The SAITS epidemic spreading model and its combinational optimal suppression control

Wei Ding; Li Ding; Zhengmin Kong; Feng Liu; Wei Ding; Li Ding; Zhengmin Kong; Feng Liu

doi:10.3934/mbe.2023157

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3342-3354. doi: 10.3934/mbe.2023157

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Research article

The SAITS epidemic spreading model and its combinational optimal suppression control

1.
School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China
2.
School of Systems and Enterprises, Stevens Institute of Technology, Hoboken, NJ 07030, USA

Academic Editor: Vladimir Mityushev

Received: 17 October 2022 Revised: 25 November 2022 Accepted: 29 November 2022 Published: 05 December 2022

In this paper, an SAITS epidemic model based on a single layer static network is proposed and investigated. This model considers a combinational suppression control strategy to suppress the spread of epidemics, which includes transferring more individuals to compartments with low infection rate and with high recovery rate. The basic reproduction number of this model is calculated and the disease-free and endemic equilibrium points are discussed. An optimal control problem is formulated to minimize the number of infections with limited resources. The suppression control strategy is investigated and a general expression for the optimal solution is given based on the Pontryagin's principle of extreme value. The validity of the theoretical results is verified by numerical simulations and Monte Carlo simulations.
- SAITS model,
- complex network,
- epidemic spreading,
- optimal control
Citation: Wei Ding, Li Ding, Zhengmin Kong, Feng Liu. The SAITS epidemic spreading model and its combinational optimal suppression control[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3342-3354. doi: 10.3934/mbe.2023157

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Abstract

In this paper, an SAITS epidemic model based on a single layer static network is proposed and investigated. This model considers a combinational suppression control strategy to suppress the spread of epidemics, which includes transferring more individuals to compartments with low infection rate and with high recovery rate. The basic reproduction number of this model is calculated and the disease-free and endemic equilibrium points are discussed. An optimal control problem is formulated to minimize the number of infections with limited resources. The suppression control strategy is investigated and a general expression for the optimal solution is given based on the Pontryagin's principle of extreme value. The validity of the theoretical results is verified by numerical simulations and Monte Carlo simulations.

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