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In the study, measles disease was modelled using mathematical modelling approach of compartmental Susceptible-Exposed-Infectives-Recovered (SEIR) epidemiological model to study the prevalence and control of the measles disease. By using measles data pertinent to Senegal, we derived the reproduction number for the model, carried out the stability of the model, established the existence and uniqueness of the solution to the model. Runge-Kutta fourth-order method is used to solve the model numerically. This is used to do a simulation of the model by using MATLAB programming language to determine the best strategies to adopt in controlling the measles disease. The model realized that the exposed individuals at latent period play a significant role in controlling the disease. It is established that if more people at the latent period go for treatment and therapy during this state, before they become infective, the disease will be eradicated more speedily with time.