Electronic Thesis and Dissertation Repository


Master of Science


Applied Mathematics


Linda Wahl


A deterministic model is developed of the within-host dynamics of a budding virus, and coupled with a detailed life-history model using a branching process approach to follow the fate of de novo beneficial mutations affecting five life-history traits: clearance, attachment, eclipse, budding, and cell death. Although the model can be generalized for any given budding virus, our work was done with a major emphasis on the early stages of infection with influenza A virus in human populations. The branching process was then interleaved with a stochastic process describing the disease transmission of this virus. These techniques allowed us to predict that mutations affecting clearance and cell death rate, two adaptive changes in influenza A's life-history traits, are most likely to persist for small selective advantage (s<0.08) when rare. These results also show that the overall adaptability of the virus is much higher than classically predicted, and that the period of growth between bottlenecks has a greater impact on increasing survival probability relative to the impact of bottlenecks, which is consistent with previous work.