Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters

Bevia, V.; Burgos, C.; López, Juan Carlos Cortés; Navarro‐Quiles, A.; Villanueva, Rafael

doi:10.1016/j.chaos.2020.109908

Cited by 14 publications

(3 citation statements)

References 31 publications

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“…It has already been established that dealing with parameter inaccuracy is not always suitable due to a lack of comprehensive knowledge or estimation failure. A basic technique of coping with Gompertz equation uncertainties ( 6) is utilized to obtain these parameter estimations by utilizing the equation (7) to calculate the average approximations and to assess the complexity [42,43,[45][46][47].…”

Section: Tumor Growth In a Fuzzy Environment Using The Gompertz Modelmentioning

confidence: 99%

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Sheergojri

Iqbal

Agarwal

et al. 2022

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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For treating cancer, tumor growth models have shown to be a valuable resource, whether they are used to develop therapeutic methods paired with process control or to simulate and evaluate treatment processes. In addition, a fuzzy mathematical model is a tool for monitoring the influences of various elements and creating behavioral assessments. It has been designed to decrease the ambiguity of model parameters to obtain a reliable mathematical tumor development model by employing fuzzy logic.The tumor Gompertz equation is shown in an imprecise environment in this study. It considers the whole cancer cell population to be vague at any given time, with the possibility distribution function determined by the initial tumor cell population, tumor net population rate, and carrying capacity of the tumor. Moreover, this work provides information on the expected tumor cell population in the maximum period. This study examines fuzzy tumor growth modeling insights based on fuzziness to reduce tumor uncertainty and achieve a degree of realism. Finally, numerical simulations are utilized to show the significant conclusions of the proposed study.

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Section: Tumor Growth In a Fuzzy Environment Using The Gompertz Modelmentioning

confidence: 99%

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Sheergojri

Iqbal

Agarwal

et al. 2022

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Our context for random ordinary differential equations (Proposition 3.9 and below) assumes that the number of random terms is finite. When there is a stochastic process with infinite dimensionality, such as Brownian motion, a possible approach consists in truncating its Karhunen-Loève expansion [21]. This is legitimate.…”

Section: Path-wise Stochastic Integrals and First-order Random Ordina...mentioning

confidence: 99%

“…6.2.2], dynamical systems theory [15,Th. 8.4], and the principle of preservation of probability [16], with some applications in various fields [17][18][19][20][21]. But our derivation, based on semilinear random partial differential equations, seems to be novel.…”

Section: Introductionmentioning

confidence: 99%

Liouville’s equations for random systems

Jornet

2021

Stochastic Analysis and Applications

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Given a random system, a Liouville's equation is an exact partial differential equation that describes the evolution of the probability density function of the solution. In this paper, we derive Liouville's equations for the first-order homogeneous semilinear random partial differential equation. This is done for all finite-dimensional distributions of the random field solution, starting with dimension one, then dimension two, and finally generalizing to any dimension. Several examples, including the linear advection equation with random coefficients, are treated. As a corollary, we deduce Liouville's equations for path-wise stochastic integrals and nonlinear random ordinary differential equations.

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Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Bevia

López

Micó

2023

Math Methods in App Sciences

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This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be extracted. We combine the Liouville partial differential equation and the random variable transformation method to conduct our study. Finally, all our theoretical findings are illustrated on two stochastic models, widely used in mathematical modeling, for which numerical simulations are carried out.

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Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters

Cited by 14 publications

References 31 publications

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Liouville’s equations for random systems

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

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