Optimization and control in rubella transmission dynamics: A boundedness-preserving numerical model with vaccination

Abstract

Rubella is an infectious disease that can spread globally. It spreads in the subtropics as well as the tropics. Although it is commonly thought to be a non-fatal condition, there are several circumstances in which it can be fatal. Pregnant women infected with the Rubella virus face a high risk of fetal development. The main goal of this study is to look into a model for the spread of Rubella while considering a vaccination campaign as a control measure. The positivity and boundedness of the re-infection rubella transmission and vaccination model are investigated. The local and global stability of the equilibrium points is examined. The sensitivity of parameters is also investigated. Three different techniques forward Euler, RK-4, and non-standard finite difference (NSFD) method are developed for the numerical solution, and their simulation results are examined. Among these three, the NSFD method is superior due to its convergence and positive behavior for all step size values. For some values of the step size, the other two techniques failed to produce positivity and convergent solutions. Analytically, the proposed model's convergence, positivity, boundedness, and consistency are investigated. Finally, the impact of the Rubella vaccine on infected populations has been examined, revealing that vaccination is one of the most effective ways to prevent rubella transmission.