Long-term Coexistence of Epidemics and Risk Awareness: Impacts of Adaptive Human Response and Fatigue

Mozzamil Mohammed; Abdallah Alsammani

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arXiv · 2607.18301

Long-term Coexistence of Epidemics and Risk Awareness: Impacts of Adaptive Human Response and Fatigue

Mozzamil Mohammed·Abdallah Alsammani

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Abstract

Human behavior shapes epidemic dynamics, yet most models represent it by rescaling the transmission rate, which conflates behavior with biology and fails to capture the memory associated with sustained protective behavior. We develop and analyze a susceptible-infected-recovered-aware model in which awareness is generated by prevalence and eroded by fatigue. Rather than modifying transmission probabilities, awareness moves susceptible and infectious individuals between accessible and inaccessible compartments. The basic reproduction number is independent of all behavioral parameters, showing that awareness cannot directly alter invasion. A unique endemic equilibrium exists exactly when the basic reproduction number is greater than one, thereby excluding backward bifurcation. Infection and awareness are uniformly persistent, ensuring robust coexistence. We derive an exact decomposition of the reduction in endemic burden into contributions from susceptible withdrawal and infectious sequestration, determine the effect of each behavioral parameter, and show that the endemic state depends on awareness response and fatigue only through their ratio. In addition, prevalence vanishes linearly as fatigue approaches zero. In the limit of instantaneous behavioral relaxation, the model reduces to the classical transmission-modulating formulation, whose endemic equilibrium is always stable. At finite relaxation rates, however, accessibility can destabilize the endemic equilibrium through a Hopf bifurcation, generating self-sustained epidemic cycles without any imposed delay.

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Mozzamil Mohammed, Abdallah Alsammani. 2026-07-16. Long-term Coexistence of Epidemics and Risk Awareness: Impacts of Adaptive Human Response and Fatigue. https://arxiv.org/abs/2607.18301

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