Androgen driven evolutionary population dynamics in prostate cancer growth

Ebraheem O. Alzahrani, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia, Muhammad Altaf Khan, Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam, and, Faculty of Mathematics and Statistics, Duc Thang University, Ho Chi Minh City, Vietnam
2018 Discrete and Continuous Dynamical Systems. Series S  
Prostate cancer worldwide is regarded the second most frequent diagnosed cancer in men with (899,000 new cases) while in common cancer it is the fifth. Regarding the treatment of progressive prostate cancer the most common and effective is the intermittent androgen deprivation therapy. Usually this treatment is effective initially at regressing tumorigenesis, mostly a resistance to treatment can been seen from patients and is known as the castration-resistant prostate cancer (CRPC), so there is
more » ... (CRPC), so there is no any treatment and becomes fatal. Therefore, we proposed a new mathematical model for the prostate cancer growth with fractional derivative. Initially, we present the model formulation in detail and then apply the fractional operator Atangana-Baleanu to the model. The fractional model will be studied further to analyze and show its existence of solution. Then, we provide a new iterative scheme for the numerical solution of the prostate cancer growth model. The analytical results are validated by considering various values assigned to the fractional order parameter α. 2020 Mathematics Subject Classification. Primary: 34A08, 92B05; Secondary: 65R99.
doi:10.3934/dcdss.2020426 fatcat:oftaex567jfc3poml7xa5infzq