A Kinetic Model of the Effector Cell Response to Cancer

The aim of this paper was to get a mathematical description on T cell-mediated cytolysis which we consider to be the dominant contributor of tumor regression, by studying a kinetic model of the effector cell response to cancer, which has been provided by R. P. Garay and R. Lefever. The methods employed were mathematical methods: differential analysis, Liapunov\´s method of stability, and linear systems theory. For the simplicity of the model, we considered the quantity of effector cells per unit to be constant and go one step further to assume that, namely the ratio of binding rate and growth rate multiplied by the constant E₁, is greater than 1, be speaking the "work efficiency" of effector cells is higher than that of cancer cells. We shown that tumor recuperation and tumor dormancy can be obtained when value of b, i.e. the ratio of the binding rate of cancer cells and effector cells and the rate of lysis, satisfies a specific condition respectively. The study indicates that tumor can be suppressed once cellular immune response is properly triggerd, in which the former condition we set is most likely to be met.