A Comparative Epidemiological Stability Analysis of Predictor Corrector Type Non-Standard Finite Difference Scheme for the Transmissibility of Measles

Abstract In this article, a predictor-corrector type non-standard finite difference scheme has been formulated to avoid unnatural chaos, and numerical instabilities depend on a long time step, lead to a better strategy for overcoming the transmission of infectious diseases. The construction, development, and analysis of our proposed numerical scheme is done for the SEIR epidemiological model regarding the transmission dynamics of measles. Based on the mathematical study of the proposed scheme, the stability analyses are performed in detail. Further, the behavior of the scheme is accessed by the evaluation of the Eigenvalues of the Jacobian at a steady state. MATLAB algorithm is used for numerical simulations, and results demonstrated that the NSFD-PC scheme double refines the solution and gives physically realistic solutions even for large step sizes. The effectiveness of the scheme has been investigated by comparison with renowned numerical methods in literature like the RK4 and Euler method of a predictor-corrector type. It has been found that the presented scheme is dynamically compatible with the continuous system, unconditionally convergent, and satisfies the positivity of the state variables involved in the system of the SEIR model. Conclusively, the proposed numerical scheme preserves all essential control measuring features of the corresponding dynamical system and reduces additional cost when examined over long periods. Therefore, it is highly recommended.