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Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

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  • Khan, Muhammad Altaf
  • Khan, Yasir
  • Islam, Saeed

Abstract

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0<1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0>1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Suggested Citation

  • Khan, Muhammad Altaf & Khan, Yasir & Islam, Saeed, 2018. "Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 210-227.
    • Handle: RePEc:eee:phsmap:v:493:y:2018:i:c:p:210-227
    DOI: 10.1016/j.physa.2017.10.038
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    References listed on IDEAS

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    1. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "A new derivative with normal distribution kernel: Theory, methods and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 1-14.
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    Cited by:

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    2. Halet Ismail & Amar Debbouche & Soundararajan Hariharan & Lingeshwaran Shangerganesh & Stanislava V. Kashtanova, 2024. "Stability and Optimality Criteria for an SVIR Epidemic Model with Numerical Simulation," Mathematics, MDPI, vol. 12(20), pages 1-29, October.
    3. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
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    7. Yu, Zhenhua & Gao, Hongxia & Wang, Dan & Alnuaim, Abeer Ali & Firdausi, Muhammad & Mostafa, Almetwally M., 2022. "SEI2RS malware propagation model considering two infection rates in cyber–physical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
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    9. Zhou, Jiaying & Zhao, Yi & Ye, Yong, 2022. "Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P2).
    10. Wei, Xiaodan & Zhao, Xu & Zhou, Wenshu, 2022. "Global stability of a network-based SIS epidemic model with a saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
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