Long-term coexistence of epidemics and risk awareness: impacts of adaptive human response and fatigue
- 1College of Business, Jumeira University, Dubai, United Arab Emirates
- 2Department of Mathematical Sciences, Delaware State University, Dover, USA
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 imposed delay. Relative to the SIR benchmark, awareness lengthens transient inter-epidemic periods and slows damping rather than creating the underlying transient oscillations.
Versions
Related
- Perceived Impacts of Generational Knowledge on Female Genital Mutilation and Barriers to Awareness Programs in Ibadan, Oyo State
- Health Impacts of Extreme Climate on Under-Fives in the Sahel: Adaptive Strategies
- Assessment of teachers' knowledge, awareness, and response to students with asthma in Greater Cairo schools.
- Reversing the Hypoxic Adaptive Response in Breast Cancer Cells through Small-Molecule Inhibition of Oncogenic MicroRNA-210
- Efficacy of a personalized, response-based transdiagnostic intervention for emotional disorders delivered via the Internet: a protocol for an adaptive randomized controlled trial
BibTeX
@article{mohammed2026longterm,
title = {{Long-term coexistence of epidemics and risk awareness: impacts of adaptive human response and fatigue}},
author = {Mozzamil Mohammed and Abdallah Alsammani},
journal = {Biomath},
year = {2026},
month = oct,
doi = {10.55630/j.biomath.2026.10.234},
url = {https://doi.org/10.55630/j.biomath.2026.10.234},
note = {CC BY},
}
RIS
TY - JOUR
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 - 2026/10/23
JO - Biomath
DO - 10.55630/j.biomath.2026.10.234
UR - https://doi.org/10.55630/j.biomath.2026.10.234
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 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 imposed delay. Relative to the SIR benchmark, awareness lengthens transient inter-epidemic periods and slows damping rather than creating the underlying transient oscillations.
SN - 1314-684X
SN - 1314-7218
ER -