Optimality of a time-dependent treatment profile during an epidemic

References

• A.A. Agrachev and Y.L. Sachkov, Control Theory from the Geometric Viewpoint, Encyclopedia of Mathematical Sciences Vol. 87, Springer-Verlag, New York, 2004.
   Google Scholar
• N. Arinaminpathy and A.R. McLean, Antiviral treatment for the control of pandemic influenza: Some logistical constraints, J. R. Soc. Interface 5(22) (2008), pp. 545–553. doi: 10.1098/rsif.2007.1152
   PubMed Web of Science ®Google Scholar
• J. Arino, C.S. Bowman, and S.M. Moghadas, Antiviral resistance during pandemic influenza: Implications for stockpiling and drug use, BMC Infect. Dis. 9 (2009), p. 8. doi:10.1186/1471-2334-9-8. doi: 10.1186/1471-2334-9-8
   PubMed Web of Science ®Google Scholar
• J. Arino, F. Brauer, P. van den Driessche, J. Watmough, and J. Wu, A model for influenza with vaccination and antiviral treatment, J. Theor. Biol. 253(1) (2008), pp. 118–130. doi: 10.1016/j.jtbi.2008.02.026
   PubMed Web of Science ®Google Scholar
• F. Brauer, P. van den Driessche, and J. Wu, Mathematical Epidemiology, Springer-Verlag, Berlin, Heidelberg, 2008.
   Google Scholar
• A.E. BrysonJr. and Y.-C. Ho, Applied Optimal Control: Optimization, Estimation and Control, Taylor & Francis, New York, 1975, p. 246.
   Google Scholar
• O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building. Analysis and Interpretation, John Wiley and Sons, New York, 2000.
   Google Scholar
• N.M. Ferguson, S. Mallett, H. Jackson, N. Roberts, and P. Ward, A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antivirals, J. Antimicrob. Chemother. 51 (2003), pp. 977–990. doi:10.1093/jac/dkg136. doi: 10.1093/jac/dkg136
   PubMed Web of Science ®Google Scholar
• N.M. Ferguson, D.A.T. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn, and D.S. Burke, Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature 437 (2005), pp. 209–214. doi:10.1038/nature04017. doi: 10.1038/nature04017
   PubMed Web of Science ®Google Scholar
• K.R. Fister and J.C. Panetta, Optimal control applied to cell-cycle-specific cancer chemotherapy, SIAM J. Appl. Math. 60 (2000), pp. 1059–1072. doi: 10.1137/S0036139998338509
   Web of Science ®Google Scholar
• W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer-Verlag, New York, 1975.
   Google Scholar
• E. Hansen and T. Day, Optimal control of epidemics with limited resources, J. Math. Biol. 62(3) (2011), pp. 423–451. doi 10.1007/s00285-010-0341-0. doi: 10.1007/s00285-010-0341-0
   PubMed Web of Science ®Google Scholar
• E. Hansen and T. Day, Optimal antiviral treatment strategies and the effects of resistance, Proc. R. Soc. B 278(1708) (2011), pp. 1082–1089. doi 10.1098/rspb.2010.1469. doi: 10.1098/rspb.2010.1469
   PubMed Web of Science ®Google Scholar
• M. Jaberi-Douraki, J. Hefffernan, J. Wu, and S.M. Moghadas, Optimal treatment profile during an influenza epidemic. Differ. Equ. Dyn. Syst. 21(3) (2013), pp. 237–252. doi: 10.1007/s12591-012-0149-z. doi: 10.1007/s12591-012-0149-z
   Google Scholar
• H.R. Joshi, Optimal control of an HIV immunology model, Optim. Control Appl. Methods 23 (2002), pp. 199–213. doi: 10.1002/oca.710
   Web of Science ®Google Scholar
• H.R. Joshi, S. Lenhart, and H. Gaff, Optimal harvesting in an integro-difference population model, Optim. Control Appl. Methods 27 (2006), pp. 61–75. doi: 10.1002/oca.763
   Web of Science ®Google Scholar
• H.R. Joshi, S. Lenhart, H. Lou, and H. Gaff, Harvesting control in an integro-difference population model with concave growth term, Nonlinear Anal. Hybrid Syst. 1 (2007), pp. 417–429. doi: 10.1016/j.nahs.2006.10.010
   Web of Science ®Google Scholar
• E. Jung, S. Lenhart, and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete Contin. Dyn. Syst. B 2 (2002), pp. 473–482. doi: 10.3934/dcdsb.2002.2.473
   Web of Science ®Google Scholar
• E. Jung, Y. Takeuchi, and T.C. Jo, Optimal control strategy for prevention of avian influenza pandemic, J. Theoret. Biol. 260 (2009), pp. 220–229. doi: 10.1016/j.jtbi.2009.05.031
   PubMed Web of Science ®Google Scholar
• D.E. Kirk, Optimal Control Theory: An Introduction, Dover Publications, Inc. Mineola, New York, 2004.
   Google Scholar
• E.G. Kyriakidis and A. Pavitsos, Optimal intervention policies for a multidimensional simple epidemic process, Math. Comput. Model. 50 (2009), pp. 1318–1324. doi: 10.1016/j.mcm.2009.06.012
   Web of Science ®Google Scholar
• S. Lenhart and J.T. Workman, Optimal Control Applied to Biological Models, Chapman & Hall, CRC Press, Boca Raton, FL, 2007.
   Google Scholar
• M. Lipsitch, T. Cohen, M. Murray, and B.R. Levin, Antiviral resistance and the control of pandemic influenza, PLoS Med. 4(1) (2007), p. e15. doi:10.1371/journal.pmed.0040015. doi: 10.1371/journal.pmed.0040015
   Google Scholar
• I.M. LonginiJr, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakul, D.A.T. Cummings, and M.E. Halloran, Containing pandemic influenza at the source, Science 309 (2005), pp. 1083–1087. doi:10.1126/science.1115717. doi: 10.1126/science.1115717
   PubMed Web of Science ®Google Scholar
• D.L. Lukes, Differential Equations: Classical to Controlled, Mathematics in Science and Engineering Vol. 162, Academic Press, New York, 1982.
   Google Scholar
• S.M. Moghadas, Management of drug resistance in the population: Influenza as a case study, Proc. R. Soc. B 275 (2008), pp. 1163–1169. doi: 10.1098/rspb.2008.0016
   PubMed Web of Science ®Google Scholar
• S.M. Moghadas, Dynamics of resistance in influenza with compensatory mutations, Math. Popul. Stud. 18 (2011), pp. 106–121. doi: 10.1080/08898480.2011.564565
   Web of Science ®Google Scholar
• S.M. Moghadas, C.S. Bowman, G. Röst and J. Wu, Population-wide emergence of antiviral resistance during pandemic influenza, PLoS ONE 3(3) (2008), p. e1839. doi: 10.1371/journal.pone.0001839. doi: 10.1371/journal.pone.0001839
   PubMed Web of Science ®Google Scholar
• S.M. Moghadas, C.S. Bowman, G. Röst, D.N. Fisman, and J. Wu, Post-exposure prophylaxis during pandemic outbreaks, BMC Med. 7 (2009), p. 73. doi: 10.1186/1741-7015-7-73. doi: 10.1186/1741-7015-7-73
   PubMed Web of Science ®Google Scholar
• T.C. Porco, J.O. Lloyd-Smith, K.L. Gross, and A.P. Galvani, The effect of treatment on pathogen virulence, J. Theor. Biol. 233 (2005), pp. 91–102. doi: 10.1016/j.jtbi.2004.09.009
   PubMed Web of Science ®Google Scholar
• R.R. Regoes and S. Bonhoeffer, Emergence of drug resistance influenza virus: Population dynamical considerations, Science 312 (2006), pp. 389–391. doi:10.1126/science.1122947. doi: 10.1126/science.1122947
   PubMed Web of Science ®Google Scholar