An Extensive Statistical Study for the Leukemia Mathematical Model using the RVT Technique

Year 2020, Volume: 3 Issue: 1, 1 - 10, 15.12.2020

Abdallah Mostafa , Howida Slama , Nabila El-bedwhey Mustafa Selim

Abstract

This paper provides a probabilistic study for the four compartmental leukemia mathematical model. Our study focuses on the randomized endemic equilibrium state considering the proliferation rate of the immune cells due to the cancer relapse is a continuous random variable. This treatment makes the presented model to be more realistic and efficient. Depending on the Random Variable Transformation (RVT) technique, the first probability density functions (1-PDFs) for the solution processes of susceptible blood cells, infected blood cells, cancer cells and immune cells are explicitly derived at the equilibrium state. These PDFs are general and valid for any probabilistic distribution of the input random variable. Relying on the obtained PDFs, the main statistical properties, specifically, the mean and the variance functions for the solution processes are conducted. To test the validity of the theoretical findings associated to the proposed randomized leukemia model, some numerical results are presented through an illustrative example.

Keywords

Leukemia mathematical model, Random Variable Transformation (RVT) technique, first probability density function (1-PDF), randomized endemic equilibrium state, random proliferation rate

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