Mathematical analysis of SIR Model with Virus Mutation using Delay Differential Equation


  • Pankaj Kumar, Raminder Pal Singh


SIR model, Non-zero Equilibrium, Delay, Time lag, Incubation period, Asymptotic stability, Hopf-bifurcation, Critical Point, Mutation


This work presents a mathematical analysis of the SIR model with mutation by incorporating an incubation time lag and a generic non-linear incidence rate based on law of mass action. When the virus mutates, the restored population loses immunity and becomes susceptible again at the mutation rate, denoted by the letter ‘c’. This mutation takes a grace time given by τ before occurring. S(t), I(t), and R(t) respectively denote the three-state variables susceptible population, infected population, and recovered population. The fundamental reproduction number ‘R_0’ is computed, and its importance to infected and recovered populations is visually illustrated. The non-zero equilibrium is considered for stability and bifurcation study. The Hopf-bifurcation condition occurs for critical point value of delay parameter. Using the direct technique, sensitivity analysis and directional analysis are carried out. MATLAB is used to do numerical simulations to support analytical conclusions