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A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence

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  • Xie, Yingkang
  • Wang, Zhen

Abstract

In this paper, the ratio-dependent impulsive control is used in an SIQS epidemic model with non-linear incidence. Compared with most of existing results, there are two advantages. On the one hand, the impulsive control strategy is economical, efficient and simple. On the other hand, the ratio-dependent impulsive control can deal with the changing population well. Besides, by using analogue of the Poincare criterion, vector field analysis, Poincare map and the method of qualitative analysis, the stability of the disease-free equilibrium and the existence and stability of positive order-k periodic solution of the SIQS epidemic model under ratio-dependent impulsive control are studied. Moreover, our results show that order-k (k>2) periodic solutions don’t exist. Finally, some simple numerical examples are used to verify our theoretical results.

Suggested Citation

  • Xie, Yingkang & Wang, Zhen, 2022. "A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    • Handle: RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322001047
    DOI: 10.1016/j.amc.2022.127018
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    References listed on IDEAS

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    6. Zaman, Gul & Kang, Yong Han & Cho, Giphil & Jung, Il Hyo, 2017. "Optimal strategy of vaccination & treatment in an SIR epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 63-77.
    7. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
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    Cited by:

    1. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Li, Wenjie & Ji, Jinchen & Huang, Lihong & Zhang, Ying, 2023. "Complex dynamics and impulsive control of a chemostat model under the ratio threshold policy," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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