Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 11, Number 4, 2016
Ecology, Epidemiology and Evolution
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Page(s) | 89 - 104 | |
DOI | https://doi.org/10.1051/mmnp/201611407 | |
Published online | 19 July 2016 |
- B.M. Adams, H.T. Banks, H.D. Kwon, H.T. Tran. Dynamic multidrug therapies for HIV: optimal and STI control approaches. Math. Biosci. Eng., 1 (2004), 223–241. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- S. Anita, V. Arnăutu, V. Capasso. Introduction to Optimal Control Problems in Life Sciences and Economics. Birkhäuser, USA, 2011. [Google Scholar]
- S. Butler, D. Kirschner, S. Lenhart. Optimal control of the chemotherapy affecting the infectivity of HIV, in Advances in Mathematical Population Dynamics - Molecules, Cells and Man, (Eds. O. Arino, D. Axelrod, and M. Kimmel), Vol. 6, World Scientific, Singapore, 1997, 557–569. [Google Scholar]
- R.V. Culshaw, S. Ruan, R.J. Spiteri. Optimal HIV treatment by maximising immune response. J. Math. Biol., 48 (2004), 545–562. [Google Scholar]
- B.P. Demidovich. Lectures on Stability Theory. Nauka, Moscow, 1967 (in Russian). [Google Scholar]
- A.V. Dmitruk. A generalized estimate on the number of zeros for solutions of a class of linear differential equations. SIAM J. Control Optim., 30 (1992), No. 5, 1087–1091. [CrossRef] [MathSciNet] [Google Scholar]
- K.R. Fister, S. Lenhart, J.S. McNally. Optimizing chemotherapy in an HIV model. Electronic Journal of Differential Equations, 1998 (1998), No. 32, 1–12. [Google Scholar]
- H. Gaff, E. Schaefer. Optimal control applied to vaccination and treatment strategies for various epidemiological models. Math. Biosci. Eng., 6 (2009), No. 3, 469–492. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- E. Grigorieva, N. Bondarenko, E. Khailov, A. Korobeinikov. Finite-dimensional methods for optimal control of autothermal thermophilic aerobic digestion, in Industrial Waste, (Eds. K.-Y. Show and X. Guo), InTech, Croatia, 2012, 91–120, ISBN: 978-953-51-0253-3. http://www.intechopen.com/articles/show/title/nite-dimensional-methods-for-optimal-controlof-waste-water-process [Google Scholar]
- E.V. Grigorieva, N.V. Bondarenko, E.N. Khailov, A. Korobeinikov. Three-dimensional nonlinear optimal control model of wastewater biotreatment. Neural, Parallel, and Scientific Computations, 20 (2012), No. 1, 23–36. http://www.dynamicpublishers.com/Neural/npsccontent.htm [MathSciNet] [Google Scholar]
- E.V. Grigorieva, N.V. Bondarenko, E.N. Khailov, A. Korobeinikov. Analysis of optimal control problems for the process of wastewater biological treatment. Revista de Matemática: Teoria y Aplicaciones, 20 (2013), No. 2, 103–118, ISSN: 14092433. [CrossRef] [MathSciNet] [Google Scholar]
- E.V. Grigorieva, E.N. Khailov, A. Korobeinikov. Optimal control for an epidemic in a population of varying size. Discret. Contin. Dyn. S., supplement (2015), 549–561. [Google Scholar]
- E.V. Grigorieva, E.N. Khailov, N.V. Bondarenko, A. Korobeinikov. Modeling and optimal control for antiretroviral therapy. J. Biol. Syst., 22 (2014), No. 2, 199–217 DOI: 10.1142/S0218339014400026. [CrossRef] [Google Scholar]
- E.V. Grigorieva, E.N. Khailov, A. Korobeinikov. Optimal control for a SIR infectious disease model. Journal of Coupled Systems and Multiscale Dynamics, 1 (2013), No. 3, 324–331 DOI: 10.1166/jcsmd.2013.1022. [CrossRef] [Google Scholar]
- E.V. Grigorieva, E.N. Khailov, A. Korobeinikov. An optimal control problem in HIV treatment. Discret. Contin. Dyn. S., supplement (2013), 311–322. http://aimsciences.org/journals/pdfs.jsp?paperID=9216&mode=full [Google Scholar]
- E.V. Grigorieva, E.N. Khailov, A. Korobeinikov. Parametrization of the attainable set for a nonlinear control model of a biochemical process. Math. Biosci. Eng., 10 (2013), No. 4, 1067–1094 DOI: 10.3934/mbe.2013.10.1067. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- H.R. Joshi. Optimal control of an HIV immunology model. Optim. Contr. Appl. Met., 23 (2002), 199–213. [Google Scholar]
- D. Kirschner, S. Lenhart, S. Serbin. Optimizing chemotherapy of HIV infection: scheduling, ammounts and initiation of treatment. J. Math. Biol. 35 (1997), 775–792. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Kolmogorov. Sulla teoria di Volterra della lotta per l'esistenza. Gi. Inst. Ital. Attuari, 7 (1936), 74–80. [Google Scholar]
- A. Korobeinikov. Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission. B. Math. Biol., 68 (2006), No. 3, 615–626. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Korobeinikov. Global properties of infectious disease models with non-linear incidence. B. Math. Biol., 69 (2007), No. 6, 1871–1886. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Korobeinikov. Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate. Math. Med. Biol., 26 (2009), No. 3, 225–239. http://imammb.oxfordjournals.org/cgi/reprint/dqp006 [CrossRef] [PubMed] [Google Scholar]
- A. Korobeinikov. Stability of ecosystem: global properties of a general predator-prey model. Math. Med. Biol., 26 (2009), No. 4, 309–321. http://imammb.oxfordjournals.org/cgi/reprint/dqp009 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- A. Korobeinikov, P.K. Maini. Nonlinear incidence and stability of infectious disease models. Math. Med. Biol., 22 (2005), No. 2, 113–128. [CrossRef] [PubMed] [Google Scholar]
- A. Korobeinikov, S.V. Petrovskii. Toward a general theory of ecosystem stability: plankton-nutrient interaction as a paradigm, in Aspects of Mathematical Modelling, (Eds. R.J. Hosking and E. Venturino), Birkhäuser, Basel, 2008, 27–40. [CrossRef] [Google Scholar]
- J.J. Kutch, P. Gurfil. Optimal control of HIV infection with a continuously-mutating viral population, in Proceedings of American Control Conference, Anchorage, Alaska, 2002, 4033–4038. [Google Scholar]
- E.B. Lee, L. Marcus. Foundations of Optimal Control Theory. John Wiley & Sons, New York, 1967. [Google Scholar]
- U Ledzewicz and H. Schättler, On optimal controls for a general mathematical model for chemotherapy of HIV, in Proceedings of American Control Conference, Anchorage, Alaska, 2002, 3454–3459. [Google Scholar]
- U. Ledzewicz, H. Schättler. On optimal singular controls for a general SIR-model with vaccination and treatment. Discret. Contin. Dyn. S., supplement, (2011), 981–990. [Google Scholar]
- S. Lenhart, J.T. Workman. Optimal Control Applied to Biological Models. CRC Press, Taylor & Francis Group, London, 2007. [Google Scholar]
- L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko. Mathematical Theory of Optimal Processes. John Wiley & Sons, New York, 1962. [Google Scholar]
- H. Schättler, U. Ledzewicz. Geometric Optimal Control: Theory, Methods and Examples. Springer, New York-Heidelberg-Dordrecht-London, 2012. [Google Scholar]
- R.F. Stengel, R. Ghigliazza, N. Rulkarni, O. Laplace. Optimal control of innate immune response. Optim. Contr. Appl. Met., 23 (2002), 91–104. [CrossRef] [Google Scholar]
- A.N. Tikhonov, A.B. Vasil'eva, A.G. Sveshnikov. Differential Equations. Springer, Berlin, 1985. [Google Scholar]
- V.V. Velichenko, D.A. Pritykin. Control of the medical treatment of AIDS. Automat. Rem. Contr., 67 (2006), No. 3, 493–511. [CrossRef] [Google Scholar]
- H.G. Zadeh, H.C. Nejad, M.M. Abadi, H.M. Sani. A new fast optimal control for HIV-infection dynamics based on AVK method and fuzzy estimator. American Journal of Scientific Research, 32 (2011), 11–16. [Google Scholar]
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