Global Existence and Blow-up of Solutions to a Coupled Parabolic System

In this paper, we investigate the global existence and blow-up properties of the solutions of highly nonlinear coupled SIR epidemic disease model with cross-diffusion terms and no flux type boundary conditions. Under the suitable assumptions on the nonlinear source functions we prove the global existence and blow-up of the solutions. Further, we prove that the blow-up property of the solutions only depends on the first eigenvalue of -Δ in a bounded domain Ω. Finally, we present the numerical simulations to illustrate the theoretical results.