A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation

• Autorzy: Parajdi Lorand Gabriel , Precup Radu , Haplea Ioan Ştefan

Identyfikatory

DOI

10.34768/amcs-2023-0029

• Języki publikacji: EN

Abstrakty

EN

A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka-Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.

Słowa kluczowe

EN

control problem; lower and upper solution; fixed point; approximation algorithm; numerical solution; medical application

PL

sterowanie optymalne; punkt stały; algorytm aproksymacyjny; rozwiązanie numeryczne; zastosowanie medyczne

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2023
• Tom: Vol. 33, no. 3
• Strony: 409--418
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Parajdi Lorand Gabriel

• Department of Mathematics, West Virginia University, P.O. Box 6201, Morgantown, WV 26506, USA
• Department of Mathematics, Babeş-Bolyai University, M. Kogălniceanu Street, No. 1, 400084 Cluj-Napoca, Romania

autor

Precup Radu

• Institute of Advanced Studies in Science and Technology, Babeş-Bolyai University, M. Kogălniceanu Street, No. 1, 400084 Cluj-Napoca, Romania
• Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania

autor

Haplea Ioan Ştefan

• Department of Internal Medicine, Iuliu Haţieganu University of Medicine and Pharmacy, Victor Babeş Street, No. 8, 400012 Cluj-Napoca, Romania

Bibliografia

• [1] Barbu, V. (2016). Differential Equations, Springer, Cham.
• [2] Coron, J.-M. (2007). Control and Nonlinearity, Mathematical Surveys and Monographs, Vol. 136, American Mathematical Society, Providence.
• [3] DeConde, R., Kim, P.S., Levy, D. and Lee, P.P. (2005). Post-transplantation dynamics of the immune response to chronic myelogenous leukemia, Journal of Theoretical Biology 236(1): 39-59.
• [4] Foley, C. and Mackey, M.C. (2009). Dynamic hematological disease: A review, Journal of Mathematical Biology 58(1): 285-322.
• [5] Haplea, I. ¸S., Parajdi, L.G. and Precup, R. (2021). On the controllability of a system modeling cell dynamics related to leukemia, Symmetry 13(10): 1867.
• [6] Kelley, C.T. (1995). Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia.
• [7] Kim, P.S., Lee, P.P. and Levy, D. (2007). Mini-transplants for chronic myelogenous leukemia: A modeling perspective, in I. Queinnec (Ed.), Biology and Control Theory: Current Challenges, Lecture Notes in Control and Information Sciences, Vol. 357, Springer, Berlin, pp. 3-20.
• [8] Langtangen, H.P. and Mardal, K.A. (2019). Introduction to Numerical Methods for Variational Problems, Springer, Cham.
• [9] Parajdi, L.G. (2020). Stability of the equilibria of a dynamic system modeling stem cell transplantation, Ricerche di Matematica 69(2): 579-601.
• [10] Parajdi, L.G., Patrulescu, F.-O., Precup, R. and Haplea, I.Ş. (2023). Two numerical methods for solving a nonlinear system of integral equations of mixed Volterra-Fredholm type arising from a control problem related to leukemia, Journal of Applied Analysis & Computation, DOI: 10.11948/20220197, (online first).
• [11] Precup, R. (2002). Methods in Nonlinear Integral Equations, Kluwer Academic Publishers, Dordrecht.
• [12] Precup, R. (2022). On some applications of the controllability principle for fixed point equations, Results in Applied Mathematics 13: 100236.
• [13] Precup, R., Dima, D., Tomuleasa, C., ¸Serban, M.-A. and Parajdi, L.-G. (2018). Theoretical models of hematopoietic cell dynamics related to bone marrow transplantation, in Atta-ur-Rahman and S. Anjum (Eds.), Frontiers in Stem Cell and Regenerative Medicine Research,Vol. 8, Bentham Science Publishers, Sharjah, pp. 202-241.
• [14] Precup, R., Şerban, M.-A. and Trif, D. (2013). Asymptotic stability for a model of cell dynamics after allogeneic bone marrow transplantation, Nonlinear Dynamics and Systems Theory 13(1): 79-92.
• [15] Precup, R., Şerban, M.-A., Trif, D. and Cucuianu, A. (2012). A planning algorithm for correction therapies after allogeneic stem cell transplantation, Journal of Mathematical Modelling and Algorithms 11(3): 309-323.
• [16] Precup, R., Trif, D., Şerban, M.-A. and Cucuianu, A. (2010). A mathematical approach to cell dynamics before and after allogeneic bone marrow transplantation, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity 8: 167-175.
• [17] Rahmani Doust, M.H. (2015). The efficiency of harvested factor: Lotka-Volterra predator-prey model, Caspian Journal of Mathematical Sciences 4(1): 51-59.