MATHEMATICAL ANALYSIS OF RUBELLA DISEASE DYNAMICS: THE ROLE OF VERTICAL TRANSMISSION AND VACCINATION

Abstract

Rubella known as German measles constitutes a significant threat to global health, as every individual in the human population is vulnerable to its highly contagious and severe effects. The risk of congenital rubella syndrome is significantly elevated when pregnant women contract the virus, transmitting it to the fetus. This research develops and examines a mathematical framework to simulate rubella's transmission patterns. The model categorizes the population into seven distinct compartments: Susceptible individuals S(t), Vaccinated individuals V(t), Persons with lifelong immunity after receiving a second vaccine dose P(t), Infected individuals I(t), Treated individuals T(t), Recovered individuals R(t). A detailed examination of the model's qualitative features is presented, the formulated model was shown to have non-negative solutions in feasible regions of human population. Furthermore, the model has a stable disease-free equilibrium if the basic reproduction number is less than unity, unstable otherwise. Computational experiments were performed using MATLAB R2013a to examine the effects of critical parameters on rubella transmission, yielding insightful graphical representations. Simulation studies revealed that reducing contact and vertical transmission rates, while increasing recovery rates, vaccination rates (first and second doses), and maternal immunization, are vital for mitigating rubella's impact in the population.