Prevalence and the rate of antigenic evolution are jointly determined in an eco-evolutionary SIR model
Abstract
Influenza A persists by continually changing the antigens that its host population recognizes. How fast it evolves and how many hosts it infects are not independent, because the immunity that selects new variants is produced by the infections the pathogen has already caused. We analyze a model of Andreasen et.\ al.\ that captures this eco-evolutionary feedback, and we extend it to the case where infection may kill the host. In the model infected and recovered hosts are distributions over a one-dimensional antigenic space coupled by cross-immunity. The endemic state is a traveling pulse: the infected distribution keeps a fixed shape and advances through antigenic space at constant speed. In the limit of weak antigenic mutation we construct the pulse asymptotically and find that: (i) the speed of antigenic evolution decreases as prevalence rises, (ii) less standing antigenic variation accompanies either faster or slower antigenic evolution, depending on whether pathogens differ in immune evasion or host lifespan (iii) the total number of infected hosts is largest at an intermediate virulence when the host birth rate is sufficiently low.
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BibTeX
@misc{gomez2026prevalence,
title = {{Prevalence and the rate of antigenic evolution are jointly determined in an eco-evolutionary SIR model}},
author = {Daniel Gomez and Joshua B. Plotkin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30515},
eprint = {2609.30515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30515},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prevalence and the rate of antigenic evolution are jointly determined in an eco-evolutionary SIR model
AU - Daniel Gomez
AU - Joshua B. Plotkin
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30515
UR - https://arxiv.org/abs/2609.30515
AB - Influenza A persists by continually changing the antigens that its host population recognizes. How fast it evolves and how many hosts it infects are not independent, because the immunity that selects new variants is produced by the infections the pathogen has already caused. We analyze a model of Andreasen et.\ al.\ that captures this eco-evolutionary feedback, and we extend it to the case where infection may kill the host. In the model infected and recovered hosts are distributions over a one-dimensional antigenic space coupled by cross-immunity. The endemic state is a traveling pulse: the infected distribution keeps a fixed shape and advances through antigenic space at constant speed. In the limit of weak antigenic mutation we construct the pulse asymptotically and find that: (i) the speed of antigenic evolution decreases as prevalence rises, (ii) less standing antigenic variation accompanies either faster or slower antigenic evolution, depending on whether pathogens differ in immune evasion or host lifespan (iii) the total number of infected hosts is largest at an intermediate virulence when the host birth rate is sufficiently low.
ER -