Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 6 February 2021 / Approved: 8 February 2021 / Online: 8 February 2021 (12:05:46 CET)
Version 2 : Received: 14 April 2021 / Approved: 14 April 2021 / Online: 14 April 2021 (16:10:50 CEST)

How to cite: Rao, R. Stability and Stabilization of Ecosystem for Epidemic Virus Transmission Under Neumann Boundary Value Via Impulse Control. Preprints 2021, 2021020197 (doi: 10.20944/preprints202102.0197.v2). Rao, R. Stability and Stabilization of Ecosystem for Epidemic Virus Transmission Under Neumann Boundary Value Via Impulse Control. Preprints 2021, 2021020197 (doi: 10.20944/preprints202102.0197.v2).

## Abstract

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. Moreover, delayed feedback ecosystem with reaction-diffusion item is considered, and utilizing impulse control results in the globally exponential stability criterion of the delayed ecosystem. It is worth mentioning that the Neumann zero-boundary value that the infected and the susceptible people or animals should be controlled in the epidemic prevention area and not allowed to cross the border, which is a good simulation of the actual situation of epidemic prevention. 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. Besides, utilizing Laplacian semigroup derives the $p$th moment stability criterion for the impulsive ecosystem.

## Subject Areas

Neumann boundary value; Laplacian semigroup; Poincare inequality lemma; impulse control; Lyapunov-Razumikhin method

Comment 1
Commenter: Ruofeng Rao
Commenter's Conflict of Interests: Author
Comment: Dear editor,
The main change is the addition of Theorem 4.1.
Best regards,
Ruofeng Rao, the author of this manuscript.
E-mail: [email protected]; [email protected]

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