Analysis of a stochastic hybrid Gompertz tumor growth model driven by Lévy noise

Abstract

This article investigates a stochastic hybrid Gompertz tumor growth model driven by Lévy noise. The global existence of a unique positive solution, extinction, non-persistence in mean, and persistence in mean are well explored. Then, stochastic permanence is obtained by using stochastically ultimately upper bounded and lower bounded. An interesting fact is that the white noise, Markovian noise and Lévy noise can all affect the persistence and extinction of the Gompertz tumor growth model.

Keywords:

• Lévy noise
• Markov chain
• persistence and extinction
• stochastic Gompertz model
• stochastic permanence

2020 MSC:

• 60H10
• 92B05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research work was supported by the Natural Science Foundation of Henan province (242300420247), the Fundamental Research Funds for the Universities of Henan Province (NSFRF240815), the Foundation of Henan Educational Committee (23A110009), and the Program of Young Scholar for Henan Polytechnic University (2020XQG-03).