Stochastic approach to Fisher and Kolmogorov, Petrovskii, and Piskunov wave fronts for species with different diffusivities in dilute and concentrated solutions

Morgado, Gabriel; Nowakowski, B.; Lemarchand, A.

doi:10.1016/j.physa.2020.124954

Cited by 1 publication

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“…Autocatalysis is a key ingredient in observing a dynamic behavior with an induction period before an explosion [43,52], which typically characterizes the 3Es of immunotherapy, i.e., the final escape of cancer from immunosurveillance after a long apparent equilibrium phase. Hence, the model introduces binary, autocatalytic cell-cell interactions inspired by the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) model [11,[53][54][55]. Typically, the FKPP model involves two species, A and B, which interact to lead to the formation of 2 A species and has been introduced to model the propagation of a favored trait or a virus into a population.…”

Section: A Model At Cell Scalementioning

confidence: 99%

From Cell–Cell Interaction to Stochastic and Deterministic Descriptions of a Cancer–Immune System Competition Model

2023

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We consider a cell–cell interaction model of competition between cancer cells and immune system cells, first introduced in the framework of the thermostatted kinetic theory, and derive a master equation for the probability of the number of cancer cells and immune system cells for a given activity. Macroscopic deterministic equations for the concentrations and mean activities of cancer cells and immune system cells are deduced from the kinetic equations. The conditions for which the 3Es of immunotherapy (elimination, equilibrium, and escape) are reproduced are discussed. Apparent elimination of cancer followed by a long pseudo-equilibrium phase and the eventual escape of cancer from the control of the immune system are observed in the three descriptions. The macroscopic equations provide an analytical approach to the transition observed in the simulations of both the kinetic equations and the master equation. For efficient control of activity fluctuations, the steady states associated with the elimination of either cancer or immune system disappear and are replaced by a steady state in which cancer is controlled by the immune system.

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