Analysis of a cancer dormancy model and control of immuno-therapy

Benjamin Sheller, Domenico D'Alessandro

Abstract:

The goal of this paper is to analyze a model of cancer-immune sys-
tem interactions from [16], and to show how the introduction of control in this
model can dramatically improve the hypothetical patient response and in eect
prevent the cancer from growing. We examine all the equilibrium points of the
model and classify them according to their stability properties. We identify an
equilibrium point corresponding to a survivable amount of cancer cells which
are exactly balanced by the immune response. This situation corresponds to
cancer dormancy. By using Lyapunov stability theory we estimate the region
of attraction of this equilibrium and propose two control laws which are able
to stabilize the system eectively, improving the results of [16]. Ultimately, the
analysis presented in this paper reveals that a slower, continuous introduction
of antibodies over a short time scale, as opposed to mere inoculation, may lead
to more ecient and safer treatments.