Matrix Nonstandard Numerical Schemes for Epidemic Models

Abstract

This paper is concerned with the construction and developing of several nonstandard finite difference (NSFD) schemes in matrix form in order to obtain numerical solutions of epidemic models. In particular, we deal with a classical SIR epidemic model and a seasonal model associated with the evolution of the transmission of respiratory syncytial virus RSV in the human population. The first model is an autonomous differential equation system, and the second one is a nonautonomous one which generally is more difficult to be solved. The numerical schemes developed here can be used in other general epidemic models based on ordinary differential equations. One advantage of the developed methodology is that can be used easily by the scientific community without special knowledge. In addition, these NSFD schemes which are based on the the nonstandard finite difference methods developed by Mickens solve numerically systems describing epidemics with less computational effort. Finally, with these matrix NSFD schemes it can be exploited more easily matrix operations advantages.