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Mathematical Biosciences and Engineering (MBE)
 

On application of optimal control to SEIR normalized models: Pros and cons
Pages: 111 - 126, Issue 1, February 2017

doi:10.3934/mbe.2017008      Abstract        References        Full text (709.8K)           Related Articles

Maria do Rosário de Pinho - SYSTEC, DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200–465 Porto, Portugal (email)
Filipa Nunes Nogueira - CTAC, Departamento de Engenharia Civil, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal (email)

1 M. Biswas, L. Paiva and M. de Pinho, A SEIR model for control of infectious diseases with constraints, Mathematical Biosciences and Engineering, 11 (2014), 761-784.
2 F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer-Verlag, New York, 2001.       
3 C. Buskens and D. Wassel, The ESA NLP solver WORHP, Modeling and optimization in space engineering, Springer Optim. Appl., Springer, New York, 73 (2013), 85-110.       
4 V. Capasso, Mathematical Structures of Epidemic Systems, Springer-Verlag, Berlin Heidelberg, 2008.       
5 F. Clarke, Optimization and Nonsmooth Analysis, John Wiley & Sons, New York, 1983.       
6 M. de Pinho, I. Kornienko and H. Maurer, Optimal control of a SEIR model with mixed constraints and $L^1$ cost, Springer International Publishing, Switzerland, Lecture Notes in Electrical Engineering, 312 (2015), 135-145.
7 R. Fourer, D. Gay and B. Kernighan, AMPL: A Modeling Language for Mathematical Programming, Duxbury Press, Brooks-Cole Publishing Company, USA, 1993.
8 A. Friedman and C. Kao, Mathematical Modeling of Biological Processes, Springer, Switzerland, 2014.       
9 H. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.       
10 H. Hethcote, The basic epidemiology models: Models, expressions for $r_o$, parameter estimation, and applications, Mathematical Understanding of Infectious Disease Dynamics (S. Ma and Y. Xia, Eds.), World Scientific Publishing Co. Pte. Ltd., Singapore, 16 (2009), 1-61.       
11 W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proceedings of the Royal Society of London. Series A Containing papers of a Mathematical and Physical Nature, 115.
12 A. Korobeinikov, E. V. Grigorieva and E. N. Khailov, Optimal control for an epidemic in a population of varying size, Discrete Contin. Dyn. Syst., (2015), 549-561.       
13 U. Ledzewicz and H. Schaettler, On optimal singular controls for a general sir-model with vaccination and treatment supplement, Discrete and Continuous Dynamical Systems, Series B, 2 (2011), 981-990.       
14 M. Y. Li, J. R. Graef, L. Wang and J. Karsai, Global dynamics of a SEIR model with varying total population size, Mathematical Biosciences, 160 (1999), 191-213.
15 H. Maurer, C. Buskens, J.-H. R. Kim and C. Y. Kaya, Optimization methods for the verification of second order sufficient conditions for bang-bang controls, Optimal Control Applications and Methods, 26 (2015), 129-156.
16 H. Maurer and M. R. de Pinho, Optimal control of seir models in epidemiology with $l^1$ objectives, https://hal.inria.fr/hal-01101291/file/Maurer-dePinho-SEIR.pdf (Accepted).
17 R. M. Neilan and S. Lenhart, An introduction to optimal control with an application in disease modeling, DIMACS Series in Discrete Mathematics, 75 (2010), 67-81.       
18 K. Okosun, O. Rachid and N. Marcus, Optimal control strategies and cost-effectiveness analysis of a malaria model, Biosystems, 111 (2013), 83-101.
19 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, 24, SIAM Publications, Philadelphia, 2012.       
20 H. Schaettler and U. Ledzewicz, Geometric Optimal Control. Theory, Methods and Examples, Springer, New York, 2012.       
21 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.       

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