<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A B-cell chronic lymphocytic leukemia has been modeled via a highly nonlinear system of ordinary differential equations. We consider the rather important theoretical question of the equilibria existence. Under suitable assumptions all model populations are shown to coexist.</p>
</abstract>

A B-cell chronic lymphocytic leukemia has been modeled via a highly nonlinear system of ordinary differential equations. We consider the rather important theoretical question of the equilibria existence. Under suitable assumptions all model populations are shown to coexist.

Mathematical analysis of a B-cell chronic lymphocytic leukemia model with immune response

Dipartimento di Matematica “Giuseppe Peano”

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 Public License.

A B-cell chronic lymphocytic leukemia has been modeled via a highly nonlinear system of ordinary differential equations. We consider the rather important...

b_B	constant source rate of B-CLL produced by bone marrow
r	replication rate of the leukemic B cells
d_B	natural mortality rate of the leukemic B
d_BN	killing rate of B-CLL cells by N cells
d_BT	killing rate of B-CLL cells by T cells
b_N	constant source rate of N cells
d_N	mortality rate of N cells
d_NB	deactivation rate of N cells by contact with B-CLL cells
b_T	constant production rate of T cells
d_T	natural mortality rate of T cells
d_TB	T cells activity suppression rate by contact with B-CLL cells
k	fraction of T_H cell activation that results in T cells recruitment
a_TH	maximal T_H cells activation rate by contact with B-CLL cells
b_T_H	constant production rate of T_H cells
d_T_H	natural mortality rate of T_H cells
s	half saturation constant
L	parameter shaping the saturating sigmoid response

a₆	a₅	a₄	a₃	a₂	a₁	a₀	sign variations	positive roots
-	-	+	+	+	+	+	1	1
-	-	+	+	+	-	+	3	1 or 3
-	-	+	-	+	+	+	3	1 or 3
-	-	+	-	+	-	+	5	1 or 3 or 5
-	-	-	+	+	+	+	1	1
-	-	-	+	+	-	+	3	1 or 3
-	-	-	-	+	+	+	1	1
-	-	-	-	+	-	+	3	1 or 3

a_L+3	a_L+2	a_L+1	a_L	a₃	a₂	a₁	a₀	sign variations	positive roots
-	-	+	+	+	+	+	+	1	1
-	-	+	+	+	+	-	+	3	1 or 3
-	-	+	-	+	+	+	+	3	1 or 3
-	-	+	-	+	+	-	+	5	1 or 3 or 5
-	-	-	+	+	+	+	+	1	1
-	-	-	+	+	+	-	+	3	1 or 3
-	-	-	-	+	+	+	+	1	1
-	-	-	-	+	+	-	+	3	1 or 3

Mathematical analysis of a B-cell chronic lymphocytic leukemia model with immune response

Published Online: Dec 26, 2019

Page range: 551 - 558

Received: Jun 23, 2019

Accepted: Sep 26, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00052

Keywords
Leukemia, Descartes rule, Local stability

© 2019 Youcef Belgaid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Model parameters and their meaning

Signs of the coefficients of equation (12) for the case L = 3

Signs of the coefficients of equation (7) for a general value of L

Mathematical analysis of a B-cell chronic lymphocytic leukemia model with immune response

Published Online: Dec 26, 2019

Page range: 551 - 558

Received: Jun 23, 2019

Accepted: Sep 26, 2019

DOI: https://doi.org/10.2478/AMNS.2019.2.00052

KeywordsLeukemia, Descartes rule, Local stability

© 2019 Youcef Belgaid et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Model parameters and their meaning

Signs of the coefficients of equation (12) for the case L = 3

Signs of the coefficients of equation (7) for a general value of L

Keywords
Leukemia, Descartes rule, Local stability