Combination of singularly perturbed vector field method and method of directly defining the inverse mapping applied to complex ODE system prostate cancer model. Issue 1 (1st January 2018)

• Record Type: Journal Article
• Authors: Nave, Ophir; Elbaz, Miriam
• Is Part Of: Journal of biological dynamics. Volume 12:Issue 1(2018)
• Page Start: 961
• Page End: 986
• Publication Date: 2018-01-01
• Subjects: Semi-analytical method -- prostate cancer -- PSA -- immunotherapy -- tumour -- ordinary differential equations; Mathematical Biology Model -- Asymptotic Analysis -- Qualitative theory; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2018.1541104
• Languages: English
• ISSNs: 1751-3758

Abstract

ABSTRACT: We propose a new method to solve a system of complex ordinary differential equations (ODEs) with hidden hierarchy. Given a complex system of the ODE, the hierarchy of the system is generally hidden. Once we reveal the hierarchy of the system, the system can be reduced into subsystems called slow and fast subsystems. This division of slow and fast subsystems reduces the analysis and hence reduces the computation time, which can be expensive. In our new method, we first apply the singularly perturbed vector field method that is the global quasi-linearization method. This method exposes the hierarchy of a given complex system. Subsequently, we apply a version of the homotopy analysis method called the method of directly defining the inverse mapping. We applied our new method to the immunotherapy of advanced prostate cancer.