A Dynamic Study On Cheater-Altruist Synergy In Tumor Cells

Based on the knowledge of game theory and considering the game of public goods in tumor cells,we establish the interaction model between the altruist and the cheater in tumor cells,analyze and discuss their mathematical conclusions and biological significance.In the first chapter,we briefly introduce the background and research progress of public goods game of tumor cells.Based on literature review and biological background of tumor cell growth,we consider the growth and change process of tumor cells when tumor cells randomly choose the altruists or cheaters.In the second chapter,we establish and study the interaction model between the altruist and the cheater in tumor cells.In this thesis,we consider the random choice of tumor cells as the altruists or cheaters,and the two choices of tumor cells are independent of each other.It is proved that the system is non negative and bounded.The existence of boundary equilibrium point is determined by Cartesian law and Stuart's method.Then it is determined that the boundary equilibrium point is locally asymptotically stable under appropriate parameter conditions according to Hurwitz's criterion.The parameter conditions for the existence of internal equilibrium point are determined by calculation.It is theoretically proved that when the internal equilibrium point exists,it will be locally asymptotically stable.The conclusion of theoretical analysis is verified by numerical simulation.In the third chapter,the interaction model of the altruist and the cheater in tumorcells is established and studied under the limited interaction population.On the basis of the second chapter,considering that the tumor cells are initially benign,the altruist and the cheater in tumor cells compete in a limited space.We prove that there is an effective interaction population between the altruist and the cheater in tumor cells.When the number of effective interaction population is small,the altruists occupy the dominant position.With the growth and expansion of tumor cells,the number of cheaters increases,the effective interaction population will increase,and the altruists will decrease.However,the existence of cheaters is not conducive to the growth of tumor cells,and the effective interaction population will start to decrease,and then the altruists will occupy the dominant position again,start a new cycle.The interaction between the altruist and the cheater in tumor cells is a closed cycle similar to the stone scissors and paper game.In the fourth chapter,we briefly review the main work and conclusions of this paper,and introduce the biological and practical significance of the kinetic model.At the same time,we discuss the shortcomings of this work and the problems and work that need further study...