Finite-time contraction stability of a stochastic reaction-diffusion dengue model with impulse and Markov switching

Wei You; Jie Ren; Qimin Zhang; Wei You; Jie Ren; Qimin Zhang

doi:10.3934/mbe.2023757

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 16978-17002. doi: 10.3934/mbe.2023757

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Research article

Finite-time contraction stability of a stochastic reaction-diffusion dengue model with impulse and Markov switching

1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2.
School of Medical Information and Engineering, Ningxia Medical University, Yinchuan 750004, China

Academic Editor: Mariano Torrisi

Received: 04 May 2023 Revised: 31 July 2023 Accepted: 08 August 2023 Published: 28 August 2023

From the perspective of prevention and treatment of dengue, it is important to minimize the number of infections within a limited time frame. That is, the study of finite time contraction stability (FTCS) of dengue system is a meaningful topic. This article proposes a dengue epidemic model with reaction-diffusion, impulse and Markov switching. By constructing an equivalent system, the well-posedness of the positive solution is proved. The main result is that sufficient conditions to guarantee the finite time contraction stability of the dengue model are acquired based on the average pulse interval method and the bounded pulse interval method. Furthermore, the numerical findings indicate the influences of impulse, control strategies and noise intensity on the FTCS.
- reaction-diffusion,
- finite-time contraction stability,
- bounded pulse interval method,
- Markov switching,
- average pulse interval method
Citation: Wei You, Jie Ren, Qimin Zhang. Finite-time contraction stability of a stochastic reaction-diffusion dengue model with impulse and Markov switching[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 16978-17002. doi: 10.3934/mbe.2023757

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Abstract

From the perspective of prevention and treatment of dengue, it is important to minimize the number of infections within a limited time frame. That is, the study of finite time contraction stability (FTCS) of dengue system is a meaningful topic. This article proposes a dengue epidemic model with reaction-diffusion, impulse and Markov switching. By constructing an equivalent system, the well-posedness of the positive solution is proved. The main result is that sufficient conditions to guarantee the finite time contraction stability of the dengue model are acquired based on the average pulse interval method and the bounded pulse interval method. Furthermore, the numerical findings indicate the influences of impulse, control strategies and noise intensity on the FTCS.

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