Int. J. Dynamical Systems and Differential Equations, Vol. 7, No. 2, 2017 157 Copyright © 2017 Inderscience Enterprises Ltd. Threshold for vaccination in measles and its vertical transmission Nita H. Shah* Department of Mathematics, Gujarat University, Ahmedabad, Gujarat 380009, India Email: nitahshah@ gmail.com *Corresponding author Zalak A. Patel L. D. College of Engineering, Ahmedabad, Gujarat 380015, India Email: zalak23patel@gmail.com Bijal M. Yeolekar Department of Mathematics, Gujarat University, Ahmedabad, Gujarat 380009, India Email: bijalyeolekar28@gmail.com 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. Reference to this paper should be made as follows: Shah, N.H., Patel, Z.A. and Yeolekar, B.M. (2017) ‘Threshold for vaccination in measles and its vertical transmission’, Int. J. Dynamical Systems and Differential Equations, Vol. 7, No. 2, pp.157–168. Biographical notes: Nita H. Shah is a Professor in the Department of Mathematics at the Gujarat University, Ahmedabad. She has 20 years of research experience in inventory management, forecasting and information technology and information systems. She has published 300+ articles in international journals, including APJOR (Singapore), International Journal of Production Economics, Omega, CCERO (Belgium), ECPE (Romania),