One-dimensional models are important for developing, demonstrating andtesting new methods and approaches, which can be extended to more complexsystems. We design for a linear delay differential equation a reliable numericalmethod, which consists of two time splits as follows: (a) It is an exact scheme atthe early time evolution −τ ≤ t ≤ τ, where τ is the discrete value of the delay;(b) Thereafter, it is a nonstandard finite difference (NSFD) scheme obtained bysuitable discretizations at the backtrack points. It is shown theoretically andcomputationally that the NSFD scheme is dynamically consistent with respectto the asymptotic stability of the trivial equilibrium solution of the continuousmodel. Extension of the NSFD to nonlinear epidemiological models and its goodperformance are tested on a numerical example.
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