Electron. J. Diff. Equ., Vol. 2013 (2013), No. 272, pp. 1-14.

Existence of periodic solutions in the modified Wheldon model of CML

Pablo Amster, Rocio Balderrama, Lev Idels

Abstract:
The Wheldon model (1975) of a chronic myelogenous leukemia (CML) dynamics is modified and enriched by introduction of a time-varying microenvironment and time-dependent drug efficacies. The resulting model is a special class of nonautonomous nonlinear system of differential equations with delays. Via topological methods, the existence of positive periodic solutions is proven.

Submitted October 11, 2013. Published December 17, 2013.
Math Subject Classifications: 34K20, 92D25, 34K45, 34K12, 34K25.
Key Words: Nonlinear nonautonomous delay differential equation; positive periodic solution; Leray-Schauder degree; chronic myelogenous leukemia; model with pharmacokinetics.

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Pablo Amster
Departamento de Matemática
FCEyN - Universidad de Buenos Aires & IMAS-CONICET
Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
email: pamster@dm.uba.ar
Rocío Balderrama
Departamento de Matemática
FCEyN - Universidad de Buenos Aires & IMAS-CONICET
Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
email: rbalde@dm.uba.ar
Lev Idels
Department of Mathematics
Vancouver Island University (VIU)
900 Fith St. Nanaimo BC Canada
email: lev.idels@viu.ca

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