Generalized Hamiltonian and Lagrangian aspects of a model for virus-tumor interaction in oncolytic virotherapy

We analyze the generalized Hamiltonian structure of a system of first-order ordinary differential equations for the Jenner et al. system (Letters in Biomathematics 5 (2018), no. S1, S117-S136). The system of equations is used for modeling the interaction of an oncolytic virus with a tumor cell population. Our analysis is based on the existence of a Jacobi last multiplier and a time-dependent first integral. Suitable conditions on the model parameters allow for the reduction of the problem to a planar system of equations, and the time-dependent Hamiltonian flows are described. The geometry of the Hamiltonian flows is also investigated using the symplectic and cosymplectic methods.