Dynamics of an emerging infectious disease with a behavior change and constrained treatment resources

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

At the early stage of an emerging infectious disease outbreak, the interplay between individual protective behavior and therapeutic resources profoundly influences the effectiveness of epidemic control. By extending the classic behavior–disease coupling framework, this paper developed a dynamic model that concurrently incorporates heterogeneous behavioral adoption dynamics and saturation effects in treatment resources. Two behavioral regulation parameters were introduced to quantify their synergistic influence on transmission dynamics. Theoretical analysis yielded the basic reproduction number for both homogeneous and mixed systems, thereby establishing the threshold dynamics of the model. Numerical simulations demonstrated that increasing the intensity of behavioral adoption significantly reduces both the infection scale and transmission risk, and can even lower R₀ below the epidemic. However, if the driving force for adoption is insufficient, transmission risk in the mixed system may exceed that in a system with no behavioral adoption, suggesting that ineffective interventions could exacerbate disease spread. Under resource constraints, our results indicate that large-scale, high-compliance behavioral interventions are essential for epidemic control. They further provides a mathematical basis for designing integrated strategies that balance “behavioral maintenance” and “resource allocation”.

Keywords

emerging infectious diseases / behavioral-disease coupling model / resource constraints / basic reproduction number

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] D. M. Morens, G. K. Folkers, A. S. Fauci, The challenge of emerging and re-emerging infectious diseases, Nature, 430 (2004), 242-249. https://doi.org/10.1038/nature02759

[2] K. E. Jones, N. G. Patel, M. A. Levy, A. Storeygard, D. Balk, J. L. Gittleman, et al., Global trends in emerging infectious diseases, Nature, 451 (2008), 990-993. https://doi.org/10.1038/nature06536

[3] N. Wang, L. Qi, M. Bessane, M. Hao, Global Hopf bifurcation of a two-delay epidemic model with media coverage and asymptomatic infection, J. Differ. Equations, 369 (2023), 1-40. https://doi.org/10.1016/j.jde.2023.05.036

[4] N. Wang, L. Qi, G. Cheng, Dynamical analysis for the impact of asymptomatic infective and infection delay on disease transmission, Math. Comput. Simul., 200 (2022), 525-556. https://doi.org/10.1016/j.matcom.2022.04.029

[5] P. P. Win, Z. Lin, M. Zhang, The final size and critical times of an SIVR epidemic model, Adv. Contin. Discrete Models, 2025 (2025), 31. https://doi.org/10.1186/s13662-025-03902-2

[6] M. Jusup, P. Holme, K. Kanazawa, M. Takayasu, I. Romić, Z. Wang, et al., Social physics, Phys. Rep., 948 (2022), 1-148. https://doi.org/10.1016/j.physrep.2021.10.005

[7] Y. Li, Y. Yao, M. Feng, T. P. Benko, M. Perc, J. Završnik, Epidemic dynamics in homes and destinations under recurrent mobility patterns, Chaos, Solitons Fractals, 195 (2025), 116273. https://doi.org/10.1016/j.chaos.2025.116273

[8] W. Wu, Q. Zhang, H. Wang, S. Liu, Cholera dynamics driven by human behavior change via a degenerate reaction-diffusion model, Z. Angew. Math. Phys., 76 (2025), 114. https://doi.org/10.1007/s00033-025-02495-w

[9] M. Ryan, E. Brindal, R. I. Hickson, Behavior and infection feedback loops inform early-stage behavior emergence and the efficacy of interventions, Math. Med. Life Sci., 2 (2025), 2452444. https://doi.org/10.1080/29937574.2025.2452444

[10] G. Fan, J. Li, J. Belair, H. Zhu, Delayed model for the transmission and control of COVID-19 with Fangcang shelter hospitals, SIAM J. Appl. Math., 83 (2023), 276-301. https://doi.org/10.1137/21M146154X

[11] S. Gao, P. Binod, C. W. Chukwu, T. Kwofie, S. Safdar, L. Newman, et al., A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19, Infect. Dis. Modell., 8 (2023), 427-444. https://doi.org/10.1016/j.idm.2023.04.005

[12] I. Ahmad, H. Seno, An epidemic dynamics model with limited isolation capacity, Theory Biosci., 142 (2023), 259-273. https://doi.org/10.1007/s12064-023-00399-9

[13] Z. Fu, H. Seno, SIRI+Q model with a limited capacity of isolation, Theory Biosci., 144 (2025), 121-144. https://doi.org/10.1007/s12064-025-00437-8

[14] H. Zhao, L. Wang, S. M. Oliva, H. Zhu, Modeling and dynamics analysis of Zika transmission with limited medical resources, Bull. Math. Biol., 82 (2020), 99. https://doi.org/10.1007/s11538-020-00776-1

[15] J. Wang, S. Liu, B. Zheng, Y. Takeuchi, Qualitative and bifurcation analysis using an SIR model with a saturated treatment function, Math. Comput. Modell., 55 (2012), 710-722. https://doi.org/10.1016/j.mcm.2011.08.045

[16] B. Tang, W. Zhou, X. Wang, H. Wu, Y. Xiao, Controlling multiple COVID-19 epidemic waves: an insight from a multi-scale model linking the behavior change dynamics to the disease transmission dynamics, Bull. Math. Biol., 84 (2022), 106. https://doi.org/10.1007/s11538-022-01061-z

[17] A. D. Becker, K. H. Grantz, S. T. Hegde, S. Bérubé, D. A. T. Cummings, A. Wesolowski, Development and dissemination of infectious disease dynamic transmission models during the COVID-19 pandemic: what can we learn from other pathogens and how can we move forward?, Lancet Digit. Health, 3 (2021), e41-e50. https://doi.org/10.1016/S2589-7500(20)30268-5

[18] J. Bedson, L. A. Skrip, D. Pedi, S. Abramowitz, S. Carter, M. F. Jalloh, et al., A review and agenda for integrated disease models including social and behavioral factors, Nat. Hum. Behav., 5 (2021), 834-846. https://doi.org/10.1038/s41562-021-01136-2

[19] S. Funk, S. Bansal, C. T. Bauch, K. T. D. Eames, W. J. Edmunds, A. P. Galvani, et al., Nine challenges in incorporating the dynamics of behavior in infectious diseases models, Epidemics, 10 (2015), 21-25. https://doi.org/10.1016/j.epidem.2014.12.005

[20] R. N. Shalan, R. Shireen, A. H. Lafta, Discrete an SIS model with immigrants and treatment, J. Interdiscip. Math., 24 (2020), 1201-1206. https://doi.org/10.1080/09720502.2020.1814496

[21] W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. A, 115 (1927), 700-721. https://doi.org/10.1098/rspa.1927.0118

[22] D. P. Durham, E. A. Casman, Incorporating individual health-protective decisions into disease transmission models: a mathematical framework, J. R. Soc. Interface, 9 (2012), 562-570. https://doi.org/10.1098/rsif.2011.0325

[23] C. J. Fan, Y. Jin, L. A. Huo, C. Liu, Y. P. Yang, Y. Q. Wang, Effect of individual behavior on the interplay between awareness and disease spreading in multiplex networks, Physica A, 461 (2016), 523-530. https://doi.org/10.1016/j.physa.2016.06.050

[24] L. Hébert-Dufresne, D. Mistry, B. M. Althouse, Spread of infectious disease and social awareness as parasitic contagions on clustered networks, Phys. Rev. Res., 2 (2020), 033306. https://doi.org/10.1103/PhysRevResearch.2.033306

[25] N. Perra, D. Balcan, B. Gonçalves, A. Vespignani, Towards a characterization of behavior-disease models, PLoS One, 6 (2011), e23084. https://doi.org/10.1371/journal.pone.0023084

[26] J. M. Epstein, E. Hatna, J. Crodelle, Triple contagion: a two-fears epidemic model, J. R. Soc. Interface, 18 (2021), 20210186. https://doi.org/10.1098/rsif.2021.0186

[27] M. Ryan, E. Brindal, M. Roberts, R. I. Hickson, A behavior and disease transmission model: incorporating the Health Belief Model for human behavior into a simple transmission model, J. R. Soc. Interface, 21 (2024), 20240038. https://doi.org/10.1098/rsif.2024.0038

[28] M. Ryan, R. I. Hickson, E. M. Hill, T. House, V. Isham, D. Zhang, et al., A behavior and disease model of testing and isolation, preprint, arXiv:2504.02488.

[29] A. Kaur, R. C. Tyson, I. R. Moyles, The impact of fear and behavior response to established and novel diseases, SIAM J. Appl. Math., 85 (2025), 687-710. https://doi.org/10.1137/24M1670718

[30] G. O. Agaba, Y. N. Kyrychko, K. B. Blyuss, Mathematical model for the impact of awareness on the dynamics of infectious diseases, Math. Biosci., 286 (2017), 22-30. https://doi.org/10.1016/j.mbs.2017.01.009

[31] Y. Shang, Global stability of disease-free equilibria in a two-group SI model with feedback control, Nonlinear Anal. Model. Control, 20 (2015), 501-508. https://doi.org/10.15388/NA.2015.4.3

[32] P. Van den Driessche, Reproduction numbers of infectious disease models, Infect. Dis. Modell., 2 (2017), 288-303. https://doi.org/10.1016/j.idm.2017.06.002

[33] O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R₀ in models for infectious diseases in heterogeneous populations , J. Math. Biol., 28 (1990), 365-382. https://doi.org/10.1007/BF00178324

[34] Y. Bai, X. Wang, S. Guo, Global stability of a mumps transmission model with quarantine measure, Acta Math. Appl. Sin., 37 (2021), 665-672. https://doi.org/10.1007/s10255-021-1035-7

[35] S. Guo, Y. Xue, M. He, J. Cui, Modeling and analysis of malaria transmission dynamics considering vaccination and vaccine failure, Acta Math. Appl. Sin., 47 (2024), 1-11. https://doi.org/10.20142/j.cnki.amas.202401001

[36] J. P. LaSalle, The Stability of Dynamical Systems , SIAM, 1976. https://doi.org/10.1137/1.9781611970432

[37] M. Shen, Y. Xiao, G. Zhuang, Y. Li, L. Zhang, Mass testing-An underexplored strategy for COVID-19 control, Innovation, 2 (2021), 100114. https://doi.org/10.1016/j.xinn.2021.100114

[38] D. P. Oran, E. J. Topol, Prevalence of asymptomatic SARS-CoV-2 infection: a narrative review, Ann. Intern. Med., 173 (2020), 362-367. https://doi.org/10.7326/M20-3012