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

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