On the Existence, Uniqueness, Stability of Solution and Numerical Simulations of a Mathematical Model for Measles Disease
Abstract: In the study, we model a measles disease using deterministic Susceptible-Exposed-Infectives-Recovered (SEIR) epidemiological model to study the prevalence and control of the measles disease in Senegal. By using measles data pertinent to Senegal , we 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 latent period goes for treatment and therapy during this state, before they become infectives, the disease will be eradicated more speedily with time.
Keywords: Measles Disease, Epidemiological Model, SEIR Model, Existence and Uniqueness of Solution, Stability, Basic Reproduction Number, Runge-Kutta, Numerical Simulations.
How to cite this article:
Samuel O. Sowole, Daouda Sangare, Abdullahi A. Ibrahim and Isaac A. Paul, On the Existence, Uniqueness, Stability of Solution and Numerical Simulations of a Mathematical Model for Measles Disease, International Journal of Advances in Mathematics, Volume 2019, Number 4, Pages 84-111, 2019.