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

Non-hermitian operator modelling of basic cancer cell dynamics