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

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  • Mohamed Abd Allah El-Hadidy

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).

Suggested Citation

  • Mohamed Abd Allah El-Hadidy, 2021. "Stochastically escaping model in a tumour cell growth system driven by a Poisson process," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 19(4), pages 490-499.
    • Handle: RePEc:ids:ijmore:v:19:y:2021:i:4:p:490-499
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