Modelling childhood disease outbreak in a community with inflow of susceptible and vaccinated new-born
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Date
2016
Authors
Yano, T.P.
Oluwole, D.M.
Malonza, D.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Research India Publications
Abstract
This paper investigates the transmission dynamics of a Childhood disease
outbreak in a community with direct inflow of susceptible and vaccinated
new-born. Qualitative analysis of the SEIR nonlinear model is performed for
disease free and endemic equilibria using the stability theory of differential
equations. The disease free state is found to be both locally and globally
asymptotically stable when the vaccination reproductive number v R is less than
unity. In addition, the model exhibits transcritical forward bifurcation
phenomenon and the sensitivity indices of the vaccination reproductive
number with respect to various model parameters is determined. Using the
Adomian decomposition method (ADM) and the fourth order Runge-Kutta
integration scheme (RK4), the semi-analytical and numerical solutions of the
nonlinear model are obtained. Pertinent results are displayed graphically and
in tabular form. A vaccination coverage threshold is obtained above which the
disease will be effectively eliminated from the community.
Description
Research Article
Keywords
Childhood diseases, Epidemiological model, Vaccination coverage, Forward bifurcation, Sensitivity indices, Adomian decomposition method, Runge-Kutta integration scheme
Citation
Global Journal of Pure and Applied Mathematics. I Volume 12, Number 5 (2016), pp. 3895-3916; 0973-1768