Mathematical Modeling of Influenza Infection in Humans

Influenza (commonly known as the Flu) is a respiratory infection that results in high annual mortality rates in humans. Globally, 5-10% of adults and 20-30% of children are estimated to be attacked by influenza every year. Therefore, influenza poses a global threat to public health. In order to control infection rates, we need to better understand the defense mechanisms exhibited by the human body during influenza infections. In this thesis, we used within-host mathematical models to probe influenza dynamics by considering both innate (non-specific) and adaptive (specific) immune responses. Natural killer cells, which are immune cells activated within a few hours of influenza infection, are capable of killing virus-infected cells. As a component of the innate immune response, we explicitly modeled a natural killer cell response with minimal model variables and parameters. The effectiveness of natural killer cells in inducing cytotoxicity in virus-infected cells was represented by a rate constant (destruction parameter), while a physiologically valid range for this parameter was estimated by comparing model results to experimental observations. We found that natural killer cells were initially effective in controlling the infection, but were not effective enough to resolve the infection within the known physiology of 6-8 days in this model. Therefore, we incorporated a model of an antibody response as part of the adaptive immune response. Antibodies are capable of binding to virus particles to prevent the invasion of these particles into healthy cells. They also mark the virus particles for removal by other immune cells. Including a simple antibody response to the natural killer cell model resulted in resolution of influenza infection. We further estimated a reasonable range for the antibody activation parameter in humans by comparing three different model outcomes to experimental evidence.