Threshold for vaccination in measles and its vertical transmission
by Nita H. Shah; Zalak A. Patel; Bijal M. Yeolekar
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 7, No. 2, 2017

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.

Online publication date: Tue, 15-Aug-2017

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