A cross-scale model for the evolution of influenza within a single season

Abstract

In this thesis we develop a mathematical cross-scale model for the evolution of influenza within a single season. We model evolution as the emergence and spread of a mutant strain in a population that is already invaded by a parent resident strain. This allows us to investigate both the emergence dynamics of a mutant strain as well as the subsequent competition dynamics between the two strains. Our main research goal is to study the effects of a homologous vaccine against the resident strain on the epidemiological and evolutionary dynamics of the disease. Due to the complexity of cross-scale models, we first develop a simpler population-level SIR-type model for the evolution of influenza. Assuming an outbreak that is initiated by a single resident strain, we study the significance of the mutant’s emergence time by introducing it in the population at different times. We then also derive a probability density function for the emergence of the mutant in the population. Finally we incorporate vaccination to our model, and arrive at the conclusion that intermediate levels of vaccine- induced immuno-protection are the most beneficial for the emergence and spread of the mutant strain. We then start building towards a cross-scale model by developing a dynamical within-host model for the evolution of influenza. Our goal is for emergence to be a stochastic event, so we derive a probability density for the within-host emergence of a mutant strain. We also incorporate vaccination to our model and assess its impact on the viral loads of the two strains. Having analyzed our within-host model, we then couple it with a between-host SI model. The links between the two scales are the population-level transmission rates, which we assume are linear functions of the within-host viral load. We first investigate how varying the within-host parameters affects the population-level fitness of the two strains, and then we study our model’s results under different forms of the within-host emergence density. Finally we add vaccination to our cross-scale model, and arrive at the same conclusion that intermediate values of immuno-protection are the most inducive to the emergence and spread of a mutant strain in the population.