophage-derived IFN production, but macrophages are only induced to produce IFN if the virus has been introduced to the system, so this model cannot sustain increased IFN concentration in the absence of pathogen. The Pawelek and Saenz models only contain infected epithelial cell production of IFN.
Future ODE models of influenza infection should include a better representation of innate immunity, and possibly more interactions of IFN with other components in the model, to accurately portray the impact of IFN on the system as a whole. Rather than reliance on the creation of virus-resistant cells to simulate the effect of IFN on the host, IFN could be used to directly diminish the replication rate of the virus, similar to a model proposed by Baccam et al. [40
]. Alternatively, IFN could be used to lower the infectivity of the virus and slow the creation of infected epithelial cells. These models could then be used to test the protection conferred by IFN pre-stimulation seen in many murine models of influenza A virus infection [26