Non-hermitian operator modelling of basic cancer cell dynamics

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.