# American Institute of Mathematical Sciences

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

## A stochastic model for the dynamics of a stage structured population

 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.
Citation: G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 517-525. doi: 10.3934/dcdsb.2004.4.517
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