A full probabilistic solution of a stochastic red blood cells model using RVT technique

• Published in: European physical journal plus Vol. 136; no. 4; p. 381
• Main Authors: Hussein, A., Slama, H., Selim, M. M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2021; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Blood; Bone marrow; Circulatory system; Complex Systems; Condensed Matter Physics; Confidence intervals; Difference equations; Epidemiology; Erythrocytes; Finite element analysis; Initial conditions; Mathematical and Computational Physics; Mathematical models; Molecular; Optical and Plasma Physics; Ordinary differential equations; Partial differential equations; Physics; Physics and Astronomy; Probability density functions; Probability theory; Random variables; Regular Article; Spleen; Statistical analysis; Stochastic models; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-01332-z

Mathematical modeling is one of the most interesting ways to express the problem that describe the dynamics of the number of red blood cells count in the bloodstream of the human body. This problem has been deterministically solved based on continuous or discrete differential models. However, the stochastic models of this problem are rarely available and inadequate. This paper is organized to solve the random homogeneous linear second-order difference equation that describes a stochastic discrete red blood cells model. A complete probabilistic solution of this problem is conducted via applying the random variable transformation technique. This is achieved by deriving the first probability density function of the solution processes. The probabilistic behavior of the steady-state case (when time tends to infinity) is also studied. Moreover, the fundamental statistical measures, related to the stochastic solutions, such as the mean, the variance and the confidence intervals, are obtained. For the sake of clarity, numerical results (for pre-assigned distributions to the model parameters and initial conditions) with conclusions are presented.