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Stability Analysis for an SEIQR Epidemic Model with Saturated Incidence Rate

  • Deepti MokatiEmail author
  • Nirmala Gupta
  • V. H. Badshah
Conference paper
  • 19 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 308)

Abstract

Mathematics plays an important role in study of biological systems through mathematical models. In the present paper, we extended the work of Nirwani et al. (Nonlinear Anal Differ Equ 4:43–50, 2016) [5] by introducing the transmission rate \( \eta \) from the exposed class E to infectious class I and converted the model into an Susceptible-Exposed-Infectious-Quarantine-Recovered epidemic model with saturated incidence rate. Determine the equilibrium points of the model and basic reproduction number \( R_{q} \) is obtained. Stability analysis have been discussed of both equilibrium points by Routh-Hurwitz criteria and Lyapunov function criteria. Also, Numerical simulations are carried out for the model.

Keywords

Epidemic model Compartmental model Equilibrium points Quarantine Basic reproduction number 

Mathematics Subject Classification

92D30 92D25 34D20 

References

  1. 1.
    Adebimpe, O., Waheed, A.A., Gbadamosi, B.: Modeling and analysis of an SEIRS epidemic model with saturated incidence. Int. J. Eng. Res. Appl. 3(5), 1111–1116 (2013)Google Scholar
  2. 2.
    Feng, Z., Thieme, H.: Recurrent outbreaks of childhood diseases revisited: the impact of isolation. Math. Biosci. 128, 93–130 (1995)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hethcote, H.W.: The mathematics of infectious disease. SIAM Rev. 42, 599–653 (2000)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hethcote, H.W., Zhien, M., Shengbing, L.: Effects of quarantine in six endemic models for infectious diseases. Math. Biosci. 180, 141–160 (2002)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Nirwani, N., Badshah, V.H., Khandelwal, R.: Dynamical study of an SIQR model with saturated incidence rate. Nonlinear Anal. Differ. Equ. 4(1), 43–50 (2016)CrossRefGoogle Scholar
  6. 6.
    Pathak, S., Maiti, A., Samanta, G.P.: Rich dynamics of an SIR epidemic model. Nonlinear Anal. Model. Control 15(1), 71–81 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, F., Yang, Y., Zhang, Y., Ma, J.: Global analysis of a SEIQV epidemic model for scanning worms with quarantine strategy. Int. J. Netw. Secur. 17(4), 423–430 (2015)Google Scholar
  8. 8.
    Zhang, X., Jia, J.: Stability of an SIR epidemic model with information variable and limited medical resources. Int. J. Res. Rev. Appl. Sci. (IJRRAS) 16(1), 91–103 (2013)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.School of Studies in MathematicsVikram UniversityUjjainIndia
  2. 2.Govt. Girls P.G. CollegeUjjainIndia

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