Optimization in Structure Population Models through the Escalator Boxcar Train

TL;DR

This paper demonstrates the convergence and effectiveness of the Escalator Boxcar Train method for solving structure population models and computing optimal controls, with applications to welfare policies.

Contribution

It provides a rigorous proof of convergence for the EBT method and extends its application to optimal control problems in biological models.

Findings

EBT solutions converge to exact solutions

EBT effectively computes optimal controls

Application to welfare policy models

Abstract

The Escalator Boxcar Train (EBT) is a tool widely used in the study of balance laws motivated by structure population dynamics. This paper proves that the approximate solutions defined through the EBT converge to exact solutions. Moreover, this method is rigorously shown to be effective also in computing optimal controls. As preliminary results, the well posedness of classes of PDEs and of ODEs comprising various biological models is also obtained. A specific application to welfare policies illustrates the whole procedure.