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Effect of isolation in an infectious disease

T. K. Kar, Soovoojeet Jana, Abhijit Ghorai

Abstract


In this research work we have proposed and analyzed an SIR epidemic model of an infectious disease incorporating constant isolation for the susceptible individual. By carrying out the global analysis of the model and studying the stability of the disease free equilibrium and endemic equilibrium, we show that isolation would be highly effective to control the infectious disease. It is shown that the model undergoes a transcritical bifurcation and Hopf bifurcation. Also center manifold theorem and normal form method are used to find the nature of the Hopf bifurcation as well as the nature of the bifurcating limit cycle. All the analytical results are verified through numerical simulations.

Keywords


Epidemic model, nonlinear incidence rate, isolation, basic reproduction number, transcritical bifurcation.

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