Life-time patterns of reinfections: epidemic cohorts as traveling waves
Abstract
Infectious disease models that allow for reinfection, such as the SIS or SIRS frameworks, typically treat all infections as exchangeable and independent, erasing the temporal structure of individual reinfection histories. Here, we introduce a minimal "chain SIR" model that resolves this limitation by indexing compartments by reinfection count and allowing transmission, recovery, and waning rates to depend on that count. The dynamics generate an advective flux along the reinfection ladder, producing traveling waves in reinfection space and a coherent structure in the population's lifetime infection histories. We derive an analytical expression for the wave speed and identify the general conditions under which such cohort waves exist and persist, offering a new lens to interpret long-term prevalence patterns and the emergence of age- or immunity-structured endemicity. Finally, comparing the speed formula with longitudinal cohort data, we quantify the reduction in reinfection rate attributable to immunological responses for several seasonal viruses, including influenza A/H3N2 and respiratory syncytial virus (RSV).
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BibTeX
@misc{castioni2026lifetime,
title = {{Life-time patterns of reinfections: epidemic cohorts as traveling waves}},
author = {Piergiorgio Castioni and Chiara Poletto and Alex Arenas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33466},
eprint = {2609.33466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33466},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Life-time patterns of reinfections: epidemic cohorts as traveling waves
AU - Piergiorgio Castioni
AU - Chiara Poletto
AU - Alex Arenas
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33466
UR - https://arxiv.org/abs/2609.33466
AB - Infectious disease models that allow for reinfection, such as the SIS or SIRS frameworks, typically treat all infections as exchangeable and independent, erasing the temporal structure of individual reinfection histories. Here, we introduce a minimal "chain SIR" model that resolves this limitation by indexing compartments by reinfection count and allowing transmission, recovery, and waning rates to depend on that count. The dynamics generate an advective flux along the reinfection ladder, producing traveling waves in reinfection space and a coherent structure in the population's lifetime infection histories. We derive an analytical expression for the wave speed and identify the general conditions under which such cohort waves exist and persist, offering a new lens to interpret long-term prevalence patterns and the emergence of age- or immunity-structured endemicity. Finally, comparing the speed formula with longitudinal cohort data, we quantify the reduction in reinfection rate attributable to immunological responses for several seasonal viruses, including influenza A/H3N2 and respiratory syncytial virus (RSV).
ER -