Abstract
This paper presents an SIQR patch model that combines population migration and entry–exit screening. The threshold for disease extinction is determined using the next-generation matrix method. By constructing the Lyapunov function, the global asymptotic stability of the disease-free equilibrium is demonstrated when R0 < 1. The local asymptotic stability of the endemic equilibrium is shown using the Hurwitz criterion, and it is found that the disease is uniformly persistent when R0 > 1. The influence of screening and migration on disease dynamics is discussed via numerical simulations. Our findings highlight the significance of the detection rate as a vital index in disease transmission and emphasize the effectiveness of screening strategies in preventing outbreaks. Therefore, during an outbreak, it is recommended to establish checkpoints in regions with high mobility to identify and isolate potentially infected individuals, thereby reducing the widespread dissemination of the pandemic.
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