A stochastic model for the evolution of bone metastasis: Persistence and recovery

Bone metastasis is a complex disease that modifies the natural dynamics of the bone remodeling process which is vital for maintaining a healthy bone structure. Nowadays, there are deterministic differential models that describe the bone metastasis evolution by considering interaction mechanisms between cancer cells and basic bone cells, such as osteoclasts and osteoblasts. Based on these deterministic models, a stochastic differential model is proposed to describe the bone metastasis evolution in order to analyze the effect of environmental fluctuations inclusions. Conditions for the existence and uniqueness of a nonnegative solution of the proposed stochastic model are given to characterize whether the invasion of cancer persists or is eradicated. Finally, we illustrate different dynamical behaviors of the stochastic solution by means of numerical simulations.