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

Abstract 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.