Stability analysis on a hybrid PDE–ODE system describing intermittent hormonal therapy of prostate cancer

We consider the stability of control prescribed by hybrid PDE–ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE–ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.

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A Hybrid Systems Approach to Hormonal Therapy of Prostate Cancer and its Nonlinear Dynamics

10.1063/1.2759724 ◽

2007 ◽

Cited By ~ 2

Author(s):

Kazuyuki Aihara ◽

Gouhei Tanaka ◽

Taiji Suzuki ◽

Yoshito Hirata

Keyword(s):

Prostate Cancer ◽

Nonlinear Dynamics ◽

Hybrid Systems ◽

Hormonal Therapy ◽

Systems Approach

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Bifurcation analysis on a hybrid systems model of intermittent hormonal therapy for prostate cancer

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2008.03.044 ◽

2008 ◽

Vol 237 (20) ◽

pp. 2616-2627 ◽

Cited By ~ 27

Author(s):

Gouhei Tanaka ◽

Kunichika Tsumoto ◽

Shigeki Tsuji ◽

Kazuyuki Aihara

Keyword(s):

Prostate Cancer ◽

Hybrid Systems ◽

Bifurcation Analysis ◽

Hormonal Therapy ◽

Systems Model

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Controllability of hybrid PDE‐ODE systems with structural instability and applications to mathematical models on intermittent hormonal therapy for prostate cancer

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5284 ◽

2018 ◽

Vol 41 (17) ◽

pp. 8229-8247

Author(s):

Kurumi Hiruko ◽

Shinya Okabe

Keyword(s):

Prostate Cancer ◽

Mathematical Models ◽

Hormonal Therapy ◽

Structural Instability ◽

Ode Systems

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740: Significance of Micrometastases in Pelvic Lymph Nodes Detected by Real-Time Reverse Transcriptase Polymerase Chain Reaction in Patients with Clinically Localized Prostate Cancer Undergoing Radical Prostatectomy Following Neoadjuvant Hormonal Therapy

The Journal of Urology ◽

10.1016/s0022-5347(18)30980-7 ◽

2007 ◽

Vol 177 (4S) ◽

pp. 248-248

Author(s):

Hideaki Miyake ◽

Toshifumi Kurahashi ◽

Atsushi Takenaka ◽

Isao Hara ◽

Masato Fujisawa

Keyword(s):

Prostate Cancer ◽

Polymerase Chain Reaction ◽

Radical Prostatectomy ◽

Lymph Nodes ◽

Reverse Transcriptase ◽

Real Time ◽

Hormonal Therapy ◽

Chain Reaction ◽

Pelvic Lymph Nodes ◽

Polymerase Chain

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Next generation sequencing panels to predict response to hormonal therapy in prostate cancer

Endocrine Abstracts ◽

10.1530/endoabs.42.p17 ◽

2016 ◽

Author(s):

Heini M L Kallio ◽

Matti Annala ◽

Anniina Brofeldt ◽

Reija Hieta ◽

Kati Kivinummi ◽

...

Keyword(s):

Prostate Cancer ◽

Next Generation Sequencing ◽

Hormonal Therapy ◽

Next Generation ◽

Generation Sequencing

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Faculty Opinions recommendation of Intermittent hormonal therapy in the treatment of metastatic prostate cancer: a randomized trial.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.717956656.793462055 ◽

2012 ◽

Author(s):

Thomas Flaig

Keyword(s):

Prostate Cancer ◽

Randomized Trial ◽

Hormonal Therapy ◽

Metastatic Prostate Cancer

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Monte Carlo Statistical Prediction Method for Optimal Control of Linear Hybrid Systems

ACTA AUTOMATICA SINICA ◽

10.3724/sp.j.1004.2008.01028 ◽

2009 ◽

Vol 34 (8) ◽

pp. 1028-1032

Author(s):

Chun-Yue SONG

Keyword(s):

Optimal Control ◽

Monte Carlo ◽

Hybrid Systems ◽

Prediction Method ◽

Statistical Prediction

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On adaptive optimal control for hybrid systems

2013 IEEE International Conference on Control Applications (CCA) ◽

10.1109/cca.2013.6662858 ◽

2013 ◽

Cited By ~ 3

Author(s):

H. Suda ◽

M. Yamakita

Keyword(s):

Optimal Control ◽

Hybrid Systems ◽

Adaptive Optimal Control

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A prospective clinical and transcriptomic feasibility study of oral‐only hormonal therapy with radiation for unfavorable prostate cancer in men 70 years of age and older or with comorbidity

Cancer ◽

10.1002/cncr.33556 ◽

2021 ◽

Author(s):

Benjamin E. Onderdonk ◽

Paige L. Dorn ◽

Carlos Martinez ◽

Fauzia Arif ◽

Denise Cloutier ◽

...

Keyword(s):

Prostate Cancer ◽

Feasibility Study ◽

Hormonal Therapy

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On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

Advances in Difference Equations ◽

10.1186/s13662-020-02982-6 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

N. H. Sweilam ◽

S. M. Al-Mekhlafi ◽

A. O. Albalawi ◽

D. Baleanu

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Weighted Average ◽

Necessary Optimality Conditions ◽

Numerical Approach ◽

Population Number ◽

Infected People ◽

The Stability ◽

Novel Coronavirus ◽

Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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