Mathematical model for the study of transmission and control of measles with immunity at initial stage

J. A. Akingbade; R. A. Adetona; B. S Ogundare

doi:10.26637/MJM0604/0019

Abstract

In this article, we present a transmission and control model for measles infection which is one of the most contagious diseases. The model dynamics was studied to understand the epidemic phenomenon for its control. We examined the qualitative properties with the existing techniques used to discuss the local and global stability of the disease-free and endemic equilibria. The disease-free equilibrium was found to be globally stable when $R_0<1$ and the endemic equilibrium is globally stable when $R_0>1$. To investigate whether initial immunity has any effect on the infective, we simulate our model on various sets of parameter values. The results of simulation showed that there is strong significant effect on infective if at least $50 \%$ of the population possessed strong immunity or immunized against measles infection at initial stage.

Keywords:

Measles, deterministic, open population, epidemic, immunity, basic reproductive number (R0), disease-free equilibrium, endemic equilibrium, asymptotic stability, Lyapunov function, S−I−R model

Mathematics Subject Classification:

Mathematics

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J. A. Akingbade Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun State, Nigeria.
R. A. Adetona Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun State, Nigeria.
B. S Ogundare Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun State, Nigeria.

Pages: 823-834
Date Published: 01-10-2018
Vol. 6 No. 04 (2018): Malaya Journal of Matematik (MJM)

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