Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process. (English) Zbl 1393.92008
Summary: 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 \(p \geq 1\). 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.
MSC:
| 92C37 | Cell biology |
| 92C30 | Physiology (general) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
Keywords:
bone remodeling; stochastic differential equations; Brownian motion; moment boundedness; fluctuating periodic solution; osteoclasts; osteoblastsReferences:
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