The escalator boxcar train method for a system of age-structured equations in the space of measures

Journal article

The Escalator Boxcar Train (EBT) numerical method has been designed and widely used by theoretical biologists to compute solutions of one-dimensional structured population models of McKendrick-von Foerster type. Recently the method has been derived for an age-structured twosex population model (Fredrickson-Hoppenstaedt model), which consists of three coupled hyperbolic partial differential equations with nonlocal boundary conditions. The convergence of the EBT method for the Fredrickson-Hoppenstaedt model has not been analyzed, and relevant numerical examples are still missing. In this paper, we derive a simplified EBT method for the "two-sex model"" and prove its convergence. However, due to the interest in tracking specified cohorts of individuals, the analytical results cannot be analyzed in the L1 norm. Instead, we embedded the problem in the space of nonnegative Radon measures equipped with the bounded Lipschitz distance (the flat metric). We also present numerical examples to illustrate the results, compute the error in bounded Lipschitz distance, and compare it against the total variation (TV) distance.

Authors: Carrillo de la Plata, JA; Gwiazda, P; Kropielnicka, K; Marciniak-Czochra, AK

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial & Applied Mathematics
• Journal: Society for Industrial and Applied Mathematics
• Volume: 57
• Issue: 4
• Pages: 1842-1874
• Publication date: 2019-07-30
• Acceptance date: 2019-04-09
• DOI: 10.1137/18M1189427
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: structured population models; Escalator Boxcar Train; system of equations; particle method; FFR; two-sex population models; measure-valued solutions