Preventing extinction in <i>Rastrelliger brachysoma</i> using an impulsive mathematical model

Din Prathumwan; Kamonchat Trachoo; Wasan Maiaugree; Inthira Chaiya; Din Prathumwan; Kamonchat Trachoo; Wasan Maiaugree; Inthira Chaiya

doi:10.3934/math.2022001

AIMS Mathematics

2022, Volume 7, Issue 1: 1-24. doi: 10.3934/math.2022001

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Research article

Preventing extinction in Rastrelliger brachysoma using an impulsive mathematical model

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand
3.
Division of Physics, Faculty of Science and Technology, Thammasat University, PathumThani 12120, Thailand

Received: 30 June 2021 Accepted: 25 September 2021 Published: 29 September 2021
MSC : 92-10, 34A37, 37G15

In this paper, we proposed a mathematical model of the population density of Indo-Pacific mackerel (Rastrelliger brachysoma) and the population density of small fishes based on the impulsive fishery. The model also considers the effects of the toxic environment that is the major problem in the water. The developed impulsive mathematical model was analyzed theoretically in terms of existence and uniqueness, positivity, and upper bound of the solution. The obtained solution has a periodic behavior that is suitable for the fishery. Moreover, the stability, permanence, and positive of the periodic solution are investigated. Then, we obtain the parameter conditions of the model for which Indo-Pacific mackerel conservation might be expected. Numerical results were also investigated to confirm our theoretical results. The results represent the periodic behavior of the population density of the Indo-Pacific mackerel and small fishes. The outcomes showed that the duration and quantity of fisheries were the keys to prevent the extinction of Indo-Pacific mackerel.
- implusive model,
- Indo-Pacific mackerel,
- stability,
- harvesting control,
- fisheries
Citation: Din Prathumwan, Kamonchat Trachoo, Wasan Maiaugree, Inthira Chaiya. Preventing extinction in Rastrelliger brachysoma using an impulsive mathematical model[J]. AIMS Mathematics, 2022, 7(1): 1-24. doi: 10.3934/math.2022001

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Abstract

In this paper, we proposed a mathematical model of the population density of Indo-Pacific mackerel (Rastrelliger brachysoma) and the population density of small fishes based on the impulsive fishery. The model also considers the effects of the toxic environment that is the major problem in the water. The developed impulsive mathematical model was analyzed theoretically in terms of existence and uniqueness, positivity, and upper bound of the solution. The obtained solution has a periodic behavior that is suitable for the fishery. Moreover, the stability, permanence, and positive of the periodic solution are investigated. Then, we obtain the parameter conditions of the model for which Indo-Pacific mackerel conservation might be expected. Numerical results were also investigated to confirm our theoretical results. The results represent the periodic behavior of the population density of the Indo-Pacific mackerel and small fishes. The outcomes showed that the duration and quantity of fisheries were the keys to prevent the extinction of Indo-Pacific mackerel.

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