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In this work, nonlinear epidemic models for measles, dengue fever, smoking, and SVIR are considered in order to understand the outbreaks of this epidemic disease. Developed unconditionally convergent nonstandard finite difference scheme by applying Mickens approach with as this will provide a feasible solution to overcome its disease risk as these are the main requirement for the dynamical systems in real-life solution. This method proved to be a very efficient technique for solving epidemic models to control infection diseases. Numerical simulations are carried out to support the analytic results.
Keywords: Epidemic model; Non-standard finite difference scheme; Qualitative analysis; Stability analysis