Title: Threshold for vaccination in measles and its vertical transmission

Authors: Nita H. Shah; Zalak A. Patel; Bijal M. Yeolekar

Addresses: Department of Mathematics, Gujarat University, Ahmedabad, Gujarat 380009, India ' L. D. College of Engineering, Ahmedabad, Gujarat 380015, India ' Department of Mathematics, Gujarat University, Ahmedabad, Gujarat 380009, India

Abstract: This study analyses measles transmission vertically with vaccination failure and delay of vaccination. The effect of infected newborns as a time delay is analysed. Time delay is considered as a loss of maternal immunity amongst newborns. The system of non-linear differential equations for the proposed problem is formulated. The next generation matrix method is used to find the reproduction number, and to obtain the stability of the infection free as well as the endemic equilibrium. Effect of time delay in vaccination has been studied for disease-free equilibrium. The local and global stability of the system is analysed. Sensitivity of the key parameters is measured using numerical simulation and observed that it supports the analytical results.

Keywords: measles; pulse vaccination; stability; threshold; time delays; vertical transmission.

DOI: 10.1504/IJDSDE.2017.085828

International Journal of Dynamical Systems and Differential Equations, 2017 Vol.7 No.2, pp.157 - 168

Received: 04 Aug 2016
Accepted: 15 Oct 2016

Published online: 01 Aug 2017 *

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