Mathematical and Stability Analysis of the Measles Dynamics Model with Vaccination
DOI:
https://doi.org/10.57125/FEM.2025.09.30.04Abstract
Measles, characterized by symptoms such as encephalitis, pneumonia, and blindness is the leading cause of death among young children. In an attempt to understand the mechanism behind the transmission dynamics of measles and proffer control measures to curb its spread in human population, a non-linear SEIR deterministic epidemiological model incorporating vaccination is developed and analysed in this study. The theory of positivity and boundedness of solution is used to establish the well-posedness of the model and the effective reproduction number is obtained using the next generation matrix approach. Findings from the analysis revealed that the model possesses two equilibrium points, the measles-free and endemic equilibrium points. Additionally, quadratic Lyapunov function is used to investigate the global asymptotic dynamics of the endemic equilibrium point. The analysis showed that the measles-free equilibrium point is globally asymptotically stable when the effective reproduction number is less than unity (i.e., R0=0.59765<1), while the endemic equilibrium point is also globally asymptotically stable when R0=5.97652>1. Furthermore, key epidemiological parameters driving the menace of measles are investigated and identified using the normalized forward sensitivity indices with a view to suggesting effective control measures that could be used in curbing the dynamical spread of measles in the population.References
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