CLOSED-FORM SOLUTIONS FOR A REACTION-DIFFUSION SIR MODEL WITH DIFFERENT DIFFUSION COEFFICIENTS

We use Lie point symmetries to obtain reductions and closed-form solutions for the reaction-diffusion SIR epidemic model. We determine that the Lie algebra for this model is three-dimensional. By invoking these Lie symmetries, we establish closed-form solutions for the reaction-diffusion SIR model. We employ the appropriate initial and boundary conditions to relate the derived closed-form solution to a real-world scenario. Furthermore, we utilize the closed-form solutions to generate a graphical representation of the densities of susceptible, infected, and removed individuals. We also perform a sensitivity analysis of the density of infected individuals to gain valuable insights into the transmission dynamics of the infectious disease.