A Mathematical Model of Cancer Evolution

David Moreno Martos; Andrei Korobeinikov

doi:10.1007/978-3-030-25261-8_12

A Mathematical Model of Cancer Evolution

David Moreno Martos, Andrei Korobeinikov

Research output: Chapter in Book › Chapter › Research › peer-review

Abstract

© 2019, Springer Nature Switzerland AG. Cancer appears as a result of mutations and, due to a very high mutability of cancer cells, undergoes a continuous evolution through its development. In this note, we introduce a mathematical model of the cancer initial development. The model describes the cancer evolution in a continuous variant space. It is based upon the logistic population growth model (the Lotka–Volterra model of competing populations) and includes a possibility for cell mutations and competition of different genotypes for limited resources. Numerical simulations are performed to demonstrate the model suitability.

Original language	English
Title of host publication	Trends in Mathematics
Pages	81-85
Number of pages	4
Volume	11
ISBN (Electronic)	2297-024X
DOIs	https://doi.org/10.1007/978-3-030-25261-8_12
Publication status	Published - 1 Jan 2019

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title = "A Mathematical Model of Cancer Evolution",

abstract = "{\textcopyright} 2019, Springer Nature Switzerland AG. Cancer appears as a result of mutations and, due to a very high mutability of cancer cells, undergoes a continuous evolution through its development. In this note, we introduce a mathematical model of the cancer initial development. The model describes the cancer evolution in a continuous variant space. It is based upon the logistic population growth model (the Lotka–Volterra model of competing populations) and includes a possibility for cell mutations and competition of different genotypes for limited resources. Numerical simulations are performed to demonstrate the model suitability.",

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N2 - © 2019, Springer Nature Switzerland AG. Cancer appears as a result of mutations and, due to a very high mutability of cancer cells, undergoes a continuous evolution through its development. In this note, we introduce a mathematical model of the cancer initial development. The model describes the cancer evolution in a continuous variant space. It is based upon the logistic population growth model (the Lotka–Volterra model of competing populations) and includes a possibility for cell mutations and competition of different genotypes for limited resources. Numerical simulations are performed to demonstrate the model suitability.

AB - © 2019, Springer Nature Switzerland AG. Cancer appears as a result of mutations and, due to a very high mutability of cancer cells, undergoes a continuous evolution through its development. In this note, we introduce a mathematical model of the cancer initial development. The model describes the cancer evolution in a continuous variant space. It is based upon the logistic population growth model (the Lotka–Volterra model of competing populations) and includes a possibility for cell mutations and competition of different genotypes for limited resources. Numerical simulations are performed to demonstrate the model suitability.

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M3 - Chapter

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EP - 85

BT - Trends in Mathematics

ER -

A Mathematical Model of Cancer Evolution

Abstract

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