Numerical Modeling of SEIR Measles Dynamics with Diffusion

A novel unconditionally positive finite difference (FD) scheme is developed to solve numerically SEIR measles epidemic model with diffusion. In population dynamics, positivity of subpopulations is an essential requirement. The proposed FD scheme preserves the positivity of the solution of the model. The consistency and unconditional stability is proved. The proposed FD scheme is explicit in nature which is an extra feature of this scheme. Comparisons are also made with forward Euler explicit FD scheme and Crank Nicolson implicit FD scheme. Simulations of a numerical test are also presented to verify all the attributes of the proposed scheme.