Multicompartment modeling of influenza A replication along the murine respiratory tract

Influenza A virus spreads through the respiratory tract in a compartment-specific manner, yet the mechanisms governing its progression remain unclear. Here, we investigated how viral replication and inter-compartment transport shape infection dynamics across the nose, trachea, and lungs. To address this, we developed a multicompartment mathematical model based on a target-cell framework and fitted it to reported viral-load data from mice infected with the Udorn H3N2 strain, using bootstrap estimation to quantify uncertainty. The best-performing model revealed rapid amplification and substantial target-cell depletion in the nose, limited replication, and delayed viral dynamics in the lungs, mainly driven by input from upstream compartments. Transport parameters exceeded local replication rates in deeper regions, indicating that the nose serves as the primary site of viral replication and seeding. Overall, this study highlights the dominant role of the nasal compartment in driving within-host influenza progression.

Influenza A virus (IAV) is a major cause of seasonal influenza outbreaks and occasional pandemics, resulting in up to 650,000 deaths worldwide each year and more than 25,000 deaths in the United States (1, 2). In the US alone, direct medical costs are estimated to exceed $3 billion annually (3). This underscores the need to better understand, predict and manage the impact of influenza.

At the individual level, understanding the mechanisms of IAV infection is essential for identifying the drivers of disease severity and informing treatment strategies. The standard pattern of within-host IAV infection in adults is characterized by a rapid viral replication that peaks within 1–3 days post-infection (DPI), followed by an exponential decrease until it is undetectable after 6–8 DPI (4). However, the within-host course can be influenced by factors such as viral strain (5), host age (6), immune status (7), and presence of comorbidities (8). Although influenza primarily targets the respiratory tract, it can primarily affect either the upper respiratory tract (URT) or lower one (LRT) and, in some cases, extend to multiple organs and tissues (5, 9). The temporal and spatial dynamics of viral replication, immune response, and organ-specific dissemination are critical not only for understanding disease progression but also for identifying windows for therapeutic intervention.

Experimental studies with animals have provided valuable insights into the spatio-temporal dynamics of influenza virus infection. While ferret models have been used to track infection at multiple time points (10–12), many lack detailed pathological or virological assessments throughout the whole respiratory tract. In particular, studies incorporating spatial measurements have shown that seasonal, pandemic and zoonotic influenza viruses exhibit different patterns of spread and progression within both respiratory and extra-respiratory tissues (5). The factors influencing viral progression from the upper respiratory tract (URT) to the lower respiratory tract (LRT) have been studied, showing that a salivary inhibitor can effectively neutralize specific influenza virus strains in the URT (13). This blocks the spread of the virus to the trachea and lungs, preventing severe disease and death. These findings highlight the importance of understanding the mechanisms that govern viral dissemination between different organs. Modeling these dynamics remains a challenge, often reflected in the limited data available and the reliance on non-human models.

Mathematical models are valuable tools for improving our understanding of influenza A virus infection dynamics (14–18). Additional models have been developed to incorporate the innate immune response, the adaptive immune response, or both, to better capture the host’s defense against influenza A (19–24). Many existing models successfully reproduce the overall rise and decline of viral load, yet they often struggle to capture more complex features such as bimodal viral peaks (15, 21, 22, 25) or biphasic decay (23). While modeling lung infection is essential for understanding tissue damage and disease severity, capturing the dynamics across different regions of the respiratory tract is crucial for explaining the full progression of infection.

A commonly adopted approach is to distinguish between the URT and LRT, as these regions exhibit distinct viral and cellular dynamics that together shape the course of disease. Several studies have demonstrated the value of this compartmental perspective in explaining prolonged viral persistence in the nose relative to the lungs during a SARS-CoV-2 infection (26), as well as differential responses to treatment (27). More detailed spatial models, such as those based on partial differential equations (28) or agent-based (29) frameworks, can provide an even more realistic representation of infection dynamics. However, these approaches are often computationally demanding, parameter-intensive, and tend to focus on qualitative behavior rather than quantitative parameter inference (30). As a result, relatively few modeling studies have explicitly incorporated spatial structure while remaining tractable for quantitative analysis (9, 14, 31).

In this study, we aim to advance understanding of how influenza A virus progresses through the respiratory tract by developing a multicompartment mathematical model that integrates viral replication, target-cell availability, and inter-compartment transport. Using viral-load data from the murine Udorn H3N2 model, we evaluate multiple model formulations, estimate parameters through bootstrap resampling, and report uncertainty. This approach allows us to model the compartment-specific processes governing infection dynamics and to determine how viral migration and local replication jointly shape the spatial progression of disease.

To investigate influenza A virus transmission dynamics across the respiratory tract, we developed four compartmental mathematical models, each describing virus-immune dynamics with varying complexity. All four models were fitted to the experimental viral load data described in the following subsection.

Experimental viral data

The viral load data for the influenza A Udorn strain (A/Udorn/307/72; H3N2) across different regions of the murine respiratory tract were extracted from (13) using the PlotDigitizer web application (32). Influenza A virus was intranasally inoculated into BALB/c mice, without anesthesia, with 10 µ l of 10 4.5 PFU of Udorn virus. Following infection, mice were sacrificed on days 1–8 post-inoculation, and infectious viral titers were measured in the nose, trachea, and lungs via plaque assay. Viral loads were reported as PFU per compartment and presented as the mean and standard deviation at each time point.

Mathematical modeling

The mouse respiratory tract is represented by three compartments, corresponding to the nose, trachea, and lungs, each described by a system of ordinary differential equations (ODEs). Figure 1 presents a schematic overview of a mouse model across the three respiratory compartments, highlighting the components and interactions included within each compartment.

Model 1

The first model, referred to as Model 1, is a target-cell limited model. The system is divided into three compartments representing different anatomical regions of the mouse respiratory system: the nose (i = 1), trachea (i = 2), and lungs (i = 3). Within each compartment, uninfected epithelial cells (U i) can be infected by viral particles (V i) at rate β i, producing infected cells (I i). These infected cells release new virions at rate p i and die at rate δ i. Free viruses are cleared at rate c i. In addition, viral particles can migrate between compartments at rates γ i j, capturing the physical connectivity of the respiratory tract. The resulting model is defined by Equations 1–3:

where Γ is the transition matrix that contains the transfer rates of viral particles between compartments, and is defined by Equation 4.

Model 2

In the second model, the target-cell framework is extended to implicitly include the antiviral effects mediated by type I interferons (IFN-I). In this formulation, infected cells within each compartment stimulate the production of IFN-I, which acts locally on uninfected cells to induce a refractory state, thereby providing resistance to infection. While cells in the refractory state are not explicitly represented as a separate compartment, their effects are incorporated through the transition rate ρ i, which governs the rate at which susceptible (uninfected) cells become refractory as a consequence of interactions with infected cells. The governing equations are represented by Equations 5–7:

Model 3

In the third model, the immune response mediated by IFN-I is represented explicitly as a dynamic compartment. Here, infected cells in each compartment secrete excess of IFN-I cytokines (F i) at rate α i, which decay at rate ϕ i. IFN-I acts on uninfected cells to induce the refractory state, providing temporary resistance to infection. The transition rate ξ i characterizes the rate at which uninfected cells become refractory due to local IFN-I concentrations. The model is given by Equations 8–11:

Model 4

To account for systemic T cell-mediated immunity, we considered a model incorporating a compartment representing the total pool of effector T cells T, which dynamically responds to infection across all organs. The T cell population increases through a basal source term s T = μ T (0), as well as proliferation proportional to the aggregate of infected cells in the nose, trachea, and lungs. This is governed by the parameter r, which represents the per-infected-cell expansion rate. The equation also includes a decay term μ T reflecting natural T cell death or loss of functionality. Additionally, to capture T cell-mediated clearance of infection within each organ, we introduced an extra term to the infected cell equation. Here, k i denotes the rate at which T cells eliminate infected cells in each compartment. The model is given by Equations 12–15:

Parameter assumptions and estimation

The models described above include a large number of parameters, providing substantial flexibility during optimization. To reduce parameter uncertainty and improve model identifiability, several parameters were fixed based on biological reasoning, experimental context and previous reported work (33).

We first established the initial conditions for the key state variables. Because the number of uninfected epithelial cells differs markedly across regions of the respiratory tract, each anatomical compartment was assigned a distinct initial cell population as listed in Table 1. The lungs provide the largest surface area for viral infection (80 cm 2) (34), followed by the nose (300 mm 2) (35), and the trachea (0.2 mm 2) (36) that also contains the fewest epithelial cells (37, 38). These structural differences align with the experimental observations, which show robust viral replication in the nose and lungs but minimal activity in the trachea (39). Assuming a mean apical area of 100 µ m 2 per ciliated epithelial cell (40) and that the nasal cavity and tracheal surfaces are predominantly covered by these cells, this corresponds to approximately 3 × 10 6 cells in the nose and 2 × 10 3 cells in the trachea. Alveolar type I cells have an estimated diameter of 50 µ m (41, 42), and on this basis, a total of 4 × 10 6 cells was used for the lung.

At the onset of infection (day 0), we assumed that the number of infected cells was zero in all compartments, as no viral replication had yet occurred. Based on the experimental inoculation procedure, the administered viral dose was 10 4.5 PFU delivered into the upper respiratory tract (13). However, the actual concentration of virions reaching target cells is unknown, and thus, this initial viral load in the nasal compartment was estimated during model fitting. For the trachea and lungs, the initial viral load was assumed to be negligible on the day of inoculation, consistent with the intranasal delivery route. Some parameter values were fixed, following estimates reported in a previous study (33), to reduce the number of free parameters in the model. The parameter values used for Model 1 are summarized in Table 1, while those corresponding to the other models are provided in the Supplementary Material Tables.

To calibrate the models against the viral load data for the nose, trachea, and lungs reported in (13), we minimized the Logarithmic Residual Sum of Squares (LRSS), defined as Equation 16.

where the outer summation runs over the organs, nose (i = 1), trachea (i = 2), and lungs (i = 3), and the inner summation runs over the experimental time points, with n i denoting the number of data points for each organ. Here, V i k represents the mean experimental viral titer, and V ^ i k denotes the corresponding model prediction at the same time point.

Minimization of the LRSS objective was performed using the Differential Evolution (DE) algorithm (43). The code was implemented in Python, using odeint as the ODE solver and differential_evolution as the optimizer, from SciPy library. The bounds used to estimate the free parameters for Model 1 are provided in Table 1. Note that the parameter search space was defined on a logarithmic scale.

This approach is commonly used for parameter estimation in mathematical models; however, during the search for best-fit parameters, optimization algorithms may explore regions of parameter space that produce non-biological trajectories. Consequently, selecting one parameter set over another should not rely solely on the LRSS value, but also on whether the resulting trajectories are biologically meaningful. Here, we applied an approach developed in previous work (44), which consists of defining time- and state-dependent regions where trajectories are expected to lie based on prior biological knowledge. These regions, referred to as feasible windows, allow us to distinguish biologically plausible trajectories from those that, despite fitting the data numerically, lack biological realism.

In this study, we incorporated feasible windows for viral load in the trachea and lungs, reflecting the experimental observation that viral clearance occurs between days 7 and 9 post-infection. Additional windows were imposed to ensure substantial viral loads between days 2 and 6, defined as values exceeding 10 3 PFU, consistent with observed influenza dynamics in mice (45). For Model 3, we introduced feasible windows for interferon dynamics in the lungs, as IFN levels are expected to peak between days 3 and 7 with approximately 3- to 6-fold increases (45). For Model 4, feasible windows were applied to the T cell compartment, with initial levels set to T (0) = 5 × 10 5 cells and expansion to approximately 2 × 10 6 cells after day 5 (45). This approach allowed us to restrict parameter estimation to biologically plausible regimes. Figure 2 illustrates the feasible windows applied across all model formulations.

Model selection

The models were optimized, and the best one was selected using the corrected Akaike Information Criterion (AICc), a common metric for balancing model fit (through the cost function LRSS) and model complexity (the number m of free parameters). The AICc is defined as Equation 17.

where N = ∑ i n i represents the total number of data points across the three compartments. A lower AICc value indicates a model that better describes the data (46).

Bootstrap-based confidence intervals

To estimate the confidence intervals of the free parameters, a parametric bootstrapping approach was applied (47). For each time point, five synthetic samples were generated from a normal distribution defined by the mean and standard deviation of the experimental data. The choice of five samples reflects the original experimental design, in which each group consisted of five mice (13). A total of 1000 bootstrap simulations were performed, each using a different random realization of the synthetic data. For each simulation, the model was fitted and the optimal parameters were recorded. The confidence intervals for the parameters were then derived from the resulting parameter distributions.

Here we present the outcomes of our model-fitting and model-selection analyses, evaluating how well each of our four candidate models reproduces the observed viral dynamics across the respiratory compartments. Each model was fitted using several parameterization strategies to the mean viral loads measured in the nose, trachea, and lungs of mice, as reported in (13). We then evaluated model performance using the corrected Akaike Information Criterion (AICc) criterion via Equation 17 and selected the best-fitting model for further analysis.

In principle, each compartment could be fitted independently with compartment-specific parameters (e.g., distinct δ i). However, this approach substantially increases the number of free parameters. To reduce model complexity, we fixed a subset of parameters to values reported previously (33) and assumed them to be shared across compartments (e.g., δ i = δ). This approach produced good fits for most parameters; however, the infection rate β i required compartment-specific values and proved essential for accurately reproducing the observed viral-load data. In addition, transport parameters in the matrix Γ were always estimated freely, as we were particularly interested in understanding how viral migration between compartments influences local infection dynamics. After reducing the number of free parameters as much as possible, we compared model performance across formulations. The simulated trajectories obtained with the best-fitting parameter sets are shown in Figure 2, and the corresponding parameter values are reported in Supplementary Table S1-S4 in the Supplementary Material.

We compared the four model formulations, starting from a baseline target-cell framework (M1), extending to implicit (M2) and explicit (M3) representations of interferon-mediated antiviral protection, and finally incorporating cytotoxic T cell–mediated clearance of infected cells (M4). M1, M2, and M3 produced broadly similar viral-load and cellular dynamics, with the main difference observed in the trachea, where M1 predicted a substantially higher infected cells. M4 provided a closer fit to the experimental data, most notably reproducing a secondary viral peak in the nose that is also present in the measurements. This rebound coincided with a delayed viral peak in the lungs, suggesting that enhanced replication in the lower respiratory tract could subsequently reseed the upper compartment. Consistent with this behavior, M4 predicted a larger and temporally shifted population of infected cells in the lungs.

Among all formulations, M1 achieved the lowest AICc (Table 2) and was therefore selected as the best-fitting model. Although M4 attained a lower LRSS, the smaller number of free parameters in M1 made it the more parsimonious choice. The remaining models exhibited higher AICc values but were nevertheless able to reproduce the viral-load data reasonably well.

Figure 3 summarizes the within-host viral dynamics predicted by M1 across the nose, trachea, and lungs. Each column corresponds to a different anatomical site, enabling direct comparison of the model behavior across regions of the respiratory tract. The top panels in Figure 3 show the model-predicted viral load over time (solid purple line) along with the 95% confidence interval derived from the bootstrap samples (purple shaded region). Across all three organs, the model reproduces the viral kinetics, and the relatively narrow bootstrap intervals indicate that the inferred parameters yield stable and consistent predictions. In the nose, viral load increases rapidly, reaching a peak around 2–3 days post-infection before declining. The confidence interval reveals that some bootstrap trajectories shift the peak slightly earlier than the median prediction. In the trachea, the overall pattern is similar but exhibits slightly lower peak viral loads. In the lungs, viral growth is modestly delayed relative to the upper respiratory tract, and the bootstrap envelope is noticeably wider, reflecting greater variability in both the timing and magnitude of the peak. This suggests increased parameter uncertainty for this compartment. Nonetheless, the model adequately captures the approximate peak timing and amplitude of the experimental data, which themselves display greater variability in the lungs.

The bottom panels in Figure 3 show the predicted trajectories of uninfected target cells U (dashed orange line) and infected cells I (solid red line), each accompanied by 95% bootstrap confidence intervals. In all compartments, the number of infected cells rises sharply during the first 3 days, paralleling the exponential increase in viral load, and subsequently declines as target cells are depleted or infection is cleared. The peak number of infected cells is highest in the nose, followed by the lungs, and lowest in the trachea; however, the trachea and lungs span similar orders of magnitude in infected cell counts (∼ 3). The nose also shows the most pronounced depletion of target cells U, dropping several orders of magnitude at peak infection. In the trachea and lungs, the decline is less severe with broad confidence intervals reflecting variability across bootstrap realizations. Uncertainty in both U and I typically increases around the time of peak infection.

To further investigate the mechanisms underlying the observed viral and cellular dynamics, we examined the distribution of the model parameters obtained from the bootstrap procedure. Figure 4A presents these parameter distributions as violin plots on a logarithmic scale, highlighting both the variability and central tendency of each parameter in M1. The inner box-plot denotes the median and the interquartile range. This visualization helps identify which parameters are tightly constrained by the data and which display broader uncertainty, thereby clarifying the relative influence of each parameter in shaping the infection dynamics across compartments. The corresponding median parameter estimates and their 95% confidence intervals are summarized in Table 1, consistent with the distributions shown in the violin plots. The brown dashed lines denote the search bounds for each parameter.

For V 1 (0), the distribution is relatively tight compared to the some other parameters, indicating that the initial viral inoculum in the nose is strongly constrained by the early viral-load measurements. The median value is approximately 10 2 PFU, consistent with typical inoculum levels.

Regarding the infection rates, β 1 (nose) shows a very narrow distribution, indicating that the infection process in the nose is well constrained by the data. In contrast, β 2 (trachea) displays a broader distribution, reflecting greater uncertainty in the infection dynamics of this compartment. β 3 (lungs) exhibits a moderately wide and slightly right-skewed distribution, consistent with the greater variability and the wider confidence intervals observed in the lung viral-load predictions.

The virus transport parameters given by the matrix Γ govern the movement of the virus between compartments. Among these, γ 12 exhibits a sharply concentrated distribution, suggesting that downward transport from the nose to the trachea is strongly constrained by the data. In contrast, γ 21 shows a much broader distribution, indicating weaker identifiability of upward transport. The parameters γ 23 and γ 32, which describe movement between the trachea and lungs, display substantial variability as well, with γ 32 being the broader. This wide dispersion reflects the limited information available in the data to precisely estimate inter-compartment transport involving the trachea, consistent with the higher uncertainty observed in its viral-load dynamics.

Taken together, the violin plots reveal a clear pattern of identifiability across compartments. The violin plots highlight that parameters associated with the nose compartment are highly identifiable, while those related to the lungs show moderate identifiability. By contrast, the parameters governing the trachea are poorly identifiable, indicating that the model remains flexible in these dimensions due to the weaker constraints imposed by the tracheal data.

Figure 4B displays the Pearson correlation coefficients among parameters estimated from the bootstrap fits. This matrix reveals linear dependencies between parameters and helps identify compensatory relationships within Model 1. Several parameter pairs exhibit values near zero, indicating weak or no linear relationship, for example, β 1 or β 2 with most other parameters. These near-zero correlations imply that changes in one parameter do not require proportional linear adjustments in another to maintain a good fit, suggesting independent identifiability of these parameter pairs.

Building on these observations, several parameter pairs exhibit moderate to strong positive Pearson correlations, indicating that they tend to increase or decrease together in a linear fashion. Notably, β 3 shows strong positive correlations with both γ 21 and γ 32. These relationships imply that the model can reproduce the observed lung viral-load dynamics through changes in the local infection rate and the transport parameters. This pattern reflects a trade-off in parameter estimation: the available data do not allow replication and transport rates to be uniquely distinguished.

Conversely, strong negative Pearson correlations reveal linear trade-offs. The correlation between γ 12 and V 1 (0) indicates that when downward transport from the nose to the trachea increases, the model compensates by lowering the initial inoculum or the infection rate in the nose. The very strong negative correlation between β 3 and γ 12 or γ 23 further suggests a direct linear trade-off: increased downward transport reduces the need for a high infection rate in the lungs, since more virus reaches this compartment earlier.

In this study, we developed a multicompartment mathematical model to investigate the progression of influenza A virus infection across the mice respiratory tract. The model extends a target-cell framework by incorporating key antiviral immune components, including interferon-mediated protection and cytotoxic T cell responses. Using viral-load data from the nose, trachea, and lungs (13), we evaluated several model formulations and identified the most parsimonious structure capable of capturing the organ-specific viral kinetics. Bootstrap-based parameter estimation enabled us to quantify uncertainty and reveal compensatory relationships governing replication and viral transport. Together, these analyses provide a mechanistic understanding of infection spread along the respiratory tract and clarify which biological processes are well constrained, or poorly informed, by the available data.

Although Models M1–M4 were formulated to represent immune responses at increasing levels of detail, Model 1 was selected as the best-performing formulation based on the AICc. Nonetheless, the remaining models were also able to reproduce the viral-load data reasonably well. Notably, Model 4 achieved the lowest cost function (Table 2), indicating a strong fit despite its greater complexity. While viral-load dynamics are broadly similar across models, important differences emerge in Model 4, which predicts a substantially higher number of infected cells in the lungs and a secondary viral rebound in the nose.

The model trajectories in Figure 3 reveal distinct compartment-specific infection patterns that cannot be inferred from viral-load data alone. In the nose, the rapid rise and early peak of viral load coincide with substantial target-cell depletion, and the narrow confidence intervals reflect strong constraints from the data. The trachea reaches a slightly higher viral peak than the lungs despite having fewer target cells and correspondingly fewer infected cells; this suggests that much of the virus detected in the trachea is transported from adjacent compartments rather than produced locally, consistent with its role as an intermediate bridge between the upper and lower respiratory tract (39). In the lungs, viral expansion is delayed and accompanied by modest target-cell loss, with broad confidence intervals indicating greater uncertainty in the underlying dynamics. Notably, the model predicts a markedly higher number of infected cells in the nose compared to the other compartments, implying that a substantial fraction of the total virus in the respiratory tract is generated in the upper region.

The parameter distributions and correlations in Figure 4 reveal that the infection rate β 2 associated with the trachea is poorly identifiable and uncorrelated with other parameters, indicating that the model can fit the data regardless of whether this value is high or low. In contrast, strong correlations appear among the replication rates and transition parameters linking the nose and lungs, showing that viral dynamics in these compartments are tightly coupled. The estimated viral transport rates from nose to trachea (γ 12) and from trachea to lungs (γ 23) are substantially higher than their reverse pathways. Combined with the result that the replication rate in the nose (β 1) was considerably larger than that in the lungs (β 3), these findings reinforce the idea that the nose serves as the primary site of viral amplification and significantly contributes to seeding infection in downstream compartments, including the lungs.

To further interpret the results described above, we consider the basic reproduction number (R 0,i) for each compartment under the assumption of independent target-cell dynamics, that is, in the absence of viral transport between compartments. In this case, the reproduction number is given by Equation 18.

Under this assumption, only the nasal compartment is capable of sustaining infection (R 0, 1 ≈ 6), whereas infection in the trachea (R 0, 2 ≈ 0) and lungs (R 0, 3 ≈ 0.12) is subcritical and cannot persist without continual viral input from upstream compartments. This result quantitatively supports our conclusion that lung infection relies on viral transport from the upper respiratory tract and reinforces the mechanistic interpretation of the model. This indicates that our model concludes that lung infection depends on viral transport from the upper respiratory tract.

This conclusion aligns with the findings of (13), the source of the viral-load data used in our study. In their experiments, the authors showed that both PR8 and Udorn influenza A strains reached high titers in the nose. However, Udorn replicated more efficiently than PR8 in the trachea and lungs, exhibiting substantially higher titers at later time points. They attributed this difference to salivary inhibition, which neutralizes PR8 but not Udorn. Our modeling results offer a complementary explanation: even if virus reaches the lungs, the local infection rate there is insufficient to sustain viral growth without continued seeding from the nose. Because the PR8 inoculum failed to establish a strong and sustained infection in the nasal compartment, the lungs experienced only transient infection followed by rapid clearance. In contrast, the Udorn strain successfully propagated in the nose, providing a continuous source of virus that could seed downstream compartments and support detectable infection in the lungs.

This analysis also highlights an important, though intuitive, implication. Transmission of influenza relies primarily on direct contact and the shedding of virus from the upper respiratory tract, as previously demonstrated in (48). Because the nose serves as the main route of virus export, from an infected host to the nose of a susceptible individual, successful lung infection is not required for onward transmission. Thus, even if viral replication in the lungs is insufficient to produce symptoms, robust replication in the nose may still permit efficient spread, consistent with the typical scenario of asymptomatic carriers. Consequently, reducing or preventing lung infection alone does not necessarily lower transmission risk, in agreement with the findings of (48). Effective control of respiratory disease spread therefore requires targeting viral replication in the nasal compartment.

The conclusions of this study are constrained by the available viral-load data and therefore carry several limitations. The model relies solely on viral measurements, limiting parameter identifiability, particularly in the trachea, and incorporates simplified immune dynamics without spatial or stochastic effects. These limitations can be addressed in future studies by integrating additional experimental data as they become available.