Stability and Bifurcation analysis of SIR Model with Virus Mutation
using Delay Differential Equation
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.
. Numerical simulation is done to support analytical results