American Institute of Mathematical Sciences

Advanced
November  2009, 12(4): 883-904. doi: 10.3934/dcdsb.2009.12.883

Spreading speed and traveling wavefront of an age-structured population diffusing in a 2D lattice strip

Peixuan Weng 1,

1. 

School of Mathematics, South China Normal University, Guangzhou 510631, China

Received  July 2008 Revised  April 2009 Published  August 2009

We derive an age-structured population model for the growth of a single species on a 2-dimensional (2D) lattice strip with Neumann boundary conditions. We show that the dynamics of the mature population is governed by a lattice reaction-diffusion system with delayed global interaction. Using theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows, we obtain the asymptotic speed of spread $c^$*, the nonexistence of traveling wavefronts with wave speed $0 < c < c^$*, and the existence of traveling wavefront connecting the two equilibria $w\equiv 0$ and $w\equiv w^+$ for $c\geq c^$*.
Keywords: monotone semiflow, 2D lattice strip., lattice system, age-structured population model, traveling wavefront, spreading speed.
Mathematics Subject Classification: Primary: 34K31, 34K25; Secondary: 92D2.
Citation: Peixuan Weng. Spreading speed and traveling wavefront of an age-structured population diffusing in a 2D lattice strip. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 883-904. doi: 10.3934/dcdsb.2009.12.883
[1]

Guangrui Li, Ming Mei, Yau Shu Wong. Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model. Mathematical Biosciences & Engineering, 2008, 5 (1) : 85-100. doi: 10.3934/mbe.2008.5.85
[2]

Linlin Li, Bedreddine Ainseba. Large-time behavior of matured population in an age-structured model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2561-2580. doi: 10.3934/dcdsb.2020195
[3]

Diène Ngom, A. Iggidir, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear age-structured model of a harvested fish population. Mathematical Biosciences & Engineering, 2008, 5 (2) : 337-354. doi: 10.3934/mbe.2008.5.337
[4]

Xianlong Fu, Zhihua Liu, Pierre Magal. Hopf bifurcation in an age-structured population model with two delays. Communications on Pure & Applied Analysis, 2015, 14 (2) : 657-676. doi: 10.3934/cpaa.2015.14.657
[5]

Gero Friesecke, Karsten Matthies. Geometric solitary waves in a 2D mass-spring lattice. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 105-114. doi: 10.3934/dcdsb.2003.3.105
[6]

Georgi Kapitanov, Christina Alvey, Katia Vogt-Geisse, Zhilan Feng. An age-structured model for the coupled dynamics of HIV and HSV-2. Mathematical Biosciences & Engineering, 2015, 12 (4) : 803-840. doi: 10.3934/mbe.2015.12.803
[7]

Yingli Pan, Ying Su, Junjie Wei. Bistable waves of a recursive system arising from seasonal age-structured population models. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 511-528. doi: 10.3934/dcdsb.2018184
[8]

Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1
[9]

Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li. Global stability of an age-structured cholera model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 641-665. doi: 10.3934/mbe.2014.11.641
[10]

Ryszard Rudnicki, Radosław Wieczorek. On a nonlinear age-structured model of semelparous species. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2641-2656. doi: 10.3934/dcdsb.2014.19.2641
[11]

Mohammed Nor Frioui, Tarik Mohammed Touaoula, Bedreddine Ainseba. Global dynamics of an age-structured model with relapse. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : 2245-2270. doi: 10.3934/dcdsb.2019226
[12]

Huimin Liang, Peixuan Weng, Yanling Tian. Threshold asymptotic behaviors for a delayed nonlocal reaction-diffusion model of mistletoes and birds in a 2D strip. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1471-1495. doi: 10.3934/cpaa.2016.15.1471
[13]

Z.-R. He, M.-S. Wang, Z.-E. Ma. Optimal birth control problems for nonlinear age-structured population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 589-594. doi: 10.3934/dcdsb.2004.4.589
[14]

Cui-Ping Cheng, Wan-Tong Li, Zhi-Cheng Wang. Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 559-575. doi: 10.3934/dcdsb.2010.13.559
[15]

Fred Brauer. A model for an SI disease in an age - structured population. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 257-264. doi: 10.3934/dcdsb.2002.2.257
[16]

Piotr Gwiazda, Karolina Kropielnicka, Anna Marciniak-Czochra. The Escalator Boxcar Train method for a system of age-structured equations. Networks & Heterogeneous Media, 2016, 11 (1) : 123-143. doi: 10.3934/nhm.2016.11.123
[17]

Geni Gupur, Xue-Zhi Li. Global stability of an age-structured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 643-652. doi: 10.3934/dcdsb.2004.4.643
[18]

Shengqin Xu, Chuncheng Wang, Dejun Fan. Stability and bifurcation in an age-structured model with stocking rate and time delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2535-2549. doi: 10.3934/dcdsb.2018264
[19]

Cameron J. Browne, Sergei S. Pilyugin. Global analysis of age-structured within-host virus model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 1999-2017. doi: 10.3934/dcdsb.2013.18.1999
[20]

Hao Kang, Qimin Huang, Shigui Ruan. Periodic solutions of an age-structured epidemic model with periodic infection rate. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4955-4972. doi: 10.3934/cpaa.2020220

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (54)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy