Numerical Analysis of a Modified SIR Epidemic Model with the Effect of Time Delay

In the study of disease dynamics SIR (Susceptible-Infected-Recovered) models have a great importance. In this paper, a modified SIR epidemic model for the transmission dynamics of an infectious disease with the susceptibility effect, in a human population, has been proposed. Its corresponding SIR time delay epidemic model has also been presented and analysed numerically by developing an unconditionally convergent numerical model i.e. Non Standard Finite Difference (NSFD) Scheme. It has been shown that the proposed discrete model (NSFD scheme) must exhibit the same behaviour as the continuous model and preserves all the essential properties like positivity and boundedness of the solution, stability and dynamical consistency, for all time steps h and delay factors tau. A well-known numerical scheme, RK-4, is used to compare the results, which fails at large time step and/or delay factor. Finally, the effect of time delay on the dynamics of the disease and threshold parameter R-0 has also been presented to prove the importance of delay in the dynamics of a disease and its eradication.