Modeling dynamics of influenza with antigenic change

Abstract

The main objective of the thesis is to implement a mathematical epidemic model developed by Koelle et al. 2009 and apply it to influenza A virus to simulate the disease dynamics. The influenza A virus is notable for annual epidemics and antigenic drift dynamics, where many closely related strains co-circulate. The model is evolved from a status-based multi-strain model with the innovation of incorporating the method of modeling the emergence event of newly evolved strains. Reactions between the strains in this status-based multi-strains model are modelled by introducing cross-immunity.

The core idea of the model developed by Koelle is to model from the virus's perspective instead of the host's. Instead of simulating a virus's genetic evolution, this model incorporates a way to simulate its antigenic evolution. There are two ways of modeling antigenic changes in Koelle's work, the gradual and the punctuated model, while only the gradual model of antigenic change is applied to the influenza A epidemic in this thesis work. Gradual model consider each amino acid variant to be antigenically unique and the antigenic change occurs gradually. And there are two models of gradual antigenic changes: one-dimensional model and unconstrained infinite-dimensional model.

The simulation results for both models of gradual antigenic changes managed to reproduce some behaviours of influenza's transmission: annual outbreaks, antigenic variant's coexistence, replacement and limited viral diversity. However, they exhibit some notable difference with Koelle's result. The reason might be that there are some hidden or forgotten assumptions not given a full account in the paper by Koelle.