Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

TL;DR

This paper develops and analyzes a mathematical model for anti-angiogenic therapy in metastatic cancers, including numerical schemes and simulations to support clinical relevance.

Contribution

It introduces a structured transport equation model with nonlocal boundary conditions and provides rigorous numerical analysis and error estimates.

Findings

Convergence of the numerical scheme established

Error estimates for the scheme derived

Simulations demonstrate potential clinical applications

Abstract

We introduce and analyze a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastasis that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations in view of clinical applications.