Attractivity criterion on a delayed tick population dynamics equation with a reproductive function $ f(u) = ru^{\gamma}e^{-\sigma u} $

Fawaz E Alsaadi; Chuangxia Huang; Madini O Alassafi; Reem M Alotaibi; Adil M Ahmad; Jinde Cao; Fawaz E Alsaadi; Chuangxia Huang; Madini O Alassafi; Reem M Alotaibi; Adil M Ahmad; Jinde Cao

doi:10.3934/mbe.2022600

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12852-12865. doi: 10.3934/mbe.2022600

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Attractivity criterion on a delayed tick population dynamics equation with a reproductive function $ f(u) = ru^{\gamma}e^{-\sigma u} $

1.
Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia
2.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
3.
School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea

Academic Editor: Xiaodi Li

Received: 16 June 2022 Revised: 30 July 2022 Accepted: 17 August 2022 Published: 01 September 2022

The aim of this article is to analyze the delay influence on the attraction for a scalar tick population dynamics equation accompanying two disparate delays. Taking advantage of the fluctuation lemma and some dynamic inequalities, we derive a criterion to assure the persistence and positiveness on the considered model. Furthermore, a time-lag-dependent condition is proposed to insure the global attractivity for the addressed model. Besides, we give some simulation diagrams to substantiate the validity of the theoretical outcomes.
- tick population,
- delay,
- equilibrium,
- attractivity
Citation: Fawaz E Alsaadi, Chuangxia Huang, Madini O Alassafi, Reem M Alotaibi, Adil M Ahmad, Jinde Cao. Attractivity criterion on a delayed tick population dynamics equation with a reproductive function $ f(u) = ru^{\gamma}e^{-\sigma u} $[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12852-12865. doi: 10.3934/mbe.2022600

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Abstract

The aim of this article is to analyze the delay influence on the attraction for a scalar tick population dynamics equation accompanying two disparate delays. Taking advantage of the fluctuation lemma and some dynamic inequalities, we derive a criterion to assure the persistence and positiveness on the considered model. Furthermore, a time-lag-dependent condition is proposed to insure the global attractivity for the addressed model. Besides, we give some simulation diagrams to substantiate the validity of the theoretical outcomes.

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