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arXiv · 2607.00905

Immune history shapes recurrent epidemics of antigenically related variants

Ryuichi Kumata·Yuma Fujimoto·Hisashi Ohtsuki·Akira Sasaki
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Abstract

Population immunity carried over from past epidemics of an antigenically variable pathogen influences the epidemic of new variants based on their antigenic similarity to the previous ones. We develop a recurrent SIR model where a population faces sequential, antigenically related variants. The model yields a recurrence map for the population susceptibility to successive variants under the assumption of status-based population immunity. The model reveals that stable, equal-sized recurrent epidemics occur across broad parameter ranges, but can be destabilized when transmission is strong and antigenic escape is limited, leading to period-2 or more, or even more complex epidemic dynamics. Epidemic size is maximized at an intermediate basic reproduction number: higher transmissibility boosts immediate infection but also enhances cross-immunity, reducing future susceptibility of the population. Our results clarify how immune history shapes recurrent epidemics and why success in one wave does not ensure larger future epidemics.

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Ryuichi Kumata, Yuma Fujimoto, Hisashi Ohtsuki, Akira Sasaki. 2026-07-01. Immune history shapes recurrent epidemics of antigenically related variants. https://arxiv.org/abs/2607.00905

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