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Numerical and bifurcation analysis of SIQR model

Author

Listed:
  • Ahmed, Nauman
  • Raza, Ali
  • Rafiq, Muhammad
  • Ahmadian, Ali
  • Batool, Namra
  • Salahshour, Soheil

Abstract

In this mathematical research paper, we analyze in detail the basic SIQR epidemic model. We calculate its reproductive value R0, equilibrium points and analyze the stability of the SIQR system by using Routh-Hurwitz criterion in detail. We also find out the bifurcation value of the SIQR epidemic model by using Routh-Hurwitz criterion. Also, SIQR system is solved numerically by using four different mathematical techniques that are forward Euler scheme, Runge-Kutta (RK-4) method, variational iteration method and nonstandard finite difference scheme (NSFD). Analytical and graphical calculations show that the NSFD method preserves all the important conditions of the basic SIQR epidemic model while the rest three techniques fail to preserve the essential conditions of the system. Convergence analysis of the NSFD scheme has also been performed.

Suggested Citation

  • Ahmed, Nauman & Raza, Ali & Rafiq, Muhammad & Ahmadian, Ali & Batool, Namra & Salahshour, Soheil, 2021. "Numerical and bifurcation analysis of SIQR model," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004872
    DOI: 10.1016/j.chaos.2021.111133
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    References listed on IDEAS

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    3. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li & Cheng, Ming, 2019. "Dynamics of a stochastic SIQR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
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