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Optimal control strategy for prevention of avian influenza pandemic. (English) Zbl 1402.92278

Summary: The spread of H5N1 virus to Europe and continued human infection in Southeast Asia have heightened pandemic concern. Although, fortunately, sustained human-to-human transmissions have not been reported yet, it is said that a pandemic virus which can be easily transmitted among humans certainly emerges in the future. In this study, we extended the previous studies for the prevention of the pandemic influenza to evaluate the time-dependent optimal prevention policies, which are associated with elimination policy and quarantine policy, considering its execution cost. Actually, the execution cost affects the optimal strategy of prevention policies and the prevention of the disease spread. We found that the quarantine policy is very important rather than the elimination policy during the disease spread, even if the unit execution cost of the quarantine policy is more expensive than that of the elimination policy. And also, the change of the unit execution cost does affect the total cumulative cost of the optimal prevention policies but does not affect the relative frequency of each cumulative execution cost. Furthermore, interestingly, we revealed that an optimal strategy to reduce the number of total infected humans might increase a chance of invadability of the mutant influenza.

MSC:

92C60 Medical epidemiology
92D30 Epidemiology
49N90 Applications of optimal control and differential games
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[1] Anderson, R.M.; May, R.M., Infectious disease of humans: dynamics and control, (1991), Oxford University Press Oxford
[2] Antia, R.; Regoes, R.R.; Koella, J.C.; Bergstrom, C.T., The role of evolution in the emergence of infectious diseases, Nature, 426, 658-661, (2003)
[3] Centers for Disease Control and Prevention, 2006. Avian influenza: current situation, August \(9 \langle;\) http://www.cdc.gov/flu/avian/outbreaks/pdf/current.pdf \(\rangle;\).; Centers for Disease Control and Prevention, 2006. Avian influenza: current situation, August \(9 \langle;\) http://www.cdc.gov/flu/avian/outbreaks/pdf/current.pdf \(\rangle;\).
[4] Chen, H.; Deng, G.; Li, Z.; Tian, G.; Li, Y.; Jiao, P.; Zhang, L.; Liu, Z.; Webster, R.G.; Yu, K., The evolution of H5N1 influenza viruses in ducks in southern China, Proc. natl. acad. sci. USA, 101, 10452-10457, (2004)
[5] Chen, H.; Smith, G.L.; Li, K.S.; Wang, J.; Fan, X.H.; Rayner, J.M.; Vijaykrishna, D.; Zhang, J.X.; Zhang, L.J.; Guo, C.T.; Cheung, C.L.; Xu, K.M.; Duan, L.; Huang, K.; Qin, K.; Leung, Y.H.; Wu, W.L.; Lu, H.R.; Chen, Y.; Xia, N.S.; Naipospos, T.S.; Yuen, K.Y.; Hassan, S.S.; Bahri, S.; Nguyen, T.D.; Webster, R.G.; Peiris, J.S.; Guan, Y., Establishment of multiple sublineages of H5N1 influenza virus in Asia: implications for pandemic control, Proc. natl. acad. sci. USA, 103, 2845-2850, (2006)
[6] Chowell, G.; Ammon, C.E.; Hengartner, N.W.; Hyman, J.M., Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions, J. theor. biol., 241, 193-204, (2006) · Zbl 1447.92408
[7] Chowell, G.; Nishiura, H., Quantifying the transmission potential of pandemic influenza, Phys. life rev., 5, 50-77, (2008)
[8] Fister, K.R.; Lenhart, S.; McNally, J.S., Optimizing chemotherapy in an HIV model, Electron. J. diff. equ., 32, 1-12, (1998) · Zbl 1068.92503
[9] Fleming, W.H.; Rishel, R.W., Deterministic and stochastic optimal control, (1975), Springer New York · Zbl 0323.49001
[10] Gambotto, A.; Barratt-Boyes, S.M.; de Jong, M.D.; Neumann, G.; Kawaoka, Y., Human infection with highly pathogenic H5N1 influenza virus, Lancet, 371, 1464-1475, (2008)
[11] Gilbert, M.; Xiao, X.; Domenech, J.; Lubroth, J.; Martin, V.; Slingenbergh, J., Anatidae migration in the western palearctic and spread of highly pathogenic Avian influenza H5N1 virus, Emer. infect. dis., 12, 1650-1656, (2006)
[12] Hogg, W.; Gray, D.; Huston, P.; Zhang, W., The costs of preventing the spread of respiratory infection in family Physician offices: a threshold analysis, BMC health serv. res., 7, 181, (2007)
[13] Iwami, S.; Takeuchi, Y.; Liu, X., Avian – human influenza epidemic model, Math. biosci., 207, 1-25, (2007) · Zbl 1114.92058
[14] Iwami, S.; Takeuchi, Y.; Korobeinikov, A.; Liu, X., Prevention of Avian influenza epidemic: what policy should we choose?, J. theor. biol., 252, 732-741, (2008) · Zbl 1398.92240
[15] Iwami, S.; Takeuchi, Y.; Liu, X., Avian flu pandemic: can we prevent it?, J. theor. biol., 257, 181-190, (2009) · Zbl 1400.92496
[16] Jung, E.; Lenhart, S.; Feng, Z., Optimal control of treatments in a two strain tuberculosis model, Dis. cont. dyn. syst. B, 2, 473-482, (2002) · Zbl 1005.92018
[17] Jung, E.; Lenhart, S.; Protopopescu, V.; Babbs, C., Optimal control theory applied to a difference equation model for cardiopulmonary resuscitation, Math. methods models appl. sci., 15, 1519-1532, (2005) · Zbl 1088.39015
[18] Jung, E.; Lenhart, S.; Protopopescu, V.; Babbs, C., Optimal strategy for cardiopulmonary resuscitation with continuous chest compression, Acad. emer. med., 7, 715-721, (2006)
[19] Kamien, M.I.; Schwarz, N.L., Dynamic optimization: the calculus of variations and optimal control, (1991), North-Holland Amsterdam · Zbl 0727.90002
[20] Kirschner, D.; Lenhart, S.; Serbin, S., Optimal control of the chemotherapy of HIV, J. math. biol., 35, 775-792, (1997) · Zbl 0876.92016
[21] Lam, T.T.; Hon, C.C.; Pybus, O.G.; Kosakovsky Pond, S.L.; Wong, R.T.; Yip, C.W.; Zeng, F.; Leung, F.C., Evolutionary and transmission dynamics of reassortant H5N1 influenza virus in Indonesia, Plos pathog., 4, 8, e1000130, (2007)
[22] Lenhart, S.; Protopopescu, V.; Jung, E.; Babbs, C., Optimal control for a standard CPR model, Nonlinear anal., 63, 1391-1397, (2005) · Zbl 1222.92026
[23] Lenhart, S., Workman, J.T., 2007. Optimal Control Applied to Biological Models, Chapman & Hall, CRC Mathematical and Computational Biology Series.; Lenhart, S., Workman, J.T., 2007. Optimal Control Applied to Biological Models, Chapman & Hall, CRC Mathematical and Computational Biology Series. · Zbl 1291.92010
[24] Liem, N.T., World Health Organization International Avian Influenza Investigation Team, Vietnam, Lim, W., 2005. Lack of H5N1 avian influenza transmission to hospital employees, Hanoi, 2004. Emer. Infect. Dis. 1, 210-215.; Liem, N.T., World Health Organization International Avian Influenza Investigation Team, Vietnam, Lim, W., 2005. Lack of H5N1 avian influenza transmission to hospital employees, Hanoi, 2004. Emer. Infect. Dis. 1, 210-215.
[25] Mathews, J.D.; McCaw, C.T.; McVernon, J.; McBryde, E.S.; McCaw, J.M., A biological model for influenza transmission: pandemic planning implications of asymptomatic infection and immunity, Plos one, 2, 11, e1220, (2007)
[26] McLeod, A.; Rushton, J.; Riviere-Cinnamond, A.; Brandenburg, B.; Hinrichs, J.; Loth, L., Economic issues in vaccination against highly pathogenic Avian influenza in developing countries, Dev. biol., 130, 63-72, (2007)
[27] Menach, A.L.; Vergu, E.; Grais, R.F.; Smith, D.L.; Flahault, A., Key strategies for reducing spread of Avian influenza among commercial poultry holdings: lessons for transmission to humans, Proc. R. soc. London B, 273, 2467-2475, (2006)
[28] Mills, C.E.; Robins, J.M.; Lipsitch, M., Transmissibility of 1918 pandemic influenza, Nature, 432, 904-906, (2004)
[29] Normile, D., Avian influenza. WHO proposes plan to stop pandemic in its tracks, Science, 311, 315-316, (2006)
[30] Peyre, M.; Fusheng, G.; Desvaux, S.; Roger, F., Avian influenza vaccines: a practical review in relation to their application in the field with a focus on the Asian experience, Epidemiol. infect., 14, 1-21, (2008)
[31] Pontryagin, L.S.; Boltyanskii, V.G.; Gamkrelidze, R.V.; Mishchenko, E.F., The mathematical theory of optimal processes, (1962), Wiley New York · Zbl 0102.32001
[32] Poland, G.A.; Jacobson, R.M.; Targonski, P.V., Avian and pandemic influenza: an overview, Vaccine, 25, 3057-3061, (2007)
[33] Regoes, R.R.; Bonhoeffer, S., Emergence of drug-resistant influenza virus: population dynamical considerations, Nature, 312, 389-391, (2006)
[34] Rushton, J.; Viscarra, R.; Guerne Bleich, E.; McLeod, A., Impact of avian influenza outbreaks in the poultry sectors of five south east Asian countries (Cambodia, Indonesia, lao PDR, Thailand, Vietnam) outbreak costs responses and potential long term control, World’s poult. sci. J., 61, 491-514, (2005)
[35] Sander, B., Nizam, A., Garrison, L.P., Postma, M.J., Halloran, M.E., Longini, I.M., 2008. Economic evaluation of influenza pandemic mitigation strategies in the United States using a stochastic microsimulation transmission model. Value Health July, 30.; Sander, B., Nizam, A., Garrison, L.P., Postma, M.J., Halloran, M.E., Longini, I.M., 2008. Economic evaluation of influenza pandemic mitigation strategies in the United States using a stochastic microsimulation transmission model. Value Health July, 30.
[36] Sethi, S.; Thompson, G.L., Optimal control theory: applications to management science and economics, (2000), Kluwer Academic Boston · Zbl 0998.49002
[37] Skeik, N.; Jabr, F.I., Influenza viruses and the evolution of Avian influenza virus H5N1, Int. J. infect dis., 12, 233-238, (2008)
[38] Stegeman, A.; Bouma, A.; Elbers, A.R.W.; de Jong, M.C.M.; Nodelijk, G.; de Klerk, F.; Koch, G.; van Boven, M.J., Avian influenza A virus (H7N7) epidemic in The Netherlands in 2003: course of the epidemic and effectiveness of control measures, J. infect. dis., 190, 2088-2095, (2004)
[39] Taubenberger, J.K., Reid, A.H., Fanning, T.G., 2005. Capturing a killer flu virus. Sci. Am. January.; Taubenberger, J.K., Reid, A.H., Fanning, T.G., 2005. Capturing a killer flu virus. Sci. Am. January.
[40] Tiensin, T.; Chaitaweesub, P.; Songserm, T.; Chaisingh, A.; Hoonsuwan, W.; Buranathai, C.; Parakamawongsa, T.; Premashthira, S.; Amonsin, A.; Gilbert, M.; Nielen, M.; Stegeman, A., Highly pathogenic Avian influenza H5N1, Thailand, 2004, Emer. infect. dis., 11, 1664-1672, (2005)
[41] Tiensin, T.; Nielen, M.; Vernooij, H.; Songserm, T.; Kalpravidh, W.; Chotiprasatintara, S.; Chaisingh, A.; Wongkasemjit, S.; Chanachai, K.; Thanapongtham, W.; Srisuvan, T.; Stegeman, A., Transmission of the highly pathogenic Avian influenza virus H5N1 within flocks during the 2004 epidemic in Thailand, J. infect. dis., 196, 1679-1684, (2007)
[42] The New York Times, 2006. In the Nile delta, bird flu preys on ignorance and poverty, April 13.; The New York Times, 2006. In the Nile delta, bird flu preys on ignorance and poverty, April 13.
[43] The World Health Organization, 2005. Global influenza preparedness plan \(\langle;\) http://www.who.int/csr/resources/publications/influenza/WHOCDSCSRGIP20055.pdf \(\rangle;\).; The World Health Organization, 2005. Global influenza preparedness plan \(\langle;\) http://www.who.int/csr/resources/publications/influenza/WHOCDSCSRGIP20055.pdf \(\rangle;\).
[44] The World Health Organization, 2006. Avian influenza: significance of mutations in the H5N1 virus, February \(20 \langle;\) http://www.who.int/csr/20060220/en/index.html \(\rangle;\).; The World Health Organization, 2006. Avian influenza: significance of mutations in the H5N1 virus, February \(20 \langle;\) http://www.who.int/csr/20060220/en/index.html \(\rangle;\).
[45] The Writing Committee of the World Health Organization (WHO) Consultation on Human Influenza A/H5, 2006. Avian influenza A (H5N1) infection in humans. N. Engl. J. Med. 353, 1374-1385.; The Writing Committee of the World Health Organization (WHO) Consultation on Human Influenza A/H5, 2006. Avian influenza A (H5N1) infection in humans. N. Engl. J. Med. 353, 1374-1385.
[46] van den Berg, T.; Houdart, P., Avian influenza outbreak management: action at time of confirmation, depopulation and disposal methods; the ‘belgian experience’ during the H7N7 highly pathogenic Avian influenza epidemic in 2003, Zoono. public health, 55, 54-64, (2008)
[47] Webster, R.G.; Peiris, M.; Chen, H.; Guan, Y., H5N1 outbreaks and enzootic influenza, Emer. infect. dis., 12, 3-8, (2006)
[48] White, L.F.; Pagano, M., Transmissibility of the influenza virus in the 1918 pandemic, Plos one, 3, 1, e1498, (2008)
[49] Yee, K.S.; Carpenter, T.E.; Cardona, C.J., Epidemiology of H5N1 Avian influenza, Comp. immunol. microbiol. infect. dis., 32, 325-340, (2008)
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