Numerical Treatments of the Transmission Dynamics of West Nile Virus and It’s Optimal Control N. H. Sweilam, O. M. Saad and D. G. Mohamed

Abstract

In this paper, numerical studies for transmission dynamics of West Nile Virus mathematical model are presented. The nonstandard finite difference method is introduced to solve the posed model. Positivity, boundedness, and convergence of the nonstandard finite difference scheme are studied. Also, numerical stability analysis of fixed points is studied. An optimal control problem is formulated and studied theoretically using the Pontryagin's maximum principle. The obtained results by using nonstandard finite difference method are compared with standard finite difference method. It can be concluded that the nonstandard finite difference method is more efficient and preserves the stability and positivity of the solutions in large regions.