Mathematical control theory, the immune system, and cancer

TL;DR

This paper applies mathematical control theory to analyze the immune system's principles, deriving stability conditions and risk expressions for cancer immunity, providing a theoretical framework for understanding immune responses and tissue stability.

Contribution

It introduces a control theory-based model of the immune system, linking stability conditions to tissue responses and cancer risk, offering a novel theoretical perspective.

Findings

Derivation of stability conditions for immune response in tissues.

Expression for lifetime cancer risk considering immune response and carcinogens.

Comparison of tissue stability based on control theory principles.

Abstract

Simple ideas, endowed from the mathematical theory of control, are used in order to analyze in general grounds the human immune system. The general principles are minimization of the pathogen load and economy of resources. They should constrain the parameters describing the immune system. In the simplest linear model, for example, where the response is proportional to the load, the annihilation rate of pathogens in any tissue should be greater than the pathogen's average rate of growth. When nonlinearities are added, a reference value for the number of pathogens is set, and a stability condition emerges, which relates strength of regular threats, barrier height and annihilation rate. The stability condition allows a qualitative comparison between tissues. On the other hand, in cancer immunity, the linear model leads to an expression for the lifetime risk, which accounts for both the effects of carcinogens (endogenous or external) and the immune response.