Dynamical Transmission and Mathematical Analysis of SIR Measles Epidemiological Model

Abstract

Farah Ashraf, Aqeel Ahmad, Muhammad farman and MO Ahmad

In this work, we presented a nonlinear time fractional model of measles in order to understand the outbreaks of this epidemic disease. The stability analysis and sensitivity analysis of the model is provided and the certain threshold value of the basic reproduction number R0 >1, disease free and endemic equilibrium point of the model is also calculated. We develop unconditionally convergent nonstandard finite difference scheme by applying Mickens approach Ø(h)=h+O(h2 ). This method proved to be very efficient technique for solving epidemic models to control the infection diseases. We also discussed the qualitative behavior of the model and numerical simulations are carried out to support the analytic results.

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