A study of inactivation of TSG and cancer therapy: an evolutionary game theory approach

Inactivation of alleles in tumor suppressor genes (TSG) is one of the most important issues that results in evolution of cancerous cells. In this paper, the evolution of healthy, one and two missed allele cells is modeled using the concept of evolutionary game theory and replicator dynamics. The proposed model also takes into account the interaction rates of the cells as designing parameters. Different combinations of the equilibrium points of the parameterized nonlinear system is studied and categorized to some cases. In each case, the interaction rates values are suggested in which, the equilibrium points are located in the appropriate location in the state space, such that, at least one of the desired equilibrium points are stable. Based on the suggested interaction rates, it is proved that the system doesn´t have any interior equilibrium point and will converge to one of the boundary equilibrium points. In addition, the proposed conditions for interaction rates guarantees that, when a trajectory of the system reaches to the boundaries, then it will converge to a desired equilibrium point.