An Efficient Numerical Study of Measles Transmission Dynamics With Time Delay

Measles is a highly contagious viral disease that remains a public-health concern in populations with suboptimal vaccination coverage. In this study, a delayed SEIR-type epidemic model is formulated to investigate measles transmission dynamics, where the latent period is incorporated through a discrete time delay. The model includes susceptible, exposed, infectious, and recovered compartments, and an explicit expression for the basic reproduction number R0 is derived. The disease-free and -endemic equilibria are determined, and their local and global stability are analyzed to assess the impact of delay on system dynamics. To support the theoretical findings, numerical approximations are performed using Euler, Runge–Kutta, and nonstandard finite difference (NSFD) schemes. Particular emphasis is placed on the ability of these methods to preserve key qualitative properties such as positivity and boundedness. The results demonstrate that the NSFD scheme maintains consistency with the continuous model and provides reliable qualitative behavior. Furthermore, numerical simulations illustrate the influence of time delay on the evolution of the epidemic system.