Abstract
In the study of disease dynamics SIR (Susceptible-InfectedRecovered) 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 τ .
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 R0 has
also been presented to prove the importance of delay in the dynamics of a
disease and its eradication.
Muhammad Asghar Ali, Muhammad Rafiq, Muhammad Ozair Ahmad. (2019) Numerical Analysis of a Modified SIR Epidemic Model with the Effect of Time Delay, Punjab University Journal of Mathematics, Volume 51, Issue 1.
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