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Dynamical behavior of an SIR model with nonlinear incidence and saturated treatment rate

Anupam Khatua, Tapan Kumar Kar


In this article, we have introduced an SIR type epidemic model with the saturated treatment and nonlinear incidence rates. This model is studied in terms of stability and bifurcation. The existence conditions for the unique endemic equilibrium are obtained. The local stability of both the infection free and the infected steady states are discussed. Also by appropriate Lyapunov functional the global stability of both the uninfected and infected steady states are studied. Next through theoretical analysis, the existence of transcritical bifurcation at the disease free equilibrium and the Hopf bifurcation at the endemic equilibrium are established. In addition, several numerical simulations are also carried out.


Epidemic model, nonlinear incidence, global stability, transcritical bifurcation, Hopf bifurcation.

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