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Modelling the Severity of Influenza

By Jillian Kunze

Influenza A, an RNA infection that affects the respiratory tract, causes more than 20,000 deaths each year in the U.S. alone. It is difficult to treat, as the vaccine does not protect against all strains of the virus and antiviral therapy only works properly if it is begun early in course of the infection. In addition, the symptoms of influenza A do not correspond very strongly with an infected person’s viral load, so it is important to find other methods of predicting how sick a patient will get. During a virtual minisymposium presentation at the 2020 SIAM Conference on the Life Sciences, Amber Smith of the University of Tennessee Health Science Center presented a model that connects viral load, immune response, and influenza severity. Smith and her collaborators aimed to develop their model using physical data so that it could effectively predict how the disease would advance. 

To study the progression of an influenza A infection, Smith’s team injected mice with the disease. Certain differences exist between how mice and humans respond to influenza A. For example, most humans have encountered strains of the flu before, which helps their immune response; mice have not. Mice also experience a larger viral load than humans that exhibits less change over time. Fortunately, it is fairly easy to quantitatively measure flu symptoms in mice, as disease severity is related to the amount of weight they lose while ill. 

Smith and her group measured the viral load in the mice over a period of time, as well as the quantity of CD8+ T cells—a type of cell important for immune defense—operating within their bodies. Based on that data, the team developed its own model of CD8+ T cell activity by building upon a framework of previous models established in the literature, specifically focusing on CD8+ T cell mediated clearance of damaged cells. The researchers employed a standard viral kinetic model to mathematically quantify the dynamic relationship between infected cells and CD8+ T cells. Though this model does not incorporate much actual immunology, it still fit the data fairly well. The agreement was better when the model had a dependence between the density of infected cells and the rate at which they were cleared, thus supporting a suggestion from previous studies that CD8+ T cells must interact multiple times with an infected cell to kill it. Therefore, a small change in CD8+ T cell number can lead to big changes in the number of infected cells and the time it takes to clear the infection. 

Smith and her research team measured the area of damaged cells in mouse lungs as the influenza A infection progressed over time.
To further explore their model’s ability to predict the progression of influenza A, the researchers dissected the lungs of mice that had been infected for differing amounts of time to determine how damage to the lungs had changed. Using histomorphometry, a quantitative measure of a tissue’s shape, Smith and her colleagues found the regions of the lungs that were exhibiting an active infection, an inactive infection (based upon damage to the tissue), or a mix of the two. These factors determined the percent total lesion within the lungs. 

The researchers found that the change in the infected area of the lungs over time matched the cell dynamics that their model predicted. In addition, the disease severity—as measured by weight loss in the mice—possessed similar dynamics to the total lesions in the mouse lungs, such that lung inflammation was nonlinearly related to weight loss. As Smith described in her talk, this nonlinear relation “was a clue that you might be able to predict inflammation without modelling the immune response.” It is difficult to account for all of the immunological factors in an infection but fairly easy to identify the viral load of an infected organism; thus, use of this model could bypass a lot of complicated analysis to extrapolate disease severity. These results could help researchers predict the severity of a patient’s influenza A infection based on easily measured factors, ultimately leading to better treatments. 


   Jillian Kunze is the associate editor of SIAM News.