Role of heterogeneous infection histories on variant dynamics: exact and approximate approaches
- 1Sorbonne University; Inserm; Iplesp
Abstract
Host immunity acquired through prior infections is a key factor shaping the spread of emerging variants. However, accounting for complete infection histories in mathematical models is challenging because the number of possible histories grows exponentially with the number of variants. Here, we present a flexible framework for modeling the co-circulation of multiple variants emerging at arbitrary times while incorporating cross-immunity and variant-specific characteristics. We introduce three tractable approximations: truncation, which retains only infection histories up to a given number of strains; one variant at a time, which is exact when variants circulation does not overlap; and two variants at a time, which is exact when at most two strains co-circulate. We systematically evaluate these approximations across a range of cross-immunity levels and inter-variant emergence delays. Truncation approximations perform best under short emergence delays and strong cross-immunity, whereas the other approaches outperform them at longer delays. When applied to SARS-CoV-2 variant dynamics, the second-order truncation and the two variants at a time approximation accurately capture incidence patterns, whereas the other approaches perform well only for specific subsets of variants. These results identify the parameter regimes in which simplifying assumptions remain valid, provide guidance for model selection, and highlight the key role of infection history in shaping epidemic trajectories.
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BibTeX
@misc{simin2026role,
title = {{Role of heterogeneous infection histories on variant dynamics: exact and approximate approaches}},
author = {P. Toranj Simin and P.-y. Boelle and C. Poletto},
howpublished = {medRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.03.26364599},
url = {https://www.medrxiv.org/content/10.64898/2026.10.03.26364599v1},
note = {CC BY-NC},
}
RIS
TY - UNPB
TI - Role of heterogeneous infection histories on variant dynamics: exact and approximate approaches
AU - P. Toranj Simin
AU - P.-y. Boelle
AU - C. Poletto
PY - 2026
DA - 2026/10/03
PB - medRxiv
DO - 10.64898/2026.10.03.26364599
UR - https://www.medrxiv.org/content/10.64898/2026.10.03.26364599v1
AB - Host immunity acquired through prior infections is a key factor shaping the spread of emerging variants. However, accounting for complete infection histories in mathematical models is challenging because the number of possible histories grows exponentially with the number of variants. Here, we present a flexible framework for modeling the co-circulation of multiple variants emerging at arbitrary times while incorporating cross-immunity and variant-specific characteristics. We introduce three tractable approximations: truncation, which retains only infection histories up to a given number of strains; one variant at a time, which is exact when variants circulation does not overlap; and two variants at a time, which is exact when at most two strains co-circulate. We systematically evaluate these approximations across a range of cross-immunity levels and inter-variant emergence delays. Truncation approximations perform best under short emergence delays and strong cross-immunity, whereas the other approaches outperform them at longer delays. When applied to SARS-CoV-2 variant dynamics, the second-order truncation and the two variants at a time approximation accurately capture incidence patterns, whereas the other approaches perform well only for specific subsets of variants. These results identify the parameter regimes in which simplifying assumptions remain valid, provide guidance for model selection, and highlight the key role of infection history in shaping epidemic trajectories.
ER -