Stability and Stabilization of Ecosystem for Epidemic Virus Transmission Under Neumann Boundary Value Via Impulse Control

In this paper, by using the variational method, a sufficient condition for the unique existence of the stationary solution of the reaction-diffusion ecosystem is obtained, which directly leads to the global asymptotic stability of the unique equilibrium point. Besides, employing impulse control technique derives the globally exponential stability criterion of delayed feedback ecosystem.And numerical examples illuminate the effectiveness of impulse control, which has a certain enlightening effect on the actual epidemic prevention work . That is, in the face of the epidemic situation, taking a certain frequency of positive and effective epidemic prevention measures is conducive to the stability and control of the epidemic situation. particularly, the newly-obtained theorems quantifies this feasible step.