Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay

Xue Liu; Xin You Meng; Xue Liu; Xin You Meng

doi:10.3934/mbe.2023918

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 12: 20748-20769. doi: 10.3934/mbe.2023918

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Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay

Xue Liu ,
Xin You Meng ^,

School of Science, Lanzhou University of Technology, Gansu 730050, China

Academic Editor: Mehmet Yavuz

Received: 30 August 2023 Revised: 21 October 2023 Accepted: 01 November 2023 Published: 17 November 2023

In this paper, we mainly consider a eco-epidemiological predator-prey system where delay is time-varying to study the transmission dynamics of Bacterial white spot disease in Litopenaeus Vannamei, which will contribute to the sustainable development of shrimp. First, the permanence and the positiveness of solutions are given. Then, the conditions for the local asymptotic stability of the equilibriums are established. Next, the global asymptotic stability for the system around the positive equilibrium is gained by applying the functional differential equation theory and constructing a proper Lyapunov function. Last, some numerical examples verify the validity and feasibility of previous theoretical results.
- time-varying delay,
- permanence,
- positiveness,
- local asymptotic stability,
- global asymptotic stability
Citation: Xue Liu, Xin You Meng. Dynamics of Bacterial white spot disease spreads in Litopenaeus Vannamei with time-varying delay[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20748-20769. doi: 10.3934/mbe.2023918

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Abstract

In this paper, we mainly consider a eco-epidemiological predator-prey system where delay is time-varying to study the transmission dynamics of Bacterial white spot disease in Litopenaeus Vannamei, which will contribute to the sustainable development of shrimp. First, the permanence and the positiveness of solutions are given. Then, the conditions for the local asymptotic stability of the equilibriums are established. Next, the global asymptotic stability for the system around the positive equilibrium is gained by applying the functional differential equation theory and constructing a proper Lyapunov function. Last, some numerical examples verify the validity and feasibility of previous theoretical results.

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