Antigenic waves of virus-immune co-evolution

TL;DR

This paper develops a mathematical model describing how viruses and immune systems co-evolve in antigenic space, revealing an antigenic wave driven by cross-reactivity that explains observed viral evolution patterns.

Contribution

It introduces a novel theoretical framework for virus-immune co-evolution, including analytical results on wave dynamics and implications for predictability.

Findings

Antigenic wave shape and speed are analytically characterized.

Co-evolution generates a long-lived wave direction persistence.

Model explains influenza antigenic turnover patterns.

Abstract

The evolution of many microbes and pathogens, including circulating viruses such as seasonal influenza, is driven by immune pressure from the host population. In turn, the immune systems of infected populations get updated, chasing viruses even further away. Quantitatively understanding how these dynamics result in observed patterns of rapid pathogen and immune adaptation is instrumental to epidemiological and evolutionary forecasting. Here we present a mathematical theory of co-evolution between immune systems and viruses in a finite-dimensional antigenic space, which describes the cross-reactivity of viral strains and immune systems primed by previous infections. We show the emergence of an antigenic wave that is pushed forward and canalized by cross-reactivity. We obtain analytical results for shape, speed, and angular diffusion of the wave. In particular, we show that viral-immune co-evolution generates a new emergent timescale, the persistence time of the wave's direction in antigenic space, which can be much longer than the coalescence time of the viral population. We compare these dynamics to the observed antigenic turnover of influenza strains, and we discuss how the dimensionality of antigenic space impacts on the predictability of the evolutionary dynamics. Our results provide a concrete and tractable framework to describe pathogen-host co-evolution.