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.
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The authors are very grateful to the anonymous referees whose comments and suggestions have contributed to improve this paper. This work was supported in part by the Ministerio de Economia y Competitividad, Spain, under Grant MTM2011-28962.
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Spina, S., Giorno, V., Román-Román, P. et al. A Stochastic Model of Cancer Growth Subject to an Intermittent Treatment with Combined Effects: Reduction in Tumor Size and Rise in Growth Rate. Bull Math Biol 76, 2711–2736 (2014). https://doi.org/10.1007/s11538-014-0026-8
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DOI: https://doi.org/10.1007/s11538-014-0026-8