Stability Analysis of the Disease-Free Equilibrium State of a Mathematical Model of Measles Transmission Dynamics

Abstract

Measles is an acute viral infectious disease caused by the Measles morbillivirus, a member of the paramyxovirus family. The virus is primarily transmitted through direct contact and airborne droplets. In this study, a mathematical model was developed to examine the transmission dynamics of measles and explore effective control measures. The stability of measles-free equilibrium was analyzed, and the results indicate that the equilibrium is locally asymptotically stable when the basic reproduction number R0 is less than or equal to unity. Numerical simulations were conducted to validate the analytical findings, demonstrating that measles can be eradicated if a sufficiently high level of treatment is applied to the infected population.