Analysis of a planar differential system arising from hematology
DOI:
https://doi.org/10.24193/subbmath.2018.2.07Keywords:
Nonlinear dynamic system, existence and uniqueness, continuous dependence on data, boundedness, global asymptotic stability, biomathematical model.Abstract
A complete analysis of a planar dynamic system arising from hematology is provided to confirm the conclusions of computer simulations. Existence and uniqueness for the Cauchy problem, boundedness of solutions and their asymptotic behavior to infinity are established. Particularly, the global asymptotic stability of a steady state is proved in each of the following cases related to leukemia: normal, chronic and accelerated-acute.
Mathematics Subject Classification (2010): 34A34, 34D23, 93D20.
References
Barbu, V., Differential Equations, Springer, Cham, 2017.
Cucuianu, A., Precup, R., A hypothetical-mathematical model of acute myeloid leukemia pathogenesis, Comput. Math. Methods Med., 11(2010), 49-65.
Dingli, D., Michor, F., Successful therapy must eradicate cancer stem cells, Stem Cells, 24(2006), 2603-2610.
Parajdi, L.G., Modeling the treatment of tumor cells in a solid tumor, J. Nonlinear Sci. Appl., 7(2014), 188-195.
Parajdi, L.G., Precup, R., Bonci, E.A., A mathematical model of the transition from the normal hematopoiesis to the chronic and accelerated acute stages in myeloid leukemia, submitted.
Precup, R., Ordinary Differential Equations, De Gruyter, Berlin, 2018.
Precup, R., Arghirescu, S., Cucuianu, A., S¸erban, M., Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation, Int. J. Biomath., 5(2012), no. 2, Article 1250026, 1-18.
Precup, R., S¸erban, M.., Trif, D., Cucuianu, A., A planning algorithm for correction therapies after allogeneic stem cell transplantation, J. Math. Model. Algor., 11(2012), 309-323.
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