A Stage-Structured Population Model with Time-Dependent Delay in an Almost Periodic Environment

• Published in: Journal of dynamics and differential equations Vol. 34; no. 1; pp. 341 - 364
• Main Authors: Qiang, Lizhong, Wang, Bin-Guo, Zhao, Xiao-Qiang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Growth models; Mathematical models; Mathematics; Mathematics and Statistics; Maturation; Ordinary Differential Equations; Partial Differential Equations; Population growth; Time dependence; Almost periodicity; 92D30; Time-dependent delay; Uniform persistence; Global stability; 34D20; 37B55; Age-structure; Skew-product semiflow
• ISSN: 1040-7294; 1572-9222
• DOI: 10.1007/s10884-020-09827-6

In this paper, we derive and investigate a stage-structured population growth model with time-dependent maturation delays in an almost periodic environment. We introduce the basic reproduction ratio R 0 for this model and then obtain a threshold-type result on its global dynamics in terms of R 0 . It is shown that the population tends to die out if R 0 < 1 , while remains persistent if R 0 > 1 . In the monotone case and a specific non-monotone case, we also prove that there exists a globally stable almost periodic solution when R 0 > 1 . For the Nicholson blowflies model, we further study the influence of time-dependent maturation delay on R 0 via numerical simulations.