| Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
|---|---|---|
| Article Number | 5 | |
| Number of page(s) | 27 | |
| Section | Population dynamics and epidemiology | |
| DOI | https://doi.org/10.1051/mmnp/2023003 | |
| Published online | 03 March 2023 | |
Forecast analysis and sliding mode control on a stochastic epidemic model with alertness and vaccination*
College of sciences, Northeastern University, Liaoning, Shenyang, 110004, China
** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
2
April
2022
Accepted:
12
January
2023
Abstract
In this paper, a stochastic SEIR epidemic model is studied with alertness and vaccination. The goal is to stabilize the infectious disease system quickly. The dynamic behavior of the model is analyzed and an integral sliding mode controller with distributed compensation is designed. By using Lyapunov function method, the sufficient conditions for the existence and uniqueness of global positive solutions and the existence of ergodic stationary distributions are obtained. The stochastic center manifold and stochastic average method are used to simplify the system into a one-dimensional Markov diffusion process. The stochastic stability and Hopf bifurcation are analyzed using singular boundary theory. An integral sliding mode controller with non-parallel distributed compensation is designed by linear matrix inequality (LMI) method, which realizes the stability of system and prevents the outbreak of epidemic disease. The correction of theoretical analysis and the effectiveness of controller are validated using numerical simulation performed in MATLAB/Simulink.
Mathematics Subject Classification: 37H20 / 92B05 / 93E03
Key words: Stochastic SEIR model / stationary distribution / Hopf bifurcation / sliding mode control
This study was funded by National Natural Science Foundation of China (61703083 and 61673100), China Scholarship Council (201706085041) and Fundamental Research Funds for the Central Universities (N2104007).
© The authors. Published by EDP Sciences, 2023
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