### African Journal ofMathematics and Computer Science Research

• Abbreviation: Afr. J. Math. Comput. Sci. Res.
• Language: English
• ISSN: 2006-9731
• DOI: 10.5897/AJMCSR
• Start Year: 2008
• Published Articles: 254

Article in Press

## Analysis of A Vaccination Mathematical Model of An Infectious Measles Disease

###### Ugochukwu Emmanuel Nwafor , Simeon Chioma Inyama, Andrew Omame and Hope Ifeyinwa Mbachu

•  Received: 31 January 2018
•  Accepted: 23 August 2018
Mathematical modeling has provided a lot of solutions to the control of spread of epidemic diseases. In this paper, the analysis of a vaccination Mathematical model of an infectious Measles disease was carried out. The Model which is an SVEIR epidemic model was investigated in which the incidence rate was considered. The model was formulated and analytical study of the formulated model showed that the model has two equilibrium points (disease free equilibrium (DFE) and endemic equilibrium (EE)). Using our model, we proved the positivity of solutions and then obtained the basic reproduction number for determining whether the disease dies out completely or not. The local stability of disease-free equilibrium was proved, and determined by the basic reproduction number. Using Lyapunov function method it was proved that the DFE and EE were globally asymptotically stable. Furthermore, numerical simulations were carried out on the model to make the analytical studies easy to understand. Simulation results show that the number of susceptible, infected and vaccinated individuals is consistent with theoretical analysis (as could be seen in the attached graphs) and the results are presented and discussed quantitatively to illustrate the solution.