The Exact Solutions of a Diffusive SIR Model via Symmetry Groups

Abstract

The focus of this paper is to investigate the exact solutions of a diffusive susceptible‐infectious‐recovered (SIR) epidemic model, characterized by a nonlinear incidence. A four‐dimensional Lie point symmetry algebra is obtained for this model. We utilize the Lie symmetries to deduce the optimal system of one‐dimensional subalgebras. The reductions and group‐invariant solutions are obtained with the aid of these subalgebras. We also derive new group‐invariant solutions and reductions for the underlying model via subalgebras that are related to the optimal system by adjoint maps. We developed the diffusive susceptible‐infectious‐quarantined (SIQ) model with quarantine‐adjusted incidence function to understand the transmission dynamics of COVID‐19.