A Mathematical Model for the Transmission of Measles with Passive Immunity

E.M. Musyoki¹ , R.M. Ndung’u² , S. Osman³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.1-8, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.18

Online published on Apr 30, 2019

Copyright © E.M. Musyoki, R.M. Ndung’u, S. Osman . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
A mathematical model of the transmission dynamics of measles incorporating passively immune class is developed. The dynamics of the disease are expressed with the help of a set of ordinary differential equations. The model is analysed qualitatively and quantitatively. Equilibrium points of the determined and their stability analysed. From the study it has been shown that for a stable disease-free equilibrium the reproduction number is less than 1 and more than 1 for an unstable disease-free equilibrium. The spread of the disease in the population is dependent on the level of between the susceptible individuals and the infected individuals. The rate at which passive immunity in an infant is lost also has a great impact on the spread of the disease.

Key-Words / Index Term :
Equilibrium points, disease free equilibrium, measles, basic reproduction number, stability

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