Reduction and Hamiltonian aspects of a model for virus-tumour interaction in oncolytic virotherapy

TL;DR

This paper explores the Hamiltonian structure of a virus-tumour interaction model, revealing reduction techniques and geometric properties of the system's flows to better understand oncolytic virotherapy dynamics.

Contribution

It introduces a Hamiltonian framework for the model, utilizing a Jacobi Last Multiplier and first integral to analyze and reduce the system.

Findings

Reduction to planar Hamiltonian system

Identification of Hamiltonian flows and geometry

Application of symplectic and cosymplectic methods

Abstract

We analyse the Hamiltonian structure of a system of first-order ordinary differential equations used for modeling the interaction of an oncolytic virus with a tumour cell population. The analysis is based on the existence of a Jacobi Last Multiplier for the system and a time dependent first integral. For suitable conditions on the model parameters this allows for the reduction of the problem to a planar system of equations for which the time dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows are finally investigated using the symplectic and cosymplectic methods.