Title: Stochastically escaping model in a tumour cell growth system driven by a Poisson process

Authors: Mohamed Abd Allah El-Hadidy

Addresses: Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt; Mathematics and Statistics Department, College of Science, Taibah University, Yanbu, Saudi Arabia

Abstract: We present a new model for the stochastic escaping phenomenon from the chemical treatment in a tumour cell growth system subjected to a Poisson process. This phenomenon has the same behaviour of the reneging units in M/M/1/N queue where these units have stochastically grown by a Poisson process. More than finding the statistical distribution of these cells (reneging units), we get the expected value and the variance of these units at any time. This time is depending on the total number of infected cells (N units) in the system. In addition, by knowing the average number of units in M/M/1/N queue, we can get the expected value of the treatment cells (servicing units number).

Keywords: statistical physics; tumour cells growth system; Poisson process; stochastic growth.

DOI: 10.1504/IJMOR.2021.117623

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.4, pp.490 - 499

Received: 01 Jun 2020
Accepted: 08 Jun 2020
Published online: 16 Sep 2021 *

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