Abstract
It was suggested that the ability of cancer to avoid immune response pressure (that should be expected to be capable to annihilate cancer at its early stage) can be attributed to the ability of the cancer cells to evolve. The goal of this notice is to illustrate this possibility by the means of mathematical modelling. In this notice, we construct a simple mechanistic model of cancer evolution, which is based upon a classical model of cancer-immune response interaction. Numerical simulations confirm the hypothesis that if cancer mutates fast enough and if immune response is not sufficiently strong, then cancer is able to avoid immune response pressure by evolution.
Highlights
The very general term “cancer” usually refer a set of diseases caused by an atypical growth of a certain kind of cells
In order to construct a model of evolution on the basis of this model, we assume the existence of multiple variants of cancer cells and postulate that these are distributed in a continuous variant space
Please note that for a given variant s, this term summarizes all the cancer cells that get killed by this particular immune cell variant, whereas in equation (5), in contrast, we summarize, for a given cancer variant s, all the immune cells that kill cancer cells of this variant
Summary
The very general term “cancer” usually refer a set of diseases caused by an atypical growth of a certain kind of cells. In order to construct a model of evolution on the basis of this model, we assume the existence of multiple variants of cancer cells and postulate that these are distributed in a continuous variant space. In this notice we assume that the variant space is one-dimensional and is parameterized by a parameter s. At the same time we assume that immune response cells can with some probability kill cancer cells of variants different from the one that activated them. We assume here that immune effector cells of all variants kill an average of 1/b cancer cells before get exhausted, which is the reason why the factor b appears in the equation. It may be noteworthy that a discrete variant space model equivalent to this model is reported in [9]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
