scholarly journals A Gentle Introduction to Structured Population Models: Three Worked Examples

Author(s):  
J. A. J. Metz ◽  
O. Diekmann
2021 ◽  
pp. 213-250
Author(s):  
Timothy E. Essington

The chapter “Skills for Dynamic Models” provides worked examples of the dynamic models presented in Part 1, both in spreadsheets and in R. It also covers some of the mathematical steps used in model analysis. In most cases, instructions are given for both spreadsheets and R. However, when some activities are far easier to do in a programming environment than in spreadsheets, only the instructions for R are shown. The chapter starts out by discussing the skills needed for structured population models, including setting up age structure and creating cobweb plots. Next, it reviews the skills needed for multivariable models, including calculating isoclines and Jacobian matrices. Finally, it introduces the concept of Monte Carlo methods and provides guidance on how to implement them.


2001 ◽  
Vol 43 (2) ◽  
pp. 157-189 ◽  
Author(s):  
O. Diekmann ◽  
M. Gyllenberg ◽  
H. Huang ◽  
M. Kirkilionis ◽  
J.A.J. Metz ◽  
...  

2014 ◽  
Vol 24 (11) ◽  
pp. 2171-2197 ◽  
Author(s):  
J. A. Carrillo ◽  
P. Gwiazda ◽  
A. Ulikowska

We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used in biology, which is in essence an analogue of particle methods used in physics. Our method exploits the split-up technique, thanks to which the transport step and the nonlocal integral terms in the equation can be separately considered. The order of convergence of the proposed method is obtained in the natural space of finite non-negative Radon measures equipped with the flat metric. This convergence is studied even adding reconstruction and approximation steps in the particle simulation to keep the number of approximation particles under control. We validate our scheme in several test cases showing the theoretical convergence error. Finally, we use the scheme in situations in which the EBT method does not apply showing the flexibility of this new method to cope with the different terms in general structured population models.


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