Dynamic analysis of a stochastic vector-borne model with direct transmission and media coverage

Yue Wu; Shenglong Chen; Ge Zhang; Zhiming Li; Yue Wu; Shenglong Chen; Ge Zhang; Zhiming Li

doi:10.3934/math.2024444

AIMS Mathematics

2024, Volume 9, Issue 4: 9128-9151. doi: 10.3934/math.2024444

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Research article

Dynamic analysis of a stochastic vector-borne model with direct transmission and media coverage

College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China

Received: 05 December 2023 Revised: 04 February 2024 Accepted: 07 February 2024 Published: 06 March 2024
MSC : 60G51, 60G57, 92B05

This paper presents a stochastic vector-borne epidemic model with direct transmission and media coverage. It proves the existence and uniqueness of positive solutions through the construction of a suitable Lyapunov function. Immediately after that, we study the transmission mechanism of vector-borne diseases and give threshold conditions for disease extinction and persistence; in addition we show that the model has a stationary distribution that is determined by a threshold value, i.e., the existence of a stationary distribution is unique under specific conditions. Finally, a stochastic model that describes the dynamics of vector-borne diseases has been numerically simulated to illustrate our mathematical findings.
- vector-borne disease,
- direct transmission,
- media coverage,
- stationary distribution
Citation: Yue Wu, Shenglong Chen, Ge Zhang, Zhiming Li. Dynamic analysis of a stochastic vector-borne model with direct transmission and media coverage[J]. AIMS Mathematics, 2024, 9(4): 9128-9151. doi: 10.3934/math.2024444

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Abstract

This paper presents a stochastic vector-borne epidemic model with direct transmission and media coverage. It proves the existence and uniqueness of positive solutions through the construction of a suitable Lyapunov function. Immediately after that, we study the transmission mechanism of vector-borne diseases and give threshold conditions for disease extinction and persistence; in addition we show that the model has a stationary distribution that is determined by a threshold value, i.e., the existence of a stationary distribution is unique under specific conditions. Finally, a stochastic model that describes the dynamics of vector-borne diseases has been numerically simulated to illustrate our mathematical findings.

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