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.