Feedback-driven strategies for controlling infectious outbreaks

Mohammed Azoua; Marouane Karim; Amine Rachih; Mostafa Rachik; Mahmoud A. Zaky; Mohammed Azoua; Marouane Karim; Amine Rachih; Mostafa Rachik; Mahmoud A. Zaky

doi:10.3934/math.20251233

AIMS Mathematics

2025, Volume 10, Issue 11: 28059-28076. doi: 10.3934/math.20251233

Previous Article Next Article

Research article Special Issues

Feedback-driven strategies for controlling infectious outbreaks

1.
Laboratory of Process Engineering Computer Science and Mathematics, University Sultan Moulay Slimane, BeniMellal, Morocco
2.
Multidisciplinary Research and Innovation Laboratory (LPRI), Moroccan School of Engineering Sciences (EMSI), Casablanca 20250, Morocco
3.
Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, University Hassan Ⅱ, Casablanca, Morocco
4.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia

Received: 07 August 2025 Revised: 29 October 2025 Accepted: 12 November 2025 Published: 28 November 2025
MSC : 49Jxx, 49Kxx, 93Axx, 93Cxx

In response to the global health crises posed by infectious diseases like COVID-19, this study presents an enhanced SEIR model by introducing a novel feedback control mechanism. This mechanism dynamically adapts not only to the current state of the infected population but also to its rate of change, offering a dual-dependence control strategy. Such an approach significantly enhances the responsiveness and precision of epidemic management interventions, leading to a substantial reduction in peak infection rates and overall disease burden. To achieve optimal control, we employed the gradient descent method for mathematical analysis, ensuring both theoretical robustness and computational efficiency. Theoretical results were validated through comprehensive numerical simulations, demonstrating the efficacy of our control strategy across various epidemic scenarios. Furthermore, a comparative analysis with Pontryagin's maximum principle highlights the superior performance of our model, underscoring the critical role of incorporating both state and rate of change information in designing effective public health interventions. These findings reveal new possibilities for improving epidemic containment strategies, offering valuable insights for real-world disease management.
- epidemiological model,
- feedback control,
- adjoint sensitivity method,
- optimal control
Citation: Mohammed Azoua, Marouane Karim, Amine Rachih, Mostafa Rachik, Mahmoud A. Zaky. Feedback-driven strategies for controlling infectious outbreaks[J]. AIMS Mathematics, 2025, 10(11): 28059-28076. doi: 10.3934/math.20251233

Related Papers:

Abstract

In response to the global health crises posed by infectious diseases like COVID-19, this study presents an enhanced SEIR model by introducing a novel feedback control mechanism. This mechanism dynamically adapts not only to the current state of the infected population but also to its rate of change, offering a dual-dependence control strategy. Such an approach significantly enhances the responsiveness and precision of epidemic management interventions, leading to a substantial reduction in peak infection rates and overall disease burden. To achieve optimal control, we employed the gradient descent method for mathematical analysis, ensuring both theoretical robustness and computational efficiency. Theoretical results were validated through comprehensive numerical simulations, demonstrating the efficacy of our control strategy across various epidemic scenarios. Furthermore, a comparative analysis with Pontryagin's maximum principle highlights the superior performance of our model, underscoring the critical role of incorporating both state and rate of change information in designing effective public health interventions. These findings reveal new possibilities for improving epidemic containment strategies, offering valuable insights for real-world disease management.

References

[1]	W. H. Fleming, R. W. Rishel, Deterministic and stochastic optimal control, J. R. Stat. Soc. A (General), Springer-Verlag, New York, 139 (1975). https://doi.org/10.2307/2344363
[2]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond. A., 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
[3]	L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The mathematical theory of optimal processes, New York-London, 1962. https://doi.org/10.1002/zamm.19630431023
[4]	O. P. Agrawal, A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dyn., 38 (2004), 323–337. https://doi.org/10.1007/s11071-004-3764-6 doi: 10.1007/s11071-004-3764-6
[5]	O. P. Agrawal, O. Defterli, D. Baleanu, Fractional optimal control problems with several state and control variables, J. Vib. Control, 16 (2010), 1967–1976. https://doi.org/10.1177/1077546309353361 doi: 10.1177/1077546309353361
[6]	M. Azoua, M. Karim, A. Azouani, I. Hafidi, Improved parameter estimation in epidemic modeling using continuous data assimilation methods, J. Appl. Math. Comput., 70 (2024), 1–26. https://doi.org/10.1007/s12190-024-02145-w doi: 10.1007/s12190-024-02145-w
[7]	A. Khan, G. Zaman, Optimal control strategies for an age‐structured SEIR epidemic model, Math. Method. Appl. Sci., 45 (2022), 8701–8717. https://doi.org/10.1002/mma.7823 doi: 10.1002/mma.7823
[8]	M. De la Sen, S. Alonso-Quesada, A. Ibeas, On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules, Appl. Math. Comput., 270 (2015), 953–976. https://doi.org/10.1016/j.amc.2015.08.099 doi: 10.1016/j.amc.2015.08.099
[9]	X. Lü, H. W. Hui, F. F. Liu, Y. L. Bai, Stability and optimal control strategies for a novel epidemic model of COVID-19, Nonlinear Dynam., 106 (2021), 1491–1507. https://doi.org/10.1007/s11071-021-06524-x doi: 10.1007/s11071-021-06524-x
[10]	E. Hansen, T. Day, Optimal control of epidemics with limited resources, J. Math. Biol., 62 (2011), 423–451. https://doi.org/10.1007/s00285-010-0341-0 doi: 10.1007/s00285-010-0341-0
[11]	L. Bolzoni, E. Bonacini, C. Soresina, M. Groppi, Time-optimal control strategies in SIR epidemic models, Math. Biosci., 292 (2017), 86–96. https://doi.org/10.1016/j.mbs.2017.07.011 doi: 10.1016/j.mbs.2017.07.011
[12]	M. Karim, A. Kouidere, M. Rachik, K. Shah, T. Abdeljawad, Inverse problem to elaborate and control the spread of COVID-19: A case study from Morocco, AIMS Math., 8 (2023), 23500–23518. https://doi.org/10.3934/math.20231194 doi: 10.3934/math.20231194
[13]	S. Cacace, A. Oliviero, Reliable optimal controls for SEIR models in epidemiology, Math. Comput. Simul., 223 (2024), 523–542. https://doi.org/10.1016/j.matcom.2024.04.034 doi: 10.1016/j.matcom.2024.04.034
[14]	H. J. Lee, Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach, Appl. Soft Comput., 132 (2023), 109802. https://doi.org/10.1016/j.asoc.2022.109802 doi: 10.1016/j.asoc.2022.109802
[15]	M. Azoua, A. Azouani, I. Hafidi, Optimal control and global stability of the SEIQRS epidemic model, Commun. Math. Biol. Neu., 2023. https://doi.org/10.28919/cmbn/7880 doi: 10.28919/cmbn/7880
[16]	A. Kouidere, L. E. Youssoufi, H. Ferjouchia, O. Balatif, M. Rachik, Optimal control of mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with cost-effectiveness, Chaos Soliton. Fract., 145 (2021), 110777. https://doi.org/10.1016/j.chaos.2021.110777 doi: 10.1016/j.chaos.2021.110777
[17]	U. Boscain, M. Sigalotti, D. Sugny, Introduction to the Pontryagin maximum principle for quantum optimal control, PRX Quantum, 2 (2021), 030203. https://doi.org/10.1103/PRXQuantum.2.030203 doi: 10.1103/PRXQuantum.2.030203
[18]	E. Jung, S. Iwami, Y. Takeuchi, T. C. Jo, Optimal control strategy for prevention of avian influenza pandemic, J. Theor. Biol., 260 (2009), 220–229. https://doi.org/10.1016/j.jtbi.2009.05.031 doi: 10.1016/j.jtbi.2009.05.031
[19]	K. Blayneh, Y. Cao, H. D. Kwon, Optimal control of vector-borne diseases: Treatment and prevention, Discrete Cont. Dyn-S., 11 (2009), 587–611. https://doi.org/10.3934/dcdsb.2009.11.587 doi: 10.3934/dcdsb.2009.11.587
[20]	K. Sarkar, S. Khajanchi, J. J. Nieto, Modeling and forecasting the COVID-19 pandemic in India, Chaos Soliton. Fract., 139 (2020), 110049. https://doi.org/10.1016/j.chaos.2020.110049 doi: 10.1016/j.chaos.2020.110049
[21]	S. Khajanchi, K. Sarkar, J. Mondal, K. S. Nisar, S. F. Abdelwahab, Mathematical modeling of the COVID-19 pandemic with intervention strategies, Results Phys., 25 (2021), 104285. https://doi.org/10.1016/j.rinp.2021.104285 doi: 10.1016/j.rinp.2021.104285
[22]	R. K. Rai, S. Khajanchi, P. K. Tiwari, E. Venturino, A. K. Misra, Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India, J. Appl. Math. Comput., 2022, 1–26. https://doi.org/10.1007/s12190-021-01507-y doi: 10.1007/s12190-021-01507-y
[23]	S. Khajanchi, Stability analysis of a mathematical model for glioma-immune interaction under optimal therapy, Int. J. Nonlin. Sci. Num., 20 (2019), 269–285. https://doi.org/10.1515/ijnsns-2017-0206 doi: 10.1515/ijnsns-2017-0206
[24]	S. S. Ezz-Eldien, E. H. Doha, Y. Wang, W. Cai, A numerical treatment of the two-dimensional multi-term time-fractional mixed sub-diffusion and diffusion-wave equation, Commun. Nonlinear Sci. Numer. Simul., 91 (2020), 105445. https://doi.org/10.1016/j.cnsns.2020.105445 doi: 10.1016/j.cnsns.2020.105445

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)