A two-tiered model for simulating the ecological and evolutionary dynamics of rapidly evolving viruses, with an application to influenza

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Abstract
Understanding the epidemiological and evolutionary dynamics of rapidly evolving pathogens is one of the most challenging problems facing disease ecologists today. To date, many mathematical and individual-based models have provided key insights into the factors that may regulate these dynamics. However, in many of these models, abstractions have been made to the simulated sequences that limit an effective interface with empirical data. This is especially the case for rapidly evolving viruses in which de novo mutations result in antigenically novel variants. With this focus, we present a simple two-tiered ‘phylodynamic’ model whose purpose is to simulate, along with case data, sequence data that will allow for a more quantitative interface with observed sequence data. The model differs from previous approaches in that it separates the simulation of the epidemiological dynamics (tier 1) from the molecular evolution of the virus's dominant antigenic protein (tier 2). This separation of phenotypic dynamics from genetic dynamics results in a modular model that is computationally simpler and allows sequences to be simulated with specifications such as sequence length, nucleotide composition and molecular constraints. To illustrate its use, we apply the model to influenza A (H3N2) dynamics in humans, influenza B dynamics in humans and influenza A (H3N8) dynamics in equine hosts. In all three of these illustrative examples, we show that the model can simulate sequences that are quantitatively similar in pattern to those empirically observed. Future work should focus on statistical estimation of model parameters for these examples as well as the possibility of applying this model, or variants thereof, to other host–virus systems.