Bifurcation analysis for a fractional‐order chemotherapy model with two different delays. (4th December 2019)

• Record Type: Journal Article
• Authors: Xu, Changjin; Li, Peiluan; Liao, Maoxin; Yuan, Shuai
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 3(2020)
• Page Start: 1053
• Page End: 1083
• Publication Date: 2019-12-04
• Subjects: cancer treatment -- chemotherapy model -- delay -- fractional order -- Hopf bifurcation -- stability; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5889
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Cancer is one of the most serious diseases in the world. The investigation on cancer treatment has attracted great attention from medical workers, mathematical researchers, and scholars in various fields. To understand the intrinsic characteristics of cancer, numerous scholars have established cancer treatment models and discussed the dynamical properties. However, the main work of many scholars only focuses on the integer‐order cancer treatment models, while the study on fractional‐order ones is quite a few. In the present article, on the basis of previous publications, we will put up a new fractional‐order chemotherapy model with two different delays. By applying the stability theory and the Hopf bifurcation of fractional‐order differential equations, we obtain a series of new stability criteria of the involved model and some sufficient conditions to ensure the existence of Hopf bifurcation of the involved model. Furthermore, the impact of two different delays and the fractional order on the stability and the emergence of Hopf bifurcation of involved model is presented. To illustrate the validity of analytical predictions, we perform computer simulations with Matlab software. The theoretical results in the manuscript are innovative and play an important role in cancer treatment.