Is the Allee effect relevant in cancer evolution and therapy?

Marcello Delitala ^{1
,
,},
Mario Ferraro ²

1.
Politecnico di Torino, Dipartimento di Scienze Matematiche, corso Duca degli Abruzzi 24, 10129 Torino, Italy
2.
Università di Torino, Dipartimento di Fisica, via P. Giuria 1, 10125 Torino, Italy

Received: 31 August 2020 Accepted: 08 September 2020 Published: 25 September 2020
MSC : 92B05, 92D25

Abstract
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Most models of cancer assume that tumor cells populations, at low densities, grow exponentially to be eventually limited by the available amount of resources such as space and nutrients. However, recent pre-clinical and clinical data of cancer onset or recurrence indicate the presence of a population dynamics in which growth rates increase with cell numbers. Such effect is analogous to the cooperative behavior in an ecosystem described by the so called Allee effect. In this work, we study the consequences of the Allee effect on cancer growth via the properties of dynamical models incorporating the Allee effect, and the implications that the occurrence of such effect has for the choice of the more appropriate therapy. Some simulations will be presented in which the model is used to fit data from in vitro experiments and clinical trials.
- cancer modelling,
- Allee effect,
- population dynamics,
- cancer treatments,
- drug resistance
Citation: Marcello Delitala, Mario Ferraro. Is the Allee effect relevant in cancer evolution and therapy?[J]. AIMS Mathematics, 2020, 5(6): 7649-7660. doi: 10.3934/math.2020489

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Abstract

Most models of cancer assume that tumor cells populations, at low densities, grow exponentially to be eventually limited by the available amount of resources such as space and nutrients. However, recent pre-clinical and clinical data of cancer onset or recurrence indicate the presence of a population dynamics in which growth rates increase with cell numbers. Such effect is analogous to the cooperative behavior in an ecosystem described by the so called Allee effect. In this work, we study the consequences of the Allee effect on cancer growth via the properties of dynamical models incorporating the Allee effect, and the implications that the occurrence of such effect has for the choice of the more appropriate therapy. Some simulations will be presented in which the model is used to fit data from in vitro experiments and clinical trials.

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