Eco-evolutionary dynamics of pathogen immune-escape: deriving a population-level phylodynamic curve

The phylodynamic curve (Grenfell <i>et al</i>. 2004 <i>Science</i> <b>303</b>, 327-332 (doi:10.1126/science.1090727)) conceptualizes how immunity shapes the rate of viral adaptation in a non-monotonic fashion, through its opposing effects on viral abundance and the strength of selection. However, concrete and quantitative model realizations of this influential concept are rare. Here, we present an analytic, stochastic framework in which a population-scale phylodynamic curve emerges dynamically, allowing us to address questions regarding the risk and timing of the emergence of viral immune escape variants. We explore how pathogen- and population-specific parameters such as strength of immunity, transmissibility, seasonality and antigenic constraints affect the emergence risk. For pathogens exhibiting pronounced seasonality, we find that the timing of likely immune-escape variant emergence depends on the level of case importation between regions. Motivated by the COVID-19 pandemic, we probe the likely effects of non-pharmaceutical interventions (NPIs), and the lifting thereof, on the risk of viral escape variant emergence. Looking ahead, the framework has the potential to become a useful tool for probing how natural immunity, as well as choices in vaccine design and distribution and the implementation of NPIs, affect the evolution of common viral pathogens.