Muhammad Iqbal2025-11-212025-11-212021-06-07https://escholar.umt.edu.pk/handle/123456789/11426This thesis is devoted for the numerical study of susceptible vaccinated exposed infected recovered (sveir) epidemic model of pneumonia disease dynamics. This model is solved numerically with three different numerical techniques, forward euler, runge-kutta scheme (rk-4) and the proposed nonstandard finite diference (nsfd) techniques. The proposed nsfd technique becomes more effective and trustable numerical technique than forward euler and rk-4 techniques. Nsfd technique employs all necessary characteristics of continuous sveir pneumonia epidemic model like positivity, stability of equilibria while well-known forward euler and rk-4 techniques cannot hold these characteristics. Furthermore, the proposed technique is independent of time step size while forward euler and rk-4 depend on the time step size. The numerical simulations with the aid of a numerical test is presented for the validations of all the traits.enThesis