|
B. Buonomo
and M. Cerasuolo
, The effect of time delay in plant-pathogen interactions with host demography, Math. Biosciences and Engineering, 12 (2015)
, 473-490.
doi: 10.3934/mbe.2015.12.473.
|
|
C. Büskens,
Optimierungsmethoden und Sensitivitätsanalyse für optimale Steuerprozesse mit Steuer- und Zustands-Beschränkungen, PhD thesis, Institut für Numerische Mathematik, Westfälische Wilhelms-Universität Münster, Germany, 1998.
|
|
C. Büskens
and H. Maurer
, SQP methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control, J. Comput. Appl. Math., 120 (2000)
, 85-108.
doi: 10.1016/S0377-0427(00)00305-8.
|
|
C. Büskens and M. Gerdts, WORHP: Large-Scale Sparse Nonlinear Optimization Solver, http://www.worhp.de.
|
|
Q. Chai
, R. Loxton
, K. L. Teo
and C. Yang
, A class of optimal state-delay control Problems, Nonlinear Analysis: Real World Applications, 14 (2013)
, 1536-1550.
doi: 10.1016/j.nonrwa.2012.10.017.
|
|
R. V. Culshaw
and S. Ruan
, A delay-differential equation model of HIV infection of CD4+ T-cells, Mathematical Biosciences, 165 (2000)
, 27-39.
doi: 10.1016/S0025-5564(00)00006-7.
|
|
S. Eikenberry
, S. Hews
, J. D. Nagy
and Y. Kuang
, The dynamics of a delay model of Hepatitis B virus infection with logistic hepatocyte growth, Mathematical Biosciences, 6 (2009)
, 283-299.
doi: 10.3934/mbe.2009.6.283.
|
|
R. Fourer, D. M. Gay and B. W. Kernighan,
AMPL: A Modeling Language for MathematicalProgramming, The Scientific Press, South San Francisco, California, 1993.
|
|
L. Göllmann
, D. Kern
and H. Maurer
, Optimal control problems with delays in state and control and mixed control-state constraints, Optimal Control Applications and Methods, 30 (2009)
, 341-365.
doi: 10.1002/oca.843.
|
|
L. Göllmann
and H. Maurer
, Theory and applications of optimal control problems with multiple time-delays, Journal of Industrial and Management Optimization, 10 (2014)
, 413-441.
|
|
T. Guinn
, Reduction of delayed optimal control problems to nondelayed problems, Journal of Optimization Theory and Applications, 18 (1976)
, 371-377.
doi: 10.1007/BF00933818.
|
|
R. F. Hartl
, S. P. Sethi
and R. G. Vickson
, A survey of the maximum principles for optimal control problems with state constraints, SIAM Review, 37 (1995)
, 181-218.
doi: 10.1137/1037043.
|
|
M. R. Hestenes,
Calculus of Variations and Optimal Control Theory, John Wiley, New York, 1966.
|
|
S. C. Huang
, Optimal Control problems with retardations and restricted phase coordinates, Journal of Optimization Theory and Applications, 3 (1969)
, 316-360.
doi: 10.1007/BF00931371.
|
|
J. Klamka
, H. Maurer
and A. Swierniak
, Local controllability and optimal control for a model of combined anticancer therapy with control delays, Mathematical Biosciences and Engineering, 14 (2017)
, 195-216.
doi: 10.3934/mbe.2017013.
|
|
Y. Kuang,
Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, 1993.
|
|
H. Maurer
, C. Büskens
, J.-H. R. Kim
and Y. Kaya
, Optimization methods for the verification of second-order sufficient conditions for bang-bang controls, Optimal Control Methods and Applications, 26 (2005)
, 129-156.
doi: 10.1002/oca.756.
|
|
R. M. May
, Time-delay versus stability in population models with two and three tropic levels, Ecology, 54 (1973)
, 315-325.
|
|
N. P. Osmolovskii and H. Maurer,
Applications to Regular and Bang-Bang Control: Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control, SIAM Advances in Design and Control, Vol. DC 24, SIAM Publications, Philadelphia, 2012.
doi: 10.1137/1.9781611972368.
|
|
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko,
The Mathematical Theory of Optimal Processes, Translation by K. N. Trirogoff, Wiley, New York, 1962.
|
|
F. Rihan, D. H. Abdelrahman, F. Al-Maskari, F. Ibrahim and M. A. Abdeen, Delay differential model for tumour-immune-response with chemoimmunotherapy and optimal control.
Computational and Mathematical Methods in Medicine, Hindawi Publishing Corporation, Vol. 2014, Article ID 982978, (2014).
doi: 10.1155/2014/982978.
|
|
H. Schättler
, U. Ledzewicz
and H. Maurer
, Sufficient conditions for strong local optimality in optimal control problems with L2-type objectives and control constraints, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014)
, 2657-2679.
doi: 10.3934/dcdsb.2014.19.2657.
|
|
C. Silva
, H. Maurer
and D.F.M. Torres
, Optimal control of a tuberculosis model with state and control delays, Mathematical Biosciences and Engineering, 14 (2017)
, 321-337.
doi: 10.3934/mbe.2017021.
|
|
C. T. Sreeramareddy
, K. V. Panduru
, J. Menten
and J. V. den Ende
, Time delays in diagnosis of pulmonary tuberculosis: A systematic review of literature, BMC Infectious Diseases, 9 (2009)
, 91-100.
doi: 10.1186/1471-2334-9-91.
|
|
J. Stoer and R. Bulirsch,
Introduction ot Numerical Analysis, Third Edition, Texts in Applied Mathematics, Springer-Verlag, Berlin, 1990.
doi: 10.1007/978-3-662-22250-8.
|
|
D. G. Storla
, S. Yimer
and G. A. Bjune
, A systematic review in delay in the diagnosis and treatment of tuberculosis, BMC Public Health, 8 (2008)
, p15.
doi: 10.1186/1471-2458-8-15.
|
|
P. van den Driessche,
Some Epidemiological Models with Delays, Report DMS-679-IR, University of Victoria, Department of Mathematics, 1994.
|
|
A. Wächter
and L. T. Biegler
, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Mathematical Programming, 106 (2006)
, 25-57.
doi: 10.1007/s10107-004-0559-y.
|
|
H. Yang
and J. Wei
, Global behaviour of a delayed viral kinetic model with general incidence rate, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015)
, 1573-1582.
doi: 10.3934/dcdsb.2015.20.1573.
|