Miao2010 - Quantifying the Early Immune Response and Adaptive Immune Response Kinetics in Mice Infected with Influenza A Virus

May 2020, model of the month by Rahuman Sheriff
Original model:  BIOMD0000000546


Epidemic and pandemic viruses pose serious threats to public health across the globe. The most recent SARS-CoV-2, the causative agent of COVID-19 has killed several thousand people in different parts of the world. A quantitative understanding of viral infection and the immune response dynamics that determine the outcome of the infection is essential to develop therapies against novel viruses. Mathematical models are used to investigate viral dynamics and immune responses, as they offset some of the experimental limitations and provide quantitative insight. The rate of HIV production and the in vivo life span of infected cells were derived from mathematical models 1. Miao et al. 2010 2 used an integrative approach where comprehensive experimental data was combined with the mathematical model to investigate influenza A virus (IAV) infection and the immune response within the lung.

Mathematical Model

The authors developed a simplified version of their previous complex differential equation model of IAV infection which involved 15 equations and 48 parameters 3. The simplified model used in Miao et al. 2010 consisted of three species (entities) viz. uninfected and infectible epithelial cells (Ep), infected epithelial cells (Ep*), and infective viral titer (V) (Figure 1). Immune components including CD8+ T-effector cells (TE), IgG (AG), and IgM (AM) antibody are encoded as time-varying parameters in the model. The direct experimental data for these parameters are derived from the mice infected with H3N2 influenza Virus A/X31 strain. The experiments involved data sampling at high frequency (every 12 to 24 h) in about 340 animals with several replicates at each time point.

Figure 1: A schematic representation of the model.  Three species in the model are uninfected and infectible epithelial cells (Ep), infected epithelial cells (Ep*), and infective viral titer (V). Experimentally derived factors include CD8+ T-effector cells (TE), IgG (AG), and IgM (AM) antibody titers.

Miao et al 2010 built two ODE models (Figure 2) referred as Model 1 and Model 2 and used them to analyzed the innate and adaptive immune responses. Model 2 which primarily focuses on innate immune response (preadaptive phase) was used to fit the viral titer data from days 0 to 5 as the adaptive immune response was not traceable during this phase. Model 1 which includes all adaptive immune response components was used to fit the viral titer data from days 5 to 14 (adaptive phase) as well as days 0 to 14 (combined phases). Except, the production rate of infectious virus per epithelial cells, all other parameters in both the models are structurally identifiable. Fixing the value did not change the estimate of other parameter values except for the initial level of Ep. The time course smoothed curves of antigen-specific CD8+ T-cell, IgG, and IgM data are inputted into the models while fitting them to the viral titers.

Figure 2: Model structure. a) Model 1 b) Model 2. For a full definition of the parameter refer to Table 1 in Miao et al. 2010 2

Results and Discussion

By fitting the data from 0 to 5 days to model 2, assuming that the adaptive immune response is negligible during this period, the preadaptive ( innate) immune response kinetic parameters were estimated with statistical significance. Figure 3 (a and b) shows the predicted dynamics of model 2 using estimated parameter values. The model estimated the net growth rate of uninfected epithelial cells and infection rate of epithelial cells as 6.2 x 10-8 / day and 2.4 x 10-6 ml / EID50 / day 
respectively. The estimated death rate of infected epithelial cells is 0.6 / day and the virus particle clearance is 4.2 / day.

Similar estimations of adaptive and overall immune response kinetics were obtained by fitting model 1 to data from day 6 - 15 and days 0 - 15 respectively. The authors also performed a comparative analysis of parameter estimates from innate (model 2), adaptive (model 1), and overall (model 1 fit to data from 0 to 15 days) immune response and looked at the relative contribution of various components against IAV infection. Miao et al. 2010 further developed 10 sub-models with various parameter values and compared them against the full model (model1). This analysis revealed that CD8+ T Lymphocytes and early IgM antibodies predominantly contribute to the clearance of free virus particles and infected epithelial cells.

Figure 3: Predicted dynamics of viral load and innate immune response. a) Simulation of model 2 with the estimated model parameters. b) Simulation of changes in the viral titer for different initial number of infectible epithelial cells (Ep).

During the innate response phase, the viral infection spreads among the infectible epithelial cells and the resulting infected cells convert into viral production source, contributing to the peak viral load. Death can occur even within a few days of moderate viral load and hence it is useful to investigate the effect of infection rate (ßαon mortality. The simulation revealed that the increase in ßα did not increase the magnitude of the peak viral load, but rather shifted the peak earlier. Interestingly, the increase in viral replication rate (παsignificantly increased viral titers. Furthermore, the model simulation also showed that the initial level of infectible epithelial cells (Ep) also significantly contributed to the viral titers (Figure 3c). When the number of Ep cells is low, no viral peak was observed. This prediction is consistent with previous findings that peak viral load depends on the infectible target cells available for infection. These findings suggest that any therapy that impedes the availability of the target cell for viral infection will have a stronger effect.


Miao et al. 2010 built a robust quantitative model for primary influenza A virus infection. The model was complemented with a high frequency sampled data of cytotoxic T lymphocytes, IgG, and IgM as well as viral titers from mice. By fitting the data to the two models, several kinetic parameters of viral infection and the immune response were estimated. The model divulged that the viral replication rate is crucial than the viral infection in determining viral load during primary infection. Virus-specific IgM and CD8+Cytotoxic T lymphocytes are key determinants of viral clearance in the adaptive immune response. The approach used by Miao et al. 2010 to study IAV infection was quite valuable and hence a similar approach could be carried out to investigate SARS-COV-2 infection.



1. Perelson, A., A. Neumann, M. Markowitz, J. Leonard, and D. Ho. 1996. HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time. Science 271:1582–1586 

2. Miao H, Hollenbaugh JA, Zand MS, Holden-Wiltse J, Mosmann TR, Perelson AS, Wu H, Topham DJ 2010 Quantifying the Early Immune Response and Adaptive Immune Response Kinetics in Mice Infected with Influenza A Virus. J. Virol. 84:6687–6698.

3. Lee, H. Y., D. J. Topham, S. Y. Park, J. Hollenbaugh, J. Treanor, T. R. Mosmann, X. Jin, B. M. Ward, H. Miao, J. Holden-Wiltse, A. S. Perelson, M. Zand, and H. Wu. 2009. Simulation and prediction of the adaptive immune response to influenza A virus infection. J. Virol. 83:7151–7165.