Inference on a non-homogeneous Gompertz process with jumps as model of tumor dynamics

We propose an inhomogeneous stochastic process with jumps based on the Gompertz diffusion to describe the evolution of a solid tumor subject to an inter- mittent therapeutic program. Each jumps represents an application of a therapy that shifts the cancer mass to a return state. The intermittent treatment leads to a reduc- tion in tumor size, but produces also an increase in the growth rate represented in the model by the inclusion of time functions depending on the cycle of application of the therapy. To find a compromise between these two aspects a strategy to select the inter-jump intervals is proposed and an estimation procedure of the model is provided, supported by several simulations illustrating the validity of the proposed procedure.