Model of strategy control for delayed panic spread in emergencies

Rongjian Lv; Hua Li; Qiubai Sun; Bowen Li; Rongjian Lv; Hua Li; Qiubai Sun; Bowen Li

doi:10.3934/mbe.2024004

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 75-95. doi: 10.3934/mbe.2024004

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Model of strategy control for delayed panic spread in emergencies

1.
School of Electronics and Information Engineering, University of Science and Technology Liaoning, Anshan, Liaoning, China
2.
School of Business Administration, University of Science and Technology Liaoning, Anshan, Liaoning, China

Academic Editor: Xiangsheng Wang

Received: 12 September 2023 Revised: 24 November 2023 Accepted: 30 November 2023 Published: 08 December 2023

In emergencies similar to virus spreading in an epidemic model, panic can spread in groups, which brings serious bad effects to society. To explore the transmission mechanism and decision-making behavior of panic, a government strategy was proposed in this paper to control the spread of panic. First, based on the SEIR epidemiological model, considering the delay effect between susceptible and exposed individuals and taking the infection rate of panic as a time-varying variable, a SEIR delayed panic spread model was established and the basic regeneration number of the proposed model was calculated. Second, the control strategy was expressed as a state delayed feedback and solved using the exact linearization method of nonlinear control system; the control law for the system was determined, and its stability was proven. The aim was to eradicate panic from the group so that the recovered group tracks the whole group asymptotically. Finally, we simulated the proposed strategy of controlling the spread of panic to illustrate our theoretical results.
- SEIR delayed model,
- nonlinear control,
- state feedback,
- strategy control,
- numerical simulation
Citation: Rongjian Lv, Hua Li, Qiubai Sun, Bowen Li. Model of strategy control for delayed panic spread in emergencies[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 75-95. doi: 10.3934/mbe.2024004

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Abstract

In emergencies similar to virus spreading in an epidemic model, panic can spread in groups, which brings serious bad effects to society. To explore the transmission mechanism and decision-making behavior of panic, a government strategy was proposed in this paper to control the spread of panic. First, based on the SEIR epidemiological model, considering the delay effect between susceptible and exposed individuals and taking the infection rate of panic as a time-varying variable, a SEIR delayed panic spread model was established and the basic regeneration number of the proposed model was calculated. Second, the control strategy was expressed as a state delayed feedback and solved using the exact linearization method of nonlinear control system; the control law for the system was determined, and its stability was proven. The aim was to eradicate panic from the group so that the recovered group tracks the whole group asymptotically. Finally, we simulated the proposed strategy of controlling the spread of panic to illustrate our theoretical results.

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