Analysis and Estimation of Chaotic Tumor Evolution under Immunotherapy Treatment

Resumen: This paper is focused on the study of the global dynamics of a chaotic-cancer system. This mathematical model describes the dynamics of cancer cells and its interaction with healthy cells and effector-immune cells, the system considers the influx of effector cells by adding an immunotherapy treatment parameter. By applying the Localization of Compact Invariant Sets method we derive lower and upper bounds with conditions written in terms of the immunotherapy treatment parameter. Furthermore, due to the diffculty to measure the population of effector-immune cells in lab environments, a nonlinear observer is designed to estimate the concentration of these cells. We design the observer by considering the measurements of cancer cells and healthy host cells, as well as the upper bounds computed with the LCIS method. Finally, numerical simulations are performed to illustrate and support the analytical results.

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Itzel Sanchez-Robles, Paul A. Valle-Trujillo & Ramon Ramirez-Villalobos. Analysis and Estimation of Chaotic Tumor Evolution under Immunotherapy Treatment. Memorias del Congreso Nacional de Control Automático, pp. 726-731, 2019.

Palabras clave

Sistemas Biomédicos, Sincronización de Sistemas, Sistemas Caóticos

• F. Hoppensteadt Getting Started in Mathematical Biology. NOTICES OF THE AMS, 42(9), 969–947, 1995.
• M. Itik and S.P. Banks Chaos in a three-dimensional cancer model. International Journal of Bifurcation and Chaos, 20(1), 71–79, 20103
• D. Kirschner and J. C. Panetta Modeling immunotherapy of the tumor–immune interaction. Journal of Mathematical, 37(3), 235–252, 1998.
• A.P. Krishchenko Localization of invariant compact sets of dynamical systems Journal of Differential Equations, 41(12), 1669–1676, 2005.
• C. Latellier and F. Denis and L.A. Aguirre What Can be Learned from a Chaotic Cancer Model? Journal of Theoretical Biology, 322, 7–16, 2013.
• H. J. Marquez Nonlinear Control Systems: Analysis and Design John Wiley & sons, 2013.
• National Cancer Institute Immunotherapy to Treat Cancer https://www.cancer.gov/aboutcancer/treatment/types/immunotherapy
• National Cancer Institute What Is Cancer? https://www.cancer.gov/about-cancer/understan ding/what-is-cancer
• G. Panomchoeng and R. Rajamani Observer Design for Lipschitz Nonlinear Systems Using Riccati Equations Proceeding of the 2010 American Control Conference ACC, 6060–6065, 2010.
• L. G. Pillis and A. Radunskaya The Dynamics of an Optimally Controlled Tumor Model: A Case Study Mathematical and Computer Modelling, 37(11), 1221– 1244, 2003.
• P. Rokhforoz and A.A. Jamshidi and N. Namazi Adaptive robust control of cancer chemotherapy with extended Kalman filter observer Informatics in Medicine Unlocked, 8, 1–7, 2017.
• K.E. Starkov and A.P. Krishchenko On the Global Dynamics of One Cancer Tumor Growth Model Communications in Nonlinear Science Numerical Simulation, 19(5), 1486–1495, 2014.
• P.A. Valle and L.N. Coria and D. Gamboa and C. Plata Bounding the Dynamics of a Chaotic-Cancer Mathematical Model Mathematical Problems in Engineering, ID 9787015, 14 pages, 2018.