Global Stability Analysis to Measles Transmission Dynamic with Vaccination

Abstract

Measles remains a significant public health concern globally, despite the availability of vaccines. Understanding the dynamics of measles transmission through mathematical modeling is crucial for designing effective control strategies. In this study, we present a  comprehensive mathematical model that incorporates susceptible, exposed, infectious, recovered and vaccinated compartmentsto  capture the complexity of measles dynamics. We conducted a global stability analysis of theproposed model to explore the long-term  behavior of measles transmission dynamics. Byanalyzing the model's equilibrium points and their stability properties, we elucidate the  conditionsunder which measles can persist or be eradicated within a population. Our analysis accountsforthe impact of vaccination  coverage and vaccine efficacy on the dynamics of measles transmission. Furthermore, we perform sensitivity analysis to identify key  parameters driving the persistenceorelimination of measles. We assess the effectiveness of vaccination strategies in  reducing measles incidence and our findings provide valuable insights into the dynamics of measles transmission and the potential impact  of vaccination programs on disease control which shows a 19.5% vaccination rate effectively prevents transmission, while a 1.25 percent  decreases transmission but cannot completely eliminate it, and a 0.57% rate suggests significant spread necessitates further actions or  higher vaccination rates.