Epidemic reaction-diffusion systems with two types of boundary conditions

Abstract

We investigate an epidemic reaction-diffusion system with two different types of boundary conditions. For the problem with the Neumann boundary condition, the global dynamics is fully determined by the basic reproduction number $\mathcal{R}_0$. For the problem with the free boundary condition, the disease will vanish if the basic reproduction number $\mathcal{R}_01$ and the initial infected radius $g_0$ is suitably large. Main results reveal that besides the basic reproduction number, the size of initial epidemic region and the diffusion rates of the disease also have an important influence to the disease transmission.

Keywords

• SIRS model
• reaction-diffusion system
• global dynamics
• Neumann boundary condition
• free boundary condition