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

doi:10.3934/mbe.2022600

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

Math Biosci Eng. 2022 Sep 1;19(12):12852-12865. doi: 10.3934/mbe.2022600.

Authors

Fawaz E Alsaadi¹, Chuangxia Huang², Madini O Alassafi¹, Reem M Alotaibi¹, Adil M Ahmad¹, Jinde Cao³

Affiliations

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.

PMID: 36654025
DOI: 10.3934/mbe.2022600

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.

Keywords: attractivity; delay; equilibrium; tick population.

MeSH terms

Animals
Computer Simulation
Population Dynamics
Ticks*