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Stability and Bifurcation analysis of SIR Model with Virus Mutation using Delay Differential Equation
  • pankaj kumar
pankaj kumar
Lovely Professional University Division of Research and Development

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A mathematical examination of the SIR model under mutation is presented in this paper, by integrating an incubation time lag and a general nonlinear incidence rate. When the virus mutates, the recovered population loss its immunity. A time lag gives for a grace period before people become vulnerable once more. At the rate ‘c,’ they become vulnerable, which is the recovery rate, depending upon their status at (t-τau). The three-state variable are S (Susceptible population), I (Infected population) and R (Recovered population). A non-zero equilibrium point has been found. Stability and Directional analysis are performed about this non zero equilibrium. Hopf-Bifurcation occurred when the delay parameter τ goes beyond a critical point value. Sensitivity analysis is performed by using direct method and Directional analysis is performed by using K. R. Schneider, ‘Hassard, B. D. [22]. Numerical simulation is done to support analytical results using MATLAB.