Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p >= 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.