Mathematical Model of Time Needed for the Immune System to Detect and Kill Cancer Cells in Blood

Disfunction of the immune system has generally been blamed for the development of cancers however, the immune system needs time to detect and kill cancer cells. To date, the chance of random collision between immune cells and cancer cells in blood has drawn less attention. In this study we used a random principle to analyse the possibility of collision between immune and cancer cells in blood. With the criterion of p>0.95, the results show that an immune cell needs, for example, five random collisions in order to hit a cancer cell when there are one cancer cell, one immune cell and one normal cell in our consideration; and 14 999 999 random collisions in order to hit a cancer cell when there are one cancer cell, one immune cell and 4 999 999 normal cells in consideration. Furthermore, we analyse how different proliferation rates of cancer cells affect the random collisions between the detecting/killing immune cells and cancer cells.