The model of the movement of tumor cells and health cells

Abstract

This study concludes two parts. In the first part, we establish\r\nthe model of the interaction between two cell populations following the concept of the random-walk, and assume the cell movement is constrained by space limitation primarily. In the other part, the interaction model is deduced from the concept of the flux motion, and the movement is constrained by space limitation, too. Furthermore, we analyze two models to obtain the behavior of two cell populations as time is close to the initial state and far into the future.

This study concludes two parts. In the first part, we establish\r\nthe model of the interaction between two cell populations following the concept of the random-walk, and assume the cell movement is constrained by space limitation primarily. In the other part, the interaction model is deduced from the concept of the flux motion, and the movement is constrained by space limitation, too. Furthermore, we analyze two models to obtain the behavior of two cell populations as time is close to the initial state and far into the future.

Contents\r\nAbstract...i\r\n1 Introduction...1\r\n2 Modelling of the interaction between two cell populations following the random-walk concept\r\n2.1 The movement of one cell population...3\r\n2.2 The interaction between two cell populations...6\r\n3 Analysis of the model of the interaction between two cell populations\r\n3.1 The behavior and the meaning ofν(x,t) =ν(z) as z→0...10\r\n3.2 The behavior and the meaning ofν(x,t) =ν(z) as z→∞...15\r\n4 Modelling of the interaction between two cell populations following the flux motion\r\n4.1 The movement of one cell population under space limitation...18\r\n4.2 The interaction between two cell populations under space limitation...21\r\n5 Analysis of the model of the interaction between two cell populations\r\n5.1 The properties of total cells as time far into the future...25\r\n5.2 The behavior of single cell population as time far into the future...28\r\nReferences...32