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Articles

Optimal control of age-structured population dynamics for spread of universally fatal diseases

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Pages 901-921 | Received 08 Aug 2011, Accepted 09 Nov 2011, Published online: 25 Jan 2012

References

  • Lin , F , Muthuraman , K and Lawley , M . An optimal control theory approach to non-pharmaceutical interventions . BMC Infect. Dis. , 10(1)(2010), 32, DOI: 10.1186/1471-2334-10-32
  • E.W. Weisstein, SIR model, from MathWorld – A Wolfram Web Resource. Available at http://mathworld.wolfram.com/SIRModel.html
  • Brauer , F . 1990 . Models for the spread of universally fatal diseases . J. Math. Biol. , 28 : 451 – 462 .
  • Hethcote , HW . 2000 . The mathematics of infectious diseases . SIAM Rev. , 42 ( 4 ) : 599 – 653 .
  • Iannelli , M . 1–5 July 2005 . Mathematical Modelling of Epidemics , Dobbiaco (Bolzano, Italy) : Lecture at Summer School on Mathematical Models in Life Science: Theory and Simulation .
  • Iannelli , M and Martcheva , M . 2003 . “ Homogeneous dynamical systems and the age-structured SIR model with proportionate mixing incidence ” . In Evolution Equations: Applications to Physics, Industry, Life Sciences and Economics, Progress in Nonlinear Differential Equations and their Applications , Edited by: Iannelli , M and Lumer , G . Vol. 55 , 227 – 251 . Basel : Birkhäuser .
  • Rowthorn , RE , Laxminarayan , R and Gilligan , CA . 2009 . Optimal control of epidemics in metapopulations . J. R. Soc. Interf. , 6 ( 41 ) : 1135 – 1144 .
  • Li , MY and Wang , LC . 2002 . “ Global stability in some SEIR epidemic models ” . In Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory, IMA Volumes in Mathematics and its Applications , Edited by: Castillo-Chavez , C , Blower , S , Driessche , Pvan d , Kirschner , D and Yakubu , A-A . Vol. 126 , 295 – 311 . New York : Springer .
  • Behncke , H . 2000 . Optimal control of deterministic epidemic . Optim. Control Appl. Methods , 21 ( 6 ) : 269 – 285 .
  • Iacoviello , D and Liuzzi , G . Optimal Control for SIR Epidemic model: A Two Treatments Strategy, The 16th Mediterranean Conference on Control and Automation, Congress Centre, Ajaccio, France, 25–27 June 2008, pp. 842–847
  • Clancy , D . 1999 . Optimal intervention for epidemic models with general infection and removal rate functions . J. Math. Biol. , 39 : 309 – 331 .
  • Morton , R and Wickwire , KH . 1974 . On the optimal control of a deterministic epidemic . Adv. Appl. Probl. , 6 ( 4 ) : 622 – 635 .
  • Sethi , SP . 1978 . Optimal quarantine programmes for controlling an epidemic spread . J. Oper. Res. Soc. , 29 ( 3 ) : 265 – 268 .
  • Sethi , SP and Staats , PW . 1978 . Optimal control of some simple deterministic epidemic models . J. Oper. Res. Soc. , 29 ( 2 ) : 129 – 136 .
  • Wickwire , K . 1977 . Optimal immunization rules for an epidemic with recovery . Adv. Appl. Probl. , 9 ( 2 ) : 222 – 223 .
  • Fattorini , HO . 1999 . “ Infinite-Dimensional Optimization and Control Theory ” . In Encyclopedia of Mathematics and its Applications , Vol. 62 , Cambridge : Cambridge University Press .
  • Li , X and Yong , J . 1995 . Optimal Control Theory for Infinite Dimensional Systems , Boston : Birhäuser .
  • Sloss , JM , Bruch , JC Jr. , Sadek , IS and Adali , S . 1998 . Maximum principle for optimal boundary control of vibrating structures with applications to beams . Dyn. Control , 8 ( 4 ) : 355 – 375 .
  • Ho , YC and Pepyne , DL . 2002 . Simple explanation of the no-free-lunch theorem and its implications . J. Optim. Theory Appl. , 115 ( 3 ) : 549 – 570 .
  • Ratmansky , I and Margaliot , M . 2010 . A simplification of the Agrachev-Gamkrelidze second-order variation for bang-bang controls . Syst. Control Lett. , 59 ( 1 ) : 25 – 32 .
  • Tachim Medjo , T . 2010 . Optimal control of the primitive equations of the ocean with state constraints . Nonlinear Anal. , 73 ( 3 ) : 634 – 649 .
  • Guo , BZ . 1995 . A controlled age-structured population model for the spread of universally fatal diseases . J. Syst. Sci. Math. Sci. , 15 ( 3 ) : 269 – 278 .
  • Anita , S . 2000 . Analysis and Control of Age-Dependent Population Dynamics , Dordrecht : Kluwer Academic .
  • Iannelli , M . 1994 . Mathematical Theory of Age-Structured Population Dynamics , Pisa : Giardini Editori E Stampatori .
  • Jacob , B and Omrane , A . 2010 . Optimal control for age-structured population dynamics of incomplete data . J. Math. Anal. Appl. , 370 ( 1 ) : 42 – 48 .
  • Chan , WL and Guo , BZ . 1989 . Optimal birth control of population dynamics . J. Math. Anal. Appl. , 144 ( 2 ) : 532 – 552 .
  • Chan , WL and Guo , BZ . 1990 . Optimal birth control of population dynamics: II. Problems with free final time, phase constraints, and mini-max costs . J. Math. Anal. Appl. , 146 ( 2 ) : 523 – 539 .
  • Sun , B . 2010 . Maximum principle for optimal boundary control of the Kuramoto-Sivashinsky equation . J. Franklin Inst. , 347 ( 2 ) : 467 – 482 .
  • Dubovitskii , AYa and Milyutin , AA . 1965 . Extremum problems in the presence of constraints . Zh. Vychisl. Mat. i Mat. Fiz. , 5 : 395 – 453 . (in Russian); English transl., USSR Comput. Math. and Math. Phys., 5(3) (1965), 1–80
  • Girsanov , IV . 1972 . “ Lectures on Mathematical Theory of Extremum Problems ” . In Lecture Notes in Economics and Mathematical Systems , Vol. 67 , Berlin : Springer-Verlag .
  • Gibson , JA and Lowinger , JF . 1974 . A predictive min-H method to improve convergence to optimal solutions . Int. J. Control , 19 ( 3 ) : 575 – 592 .
  • Xing , J , Zhang , C and Xu , H . 2003 . Basics of Optimal Control Applications , Beijing : Science Press . (in Chinese)

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