Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse

Abstract

This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due to the existence of second-order partial derivatives in the reaction–diffusion model with a delayed impulse, the methods of first-order ordinary differential equations from the previous literature cannot be effectively applied in this paper. However, with the help of the variational method and an appropriate boundedness assumption, a new synchronization criterion is derived, and its effectiveness is illustrated by numerical examples.