Long-term Coexistence of Epidemics and Risk Awareness: Impacts of Adaptive Human Response and Fatigue
Abstract
Human behavior shapes epidemic dynamics, yet most models represent it by rescaling transmission, conflating behavior with biology and removing the memory carried by sustained protective behavior. We develop and analyze a susceptible-infected-recovered-aware model in which prevalence-driven awareness, eroded by fatigue, moves susceptible and infectious individuals between accessible and inaccessible states rather than modifying transmission probabilities. The basic reproduction number is ℛ0=β/(γ+μ), independent of behavioral parameters, and a unique endemic equilibrium exists exactly when ℛ0>1, excluding backward bifurcation. Infection and awareness are uniformly persistent whenever ℛ0>1. We derive an exact decomposition of the reduction in endemic burden into susceptible withdrawal and infectious sequestration, establish the effect of each behavioral parameter, and show that the endemic state depends on awareness response and fatigue only through their ratio, with prevalence vanishing linearly as fatigue vanishes. In the instantaneous-relaxation limit, the model reduces to a transmission-modulating formulation whose endemic equilibrium is locally asymptotically stable. At finite relaxation rates, however, numerical stability and bifurcation analyses reveal a Hopf transition and self-sustained epidemic cycles without an imposed delay. Relative to the SIR benchmark, awareness lengthens transient inter-epidemic periods and slows damping rather than creating the underlying transient oscillations.
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BibTeX
@misc{mohammed2026longterm,
title = {{Long-term Coexistence of Epidemics and Risk Awareness: Impacts of Adaptive Human Response and Fatigue}},
author = {Mozzamil Mohammed and Abdallah Alsammani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.18301},
eprint = {2607.18301},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18301},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-term Coexistence of Epidemics and Risk Awareness: Impacts of Adaptive Human Response and Fatigue
AU - Mozzamil Mohammed
AU - Abdallah Alsammani
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2607.18301
UR - https://arxiv.org/abs/2607.18301
AB - Human behavior shapes epidemic dynamics, yet most models represent it by rescaling transmission, conflating behavior with biology and removing the memory carried by sustained protective behavior. We develop and analyze a susceptible-infected-recovered-aware model in which prevalence-driven awareness, eroded by fatigue, moves susceptible and infectious individuals between accessible and inaccessible states rather than modifying transmission probabilities. The basic reproduction number is ℛ_0=β/(γ+μ), independent of behavioral parameters, and a unique endemic equilibrium exists exactly when ℛ_0>1, excluding backward bifurcation. Infection and awareness are uniformly persistent whenever ℛ_0>1. We derive an exact decomposition of the reduction in endemic burden into susceptible withdrawal and infectious sequestration, establish the effect of each behavioral parameter, and show that the endemic state depends on awareness response and fatigue only through their ratio, with prevalence vanishing linearly as fatigue vanishes. In the instantaneous-relaxation limit, the model reduces to a transmission-modulating formulation whose endemic equilibrium is locally asymptotically stable. At finite relaxation rates, however, numerical stability and bifurcation analyses reveal a Hopf transition and self-sustained epidemic cycles without an imposed delay. Relative to the SIR benchmark, awareness lengthens transient inter-epidemic periods and slows damping rather than creating the underlying transient oscillations.
ER -