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Effect of Incubation Delay in an SIRS Model: Hopf Bifurcation and Stability Switch

In: Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models

Author

Listed:
  • Tanuja Das

    (Indian Institute of Technology Patna, Department of Mathematics)

  • Prashant K. Srivastava

    (Indian Institute of Technology Patna, Department of Mathematics)

Abstract

In this work, we propose and analyse an SIRS compartmental model with discrete time delay where the delay reflects the incubation period for the disease. Further, considering the inhibitory effect on healthy people of disease spread and consequent change in behavioral response, we introduce a non-monotonic incidence rate in simplified Monod-Haldane form in the model. We obtain that the disease will die out if the basic reproduction number is less than one, and otherwise it will persist in system. The local stability property of system is studied. The change is stability of endemic equilibrium is observed through Hopf bifurcation by choosing the time delay as bifurcation parameter. We observe that the stability property of endemic equilibrium change from stable to unstable due to increase of time delay and ultimately the system dynamics follows the oscillatory pattern. Numerically, for any fixed delay, it is shown that increased information level increases the possibility that system will be stable. However, for any fixed delay, increased disease transmission rate reduces the possibility that system will be stable.

Suggested Citation

  • Tanuja Das & Prashant K. Srivastava, 2022. "Effect of Incubation Delay in an SIRS Model: Hopf Bifurcation and Stability Switch," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Stability and Oscillations in Environmental, Social, and Biological Models, pages 367-382, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12515-7_20
    DOI: 10.1007/978-3-031-12515-7_20
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