Immune surveillance and neoplasia—1 a minimal mathematical model

Abstract

A deterministic predator-prey model is presented for describing the dynamics of a solid tumor in the presence of a specifically reactive lymphocyte population which is stimulated by, and antagonistic to, the tumor. The qualitative behavior of the solutions is developed and briefly compared to the results of transplantation experiments. Although the model is primitive, it leads to predictions that are in general agreement with observation and intuitive expectations. In particular, it is found that: (1) very low levels of transplanted tumor will not survive in the recipient. (2) At somewhat higher levels, tumor growth will be uncontrolled in the syngeneic recipient. However, immune intervention if early enough, can lead to control and elimination of the tumor. (3) At still higher levels of transplanted tumor, no amount of immune intervention will be effective in controlling the tumor. (4) If the recipients immune system is suppressed prior to transplantation, or is debilitated for any reason, the chance that the tumor will grow increases. (5) If the recipients immune system is stimulated prior to transplantation, the chance of tumor survival decreases. (6) The survival of the tumor is much more sensitive to changes in tumor parameters (for example, antigenicity) than in lymphocyte parameters. In addition it makes the unintuitive prediction that (7) There areisolated instances under which anincrease in the number of lymphocytes canincrease the chance of tumor survival.