TY - JOUR
T1 - Ultimate Dynamics Analysis of the 5D Structural Leukemia Model and Partitioning of the Parameter Space
AU - Starkov, K. E.
N1 - Publisher Copyright:
© World Scientific Publishing Company.
PY - 2022/12/30
Y1 - 2022/12/30
N2 - In this paper, we study the global dynamics of the 5D structural leukemia model with 14 parameters as developed by Clapp et al. [2015]. This model describes the interaction between leukemic cell populations and the immune system. Our analysis is based on the localization method of compact invariant sets. We develop this method by introducing the notion of a partitioning of the parameter space and the notion of a localization set corresponding to this partitioning as its parameters change. Further, we obtain ultimate upper and lower bounds for all variables of a state vector without imposing additional restrictions. Local asymptotic stability conditions with respect to the leukemia-free equilibrium point (EP) are given. We deduce formulas describing inner EPs expressed in terms of positive roots of one 7D equation. Based on this equation, it is shown that the number of inner EPs cannot exceed 3 and one case of a global bifurcation of EPs is detected. Next, we prove the existence of the attracting set. Further, in two theorems, the global eradication/extinction leukemia theorems are described. The impact of using parametrically variable localization sets for a qualitative analysis of the ultimate behavior of leukemic cell populations is discussed.
AB - In this paper, we study the global dynamics of the 5D structural leukemia model with 14 parameters as developed by Clapp et al. [2015]. This model describes the interaction between leukemic cell populations and the immune system. Our analysis is based on the localization method of compact invariant sets. We develop this method by introducing the notion of a partitioning of the parameter space and the notion of a localization set corresponding to this partitioning as its parameters change. Further, we obtain ultimate upper and lower bounds for all variables of a state vector without imposing additional restrictions. Local asymptotic stability conditions with respect to the leukemia-free equilibrium point (EP) are given. We deduce formulas describing inner EPs expressed in terms of positive roots of one 7D equation. Based on this equation, it is shown that the number of inner EPs cannot exceed 3 and one case of a global bifurcation of EPs is detected. Next, we prove the existence of the attracting set. Further, in two theorems, the global eradication/extinction leukemia theorems are described. The impact of using parametrically variable localization sets for a qualitative analysis of the ultimate behavior of leukemic cell populations is discussed.
KW - Ordinary differential equation
KW - compact invariant set
KW - leukemia
KW - localization
KW - partitioning
UR - http://www.scopus.com/inward/record.url?scp=85147026658&partnerID=8YFLogxK
U2 - 10.1142/S0218127422502388
DO - 10.1142/S0218127422502388
M3 - Artículo
AN - SCOPUS:85147026658
SN - 0218-1274
VL - 32
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
IS - 16
M1 - 2250238
ER -