Transmission Dynamics Model Incorporating Risk Perception and Behavioral Fatigue
DOI:
https://doi.org/10.63313/JCSFT.9078Keywords:
Transmission Dynamics, SIR Model, Risk Perception, Behavioral Fatigue, Behavioral Feedback, Numerical SimulationAbstract
The classical SIR model provides a foundational framework for studying transmission dynamics, but its standard form often assumes a fixed transmission rate and therefore cannot directly represent adaptive changes in human behavior. In real transmission processes, individuals may reduce contact when perceived risk rises, while prolonged protection may also generate behavioral fatigue and weaken adherence. To describe this coupled mechanism, this paper extends the classical SIR model by introducing two bounded behavioral variables: risk perception and behavioral fatigue. The effective transmission rate is specified as an exponential function of these variables, which guarantees positivity and captures two opposite effects: risk perception suppresses transmission, whereas fatigue amplifies transmission. Ideal numerical simulations are conducted to compare the classical SIR model, a risk-perception-only model, and a full risk-perception-fatigue model. The results show that risk perception substantially lowers the infection peak and final epidemic size, while behavioral fatigue partially offsets the protective effect and delays the infection peak. Sensitivity analysis further indicates that increasing the risk-perception suppression coefficient reduces the epidemic scale, whereas increasing the fatigue amplification coefficient produces stronger rebound effects. The model offers a compact and interpretable framework for studying behavioral feedback in transmission dynamics.
References
[1] W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proceedings of the Royal Society A, vol. 115, no. 772, pp. 700–721, 1927. doi: 10.1098/rspa.1927.0118.
[2] H. W. Hethcote, “The mathematics of infectious diseases,” SIAM Review, vol. 42, no. 4, pp. 599–653, 2000. doi: 10.1137/S0036144500371907.
[3] S. Funk, M. Salathé, and V. A. A. Jansen, “Modelling the influence of human behaviour on the spread of infectious diseases: a review,” Journal of the Royal Society Interface, vol. 7, no. 50, pp. 1247–1256, 2010. doi: 10.1098/rsif.2010.0142.
[4] S. Funk, E. Gilad, C. Watkins, and V. A. A. Jansen, “The spread of awareness and its impact on epidemic outbreaks,” Proceedings of the National Academy of Sciences, vol. 106, no. 16, pp. 6872–6877, 2009. doi: 10.1073/pnas.0810762106.
[5] P. Poletti, B. Caprile, M. Ajelli, A. Pugliese, and S. Merler, “Spontaneous behavioural changes in response to epidemics,” Journal of Theoretical Biology, vol. 260, no. 1, pp. 31–40, 2009. doi: 10.1016/j.jtbi.2009.04.029.
[6] P. Poletti, M. Ajelli, and S. Merler, “Risk perception and effectiveness of uncoordinated behavioral responses in an emerging epidemic,” Mathematical Biosciences, vol. 238, no. 2, pp. 80–89, 2012. doi: 10.1016/j.mbs.2012.04.003.
[7] H. Rahmandad, T. Y. Lim, and J. Sterman, “Behavioral dynamics of COVID-19: estimating underreporting, multiple waves, and adherence fatigue across 92 nations,” System Dynamics Review, vol. 37, no. 1, pp. 5–31, 2021. doi: 10.1002/sdr.1673.
[8] R. F. Arthur, J. H. Jones, M. H. Bonds, Y. Ram, and M. W. Feldman, “Adaptive social contact rates induce complex dynamics during epidemics,” PLOS Computational Biology, vol. 17, no. 2, e1008639, 2021. doi: 10.1371/journal.pcbi.1008639.
[9] A. Petherick, R. Goldszmidt, E. B. Andrade, R. Furst, T. Hale, A. Pott, and A. Wood, “A worldwide assessment of changes in adherence to COVID-19 protective behaviours and hypothesized pandemic fatigue,” Nature Human Behaviour, vol. 5, pp. 1145–1160, 2021. doi: 10.1038/s41562-021-01181-x.
[10] A. Hamilton et al., “Incorporating endogenous human behavior in models of COVID-19 transmission: a systematic scoping review,” Dialogues in Health, vol. 4, article 100179, 2024. doi: 10.1016/j.dialog.2024.100179.
[11] N. Gozzi, N. Perra, and A. Vespignani, “Comparative evaluation of behavioral epidemic models using COVID-19 data,” Proceedings of the National Academy of Sciences, vol. 122, no. 24, e2421993122, 2025. doi: 10.1073/pnas.2421993122.
[12] Y. Yan, A. A. Malik, J. Bayham, E. P. Fenichel, C. Couzens, and S. B. Omer, “Measuring voluntary and policy-induced social distancing behavior during the COVID-19 pandemic,” Proceedings of the National Academy of Sciences, vol. 118, no. 16, e2008814118, 2021. doi: 10.1073/pnas.2008814118.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 by author(s) and Erytis Publishing Limited.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
How to Cite
