Numerical Modelling of SEIR on Two-Dose Vaccination Against the Rubella Virus

In this article, we determine non-linear terms under the modulation of dynamic transmission in childhood diseases analyzed to explore the effect of Rubella virus, along with double-dose vaccination strategy which was suggested by WHO. Firstly, basic properties of model were calculated such as positiveness, boundedness, disease free and endemic points. Model stability was proved at the disease-free and endemic equilibrium points. The Reproductive number was calculated using the next generation matrix method. Furthermore, sensitivity analysis is used to ascertain how parameter changes impact the system's dynamic behavior. We used Euler, Rk-4 and NSFD method. The purpose of the numerical simulations is to demonstrate the importance of the theoretical findings using numerical methods and the viability of the numerical schemes. Convergence and consistency analysis of NSFD scheme were proven. Additionally, we proved that NSFD is more reliable than Euler and RK4 through graphical interpretation. Incorporating this method enhanced the model's accuracy, stability, and predictions for rubella dynamics.