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Start Over Descriptor "return process" Journal bulletin of mathematical biology
2 results on '"return process"'

1. A Stochastic Model of Cancer Growth Subject to an Intermittent Treatment with Combined Effects: Reduction in Tumor Size and Rise in Growth Rate.

Author

Spina, Serena, Giorno, Virginia, Román-Román, Patricia, and Torres-Ruiz, Francisco

Subjects
*TUMOR growth, *MATHEMATICAL models, *PHYSIOLOGY, *CARCINOGENS, *INCURABLE diseases
Abstract

A model of cancer growth based on the Gompertz stochastic process with jumps is proposed to analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context, a jump represents an application of the therapy that shifts the cancer mass to a return state and it produces an increase in the growth rate of the cancer cells. For the resulting process, consisting in a combination of different Gompertz processes characterized by different growth parameters, the first passage time problem is considered. A strategy to select the inter-jump intervals is given so that the first passage time of the process through a constant boundary is as large as possible and the cancer size remains under this control threshold during the treatment. A computational analysis is performed for different choices of involved parameters. Finally, an estimation of parameters based on the maximum likelihood method is provided and some simulations are performed to illustrate the validity of the proposed procedure. [ABSTRACT FROM AUTHOR]

Published
2014
Full Text
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2. A Stochastic Model of Cancer Growth Subject to an Intermittent Treatment with Combined Effects: Reduction in Tumor Size and Rise in Growth Rate

Author

Virginia Giorno, Patricia Román-Román, Francisco Torres-Ruiz, and Serena Spina

Subjects
Stochastic modelling, Quantitative Biology::Tissues and Organs, General Mathematics, Immunology, Gompertz function, Return process, Context (language use), Gompertz diffusion process, Intermittent therapy, First passage time, Inference, Models, Biological, General Biochemistry, Genetics and Molecular Biology, Neoplasms, Statistics, Humans, Applied mathematics, Computer Simulation, Growth rate, General Environmental Science, Mathematics, Pharmacology, Likelihood Functions, Stochastic Processes, Stochastic process, General Neuroscience, Mathematical Concepts, Computational Theory and Mathematics, Jump, First-hitting-time model, General Agricultural and Biological Sciences, Constant (mathematics)
Abstract

A model of cancer growth based on the Gompertz stochastic process with jumps is proposed to analyze the effect of a therapeutic program that provides intermittent suppression of cancer cells. In this context, a jump represents an application of the therapy that shifts the cancer mass to a return state and it produces an increase in the growth rate of the cancer cells. For the resulting process, consisting in a combination of different Gompertz processes characterized by different growth parameters, the first passage time problem is considered. A strategy to select the inter-jump intervals is given so that the first passage time of the process through a constant boundary is as large as possible and the cancer size remains under this control threshold during the treatment. A computational analysis is performed for different choices of involved parameters. Finally, an estimation of parameters based on the maximum likelihood method is provided and some simulations are performed to illustrate the validity of the proposed procedure.

Published
2014
Full Text
View/download PDF

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