Synchronization for Reaction–Diffusion Switched Delayed Feedback Epidemic Systems via Impulsive Control

Ruofeng Rao () and Quanxin Zhu ()
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Ruofeng Rao: College of Mathematics, Chengdu Normal University, Chengdu 611130, China
Quanxin Zhu: School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China

Mathematics, 2024, vol. 12, issue 3, 1-12

Abstract: Due to the facts that epidemic-related parameters vary significantly in different stages of infectious diseases and are relatively stable within the same stage, infectious disease models should be switch-type models. However, research on switch-type infectious disease models is scarce due to the complexity and intricate design of switching rules. This scarcity has motivated the writing of this paper. By assuming that switching instants and impulse times occur at different moments, this paper proposes switch rules suitable for impulse control and derives synchronization criteria for reaction–diffusion switch-type infectious disease systems under impulse control. The effectiveness of this method is validated through numerical simulations. It is important to mention that, based on the information available to us, this paper is currently the sole study focusing on switch-type reaction–diffusion models for infectious diseases.

Keywords: reaction–diffusion; Lyapunov–Krasovskii functional; switched epidemic systems; impulsive control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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