Lie symmetry analysis of stochastic SIRS model

Abstract

In this paper, we discuss the connection between Lie symmetry of a SIRS stochastic differential equations and its integrability. A derived determining equation is obtained and used to find the admitted Lie point symmetries of the stochastic model. A third dimensional system is reduced into a one dimensional to achieve a linear model by mean of Symmetry analysis techniques and obtained the corresponding Lie bracket.