This study explores an SEIR epidemic model, aiming to achieve rapid stabilization of infectious disease dynamics. The model’s dynamic behavior is analyzed with an emphasis on both local and global stability of equilibria using a Lyapunov function. The existence and uniqueness of the model are confirmed. The theoretical findings are validated, and the controller’s effectiveness is illustrated through numerical simulations conducted in MATLAB/Simulink.
[1] Z. Abbasi, I. Zamani, A. H. A. Mehra, M. Shafieirad, and A. Ibeas, Optimal control design of impulsive SQEIAR epidemic models with application to COVID-19, Chaos Solitons Fractals, 139 (2020), 110054.
[2] F. B. Agusto, E. Numfor, K. Srinivasan, E. A. Iboi, A. Fulk, and J. M. Saint Onge, A. T. Peterson, Impact of public sentiments on the transmission of COVID-19 across a geographical gradient, PeerJ, 11 (2023), e14736.
[3] R. T. Alqahtani, Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer, J. Nonlinear Sci. Appl., 9 (2016), 3647–3654.
[4] J. Arino, F. Brauer, P. van den Driessche, J. Watmough, and J. Wu, A model for influenza with vaccination and antiviral treatment, J. Theor. Biol., 253 (2008), 118–130.
[5] I. A. Baba, E. Hincal, and S. H. K. Alsaadi, Global stability analysis of a two strain epidemic model with awareness, Adv. Differ. Equ. Control Processes, 19 (2018), 83–100.
[6] D. Baleanu, A. Jajarmi, and M. Hajipour, On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag–Leffler kernel, Nonlinear Dyn., 94 (2018), 397–414.
[7] A. Basit, M. Tufail, M. Rehan, and I. Ahmed, A new event-triggered distributed state estimation approach for one-sided Lipschitz nonlinear discrete-time systems and its application to wireless sensor networks, ISA Trans., 137 (2023), 74–86.
[8] M. A. Bayrak, A. Demir, and E. Ozbilge, On solution of fractional partial differential equation by the weighted fractional operator, Alex. Eng. J., 59 (2020), 4805–4819.
[9] E. Bonyah, H. S. Panigoro, E. Rahmi, and M. L. Juga, Fractional stochastic modelling of monkeypox dynamics, Results in Control and Optimization, 12 (2023), 100277.
[10] S. K. Brooks, R. K. Webster, L. E. Smith, L. Woodland, S. Wessely, N. Greenberg, and G. Rubin, The psychological impact of quarantine and how to reduce it: rapid review of the evidence, The Lancet, 395 (2020), 912–920.
[11] A. I. K. Butt, W. Ahmad, M. Rafiq, and D. Baleanu, Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic, Alex. Eng. J., 61 (2022), 7007–7027.
[12] P. V. Den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
[13] M. El Fatini, I. Sekkak, and A. Laaribi, A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination, Physica A, 520 (2019), 151–160.
[14] P. Gahinet and P. Apkarian, A linear matrix inequality approach to control, Int. J. Robust Nonlinear Control, 4 (1994), 421–448.
[15] M. Iannelli, M. Martcheva, and X. Z. Li, Strain replacement in an epidemic model with super-infection and perfect vaccination, Math. Biosci., 195 (2005), 23–46.
[16] S. A. Jose, R. Ramachandran, D. Baleanu, H. S. Panigoro, J. Alzabut, and V. E. Balas, Computational dynamics of a fractional order substance addictions transfer model with Atangana–Baleanu–Caputo derivative, Math. Methods Appl. Sci., 46 (2023), 5060–5085.
[17] N. Leung, D. K. Chu, E. Y. Shiu, K. Chan, J. J. McDevitt, B. J. Hau, H. Yen, Y. G. Li, D. K. Ip, J. Peiris, W. Seto, G. M. Leung, D. K. Milton, and B. J. Cowling, Respiratory virus shedding in exhaled breath and efficacy of face masks, Nat. Med., 26 (2020), 676–680.
[18] Q. Liu and Q. M. Chen, Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence, Physica A, 428 (2015), 140–153.
[19] Q. Liu, D. Jiang, T. Hayat, and A. Alsaedi, Dynamics of a stochastic predator–prey model with distributed delay and Markovian switching, Physica A: Stat. Mech. Appl., 527 (2019), 121264.
[20] X. Z. Li, J. Wang, and M. Ghosh, Stability and bifurcation of an SIVS epidemic model with treatment and age of vaccination, Appl. Math. Model., 34 (2010), 437–450.
[21] G. P. Matthews and R. A. De Carlo, Decentralized tracking for a class of interconnected nonlinear systems using variable structure control, Automatica, 24 (1988), 187–193.
[22] S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178–196.
[23] A. Mehra, I. Zamani, Z. Abbasi, and A. Ibeas, Observer-based adaptive PI sliding mode control of developed uncertain SEIAR influenza epidemic model considering dynamic population, J. Theor. Biol., 482 (2019), 118–130.
[24] P. W. Nelson, M. A. Gilchrist, D. Coombs, J. M. Hyman, and A. S. Perelson, An age-structured model of HIV infection that allows for variations in the production rate of viral particles and the death rate of productively infected cells, Math. Biosci. Eng., 1 (2004), 267–288.
[25] A. T. Peterson, A. Fulk, E. Numfor, E. A. Iboi, F. B. Agusto, J. M. Saint Onge, and K. Srinivasan, Impact of public sentiments on the transmission of COVID-19 across a geographical gradient, PeerJ, 11 (2023), e14736.
[26] A. J. E. M. Saltelli, D. Cariboni, J. Gatelli, and R. Liska, The role of sensitivity analysis in ecological modelling, Ecol. Model., 203(1–2) (2007), 167–182.
[27] M. Toufik and A. Atangana, New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models, Eur. Phys. J. Plus, 132 (2017), 1–16.
[28] Y. Wang, Y. Zhou, F. Brauer, and J. M. Heffernan, Viral dynamics model with CTL immune response incorporating antiretroviral therapy, J. Math. Biol., 67 (2013), 901–934.
[29] Y. Wang, J. Liu, and J. M. Heffernan, Viral dynamics of an HTLV-I infection model with intracellular delay and CTL immune response delay, J. Math. Anal. Appl., 459(1) (2018), 506–527.
[30] Y. Wang, J. Liu, and L. Liu, Viral dynamics of an HIV model with latent infection incorporating antiretroviral therapy, Adv. Differ. Equ., 2016 (2016), 1–15.
[31] D. M. Xiao and S. G. Ruan, Global analysis of an epidemic model with nonmonotone incidence rate, Math. Biosci., 208 (2007), 419–429.
[32] X. Zhang, D. Jiang, T. Hayat, and B. Ahmad, Dynamics of a stochastic SIS model with double epidemic diseases driven by Levy jumps, Physica A: Stat. Mech. Appl., 471 (2017), 767–777.
Zafar, Z. U. A. , Ijaz, S. and Tunc, C. (2026). Numerical analysis of the SEIR epidemic model with fractional order. Computational Methods for Differential Equations, 14(1), 392-410. doi: 10.22034/cmde.2024.63428.2832
MLA
Zafar, Z. U. A. , , Ijaz, S. , and Tunc, C. . "Numerical analysis of the SEIR epidemic model with fractional order", Computational Methods for Differential Equations, 14, 1, 2026, 392-410. doi: 10.22034/cmde.2024.63428.2832
HARVARD
Zafar, Z. U. A., Ijaz, S., Tunc, C. (2026). 'Numerical analysis of the SEIR epidemic model with fractional order', Computational Methods for Differential Equations, 14(1), pp. 392-410. doi: 10.22034/cmde.2024.63428.2832
CHICAGO
Z. U. A. Zafar , S. Ijaz and C. Tunc, "Numerical analysis of the SEIR epidemic model with fractional order," Computational Methods for Differential Equations, 14 1 (2026): 392-410, doi: 10.22034/cmde.2024.63428.2832
VANCOUVER
Zafar, Z. U. A., Ijaz, S., Tunc, C. Numerical analysis of the SEIR epidemic model with fractional order. Computational Methods for Differential Equations, 2026; 14(1): 392-410. doi: 10.22034/cmde.2024.63428.2832
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