The Escalator Boxcar Train method for a system of aged-structured equations

TL;DR

This paper extends the Escalator Boxcar Train method to a complex system of age-structured, two-sex population models, providing a new numerical scheme for coupled hyperbolic PDEs with nonlocal boundary conditions.

Contribution

It develops the first EBT numerical scheme for a coupled system of age-structured population equations, advancing the method's applicability beyond scalar models.

Findings

Derived a full numerical EBT scheme for a two-sex population model

First extension of EBT to systems of structured population equations

Provides convergence framework for the new scheme

Abstract

The Escalator Boxcar Train method (EBT) is a numerical method for structured population models of McKendrick-von Foerster type. Those models consist of a certain class of hyperbolic partial differential equations and describe time evolution of the distribution density of the structure variable describing a feature of individuals in the population. The method was introduced in late eighties and widely used in theoretical biology, but its convergence was proven only in recent years using the framework of measure-valued solutions. Till now the EBT method was developed only for scalar equation models. In this paper we derive a full numerical EBT scheme for age-structured, two-sex population model (Fredrickson-Hoppensteadt model), which consists of three coupled hyperbolic partial differential equations with nonlocal boundary conditions. It is the first step towards extending the EBT method to systems of structured population equations.