Discrete Gradient Methods for Solving SIRI Epidemic Model Numerically While Preserving First Integrals

Abstract

In this paper, we use discrete gradient methods for numerical solutions of mathematical models of epidemiology: a susceptible infected recovered infected (SIRI) model. The numerical results mimic the true and qualitatively correct behavior of the SIRI model. The first integrals (also known as the constant of motion) of the SIRI model obtained in literature using partial Lagrangian approach are well preserved by the discrete gradient method. The graphical results verify the advantages of the proposed schemes.