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

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.