American Institute of Mathematical Sciences

Advanced
August  2004, 4(3): 517-525. doi: 10.3934/dcdsb.2004.4.517

A stochastic model for the dynamics of a stage structured population

G. Buffoni 1, , S. Pasquali 2, and  G. Gilioli 3,

1. 

ENEA, 19100 La Spezia, Italy
2. 

CNR-IMATI, 20133 Milano, Italy
3. 

Dipartimento di Agrochimica e Agrobiologia, Università di Reggio Calabria, 89061 Gallina di Reggio Calabria, Italy

Received  November 2002 Revised  June 2003 Published  May 2004

A stochastic model for the dynamics of a single species of a stage structured population is presented. The model (in Lagrangian or Monte Carlo formulation) describes the life history of an individual assumed completely determined by the biological processes of development, mortality and reproduction. The dynamics of the overall population is obtained by the time evolution of the number of the individuals and of their physiological age. No other assumption is requested on the structure of the biological cycle and on the initial conditions of the population. Both a linear and a nonlinear models have been implemented. The nonlinearity takes into account the feedback of the population size on the mortality rate of the offsprings. For the linear case, i.e. when the population growths without any feedback dependent on the population size, the balance equations for the overall population density are written in the Eulerian formalism (equations of Von Foerster type in the deterministic case and of Fokker-Planck type in the stochastic case). The asymptotic solutions to these equations, for sufficiently large time, are in good agreement with the results of the numerical simulations of the Lagrangian model. As a case study the model is applied to simulate the dynamics of the greenhouse whitefly, Trialeurodes vaporarioum (Westwood), a highly polyphagous pest insect, on tomato host plants.
Keywords: Microscopic stochastic model, population dynamics..
Mathematics Subject Classification: 92D2.
Citation: G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 517-525. doi: 10.3934/dcdsb.2004.4.517
[1]

MirosŁaw Lachowicz, Tatiana Ryabukha. Equilibrium solutions for microscopic stochastic systems in population dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 777-786. doi: 10.3934/mbe.2013.10.777
[2]

Cristina Anton, Alan Yong. Stochastic dynamics and survival analysis of a cell population model with random perturbations. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1077-1098. doi: 10.3934/mbe.2018048
[3]

Simone Göttlich, Stephan Knapp, Peter Schillen. A pedestrian flow model with stochastic velocities: Microscopic and macroscopic approaches. Kinetic and Related Models, 2018, 11 (6) : 1333-1358. doi: 10.3934/krm.2018052
[4]

Peter J. Witbooi, Grant E. Muller, Marshall B. Ongansie, Ibrahim H. I. Ahmed, Kazeem O. Okosun. A stochastic population model of cholera disease. Discrete and Continuous Dynamical Systems - S, 2022, 15 (2) : 441-456. doi: 10.3934/dcdss.2021116
[5]

Wei Feng, Xin Lu, Richard John Donovan Jr.. Population dynamics in a model for territory acquisition. Conference Publications, 2001, 2001 (Special) : 156-165. doi: 10.3934/proc.2001.2001.156
[6]

Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks and Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53
[7]

Jim M. Cushing. The evolutionary dynamics of a population model with a strong Allee effect. Mathematical Biosciences & Engineering, 2015, 12 (4) : 643-660. doi: 10.3934/mbe.2015.12.643
[8]

Hui Wan, Huaiping Zhu. A new model with delay for mosquito population dynamics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1395-1410. doi: 10.3934/mbe.2014.11.1395
[9]

Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi. The periodic patch model for population dynamics with fractional diffusion. Discrete and Continuous Dynamical Systems - S, 2011, 4 (1) : 1-13. doi: 10.3934/dcdss.2011.4.1
[10]

Chris Cosner, Andrew L. Nevai. Spatial population dynamics in a producer-scrounger model. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1591-1607. doi: 10.3934/dcdsb.2015.20.1591
[11]

Dianmo Li, Zhen Zhang, Zufei Ma, Baoyu Xie, Rui Wang. Allee effect and a catastrophe model of population dynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 629-634. doi: 10.3934/dcdsb.2004.4.629
[12]

Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic and Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025
[13]

Pao-Liu Chow. Stochastic PDE model for spatial population growth in random environments. Discrete and Continuous Dynamical Systems - B, 2016, 21 (1) : 55-65. doi: 10.3934/dcdsb.2016.21.55
[14]

Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predator-prey population model with Allee effect on prey. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2651-2667. doi: 10.3934/dcdsb.2017129
[15]

Hongfu Yang, Xiaoyue Li, George Yin. Permanence and ergodicity of stochastic Gilpin-Ayala population model with regime switching. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3743-3766. doi: 10.3934/dcdsb.2016119
[16]

Yanan Zhao, Daqing Jiang, Xuerong Mao, Alison Gray. The threshold of a stochastic SIRS epidemic model in a population with varying size. Discrete and Continuous Dynamical Systems - B, 2015, 20 (4) : 1277-1295. doi: 10.3934/dcdsb.2015.20.1277
[17]

Shangzhi Li, Shangjiang Guo. Dynamics of a stage-structured population model with a state-dependent delay. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3523-3551. doi: 10.3934/dcdsb.2020071
[18]

Peixuan Weng, Xiao-Qiang Zhao. Spatial dynamics of a nonlocal and delayed population model in a periodic habitat. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 343-366. doi: 10.3934/dcds.2011.29.343
[19]

Suqi Ma, Qishao Lu, Shuli Mei. Dynamics of a logistic population model with maturation delay and nonlinear birth rate. Discrete and Continuous Dynamical Systems - B, 2005, 5 (3) : 735-752. doi: 10.3934/dcdsb.2005.5.735
[20]

Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1735-1757. doi: 10.3934/dcdsb.2015.20.1735

2021 Impact Factor: 1.497

Tools

Metrics

  • PDF downloads (106)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy