Optimal control of an influenza model with seasonal forcing and age-dependent transmission rates

Journal of Theoretical Biology

Volumn 317, Issue , 2013, Pages 310-320

  Lee, Jeehyun ^a   Kim, Jungeun ^a   Kwon, Hee Dae ^b  

^a Yonsei University   (South Korea)

^b Inha University   (South Korea)

Author keywords

Age dependent transmission rate; Deterministic influenza model; Optimal control; Seasonal forcing

Indexed keywords

INFLUENZA VACCINE;

COMPUTER SIMULATION; DISEASE CONTROL; DISEASE TRANSMISSION; INFLUENZA; MODELING; VACCINE;

AGE DISTRIBUTION; ANTIVIRAL THERAPY; ARTICLE; COMPUTER SIMULATION; DISEASE TRANSMISSION; EPIDEMIC; HEALTH CARE COST; INFECTION CONTROL; INFLUENZA; PRIORITY JOURNAL; SCHOOL; SEASONAL VARIATION; SOCIAL DISTANCE; STATISTICAL MODEL; VACCINE PRODUCTION;

AGE FACTORS; AGING; BASIC REPRODUCTION NUMBER; COMPUTER SIMULATION; HUMANS; INFLUENZA, HUMAN; MODELS, BIOLOGICAL; SEASONS; VACCINES;

EID: 84869420825     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2012.10.032     Document Type: Article

References (36)

1. Arino J., Brauer F., van den Driessche P., Watmough J., Wu J. Simple models for containment of a pandemic. J. R. Soc. Interface 2006, 3:453-457.
2. Arino J., Brauer F., van den Driessche P., Watmough J., Wu J. A model for influenza with vaccination and antiviral treatment. J. Math. Biol. 2008, 253:118-130.
3. Balicer R.D., Huerta M., Davidovitch N., Grotto I. Cost-benefit of stockpiling drugs for influenza pandemic. Emerg. Infect. Dis. 2005, 11:1280-1282.
4. Blayneh K., Cao Y., Kwon H.-D. Optimal control of vector-borne disease. treatment and prevention. Discrete Contin. Dyn. Syst. Ser. B 2009, 11:587-611.
5. Brauer F. Some simple epidemic models. Math. BioSci. Eng. 2006, 3:1-15.
6. Colizza V., Barrat A., Barthelemy M., Valleron A.J., Vespignani A. Modeling the worldwide spread of pandemic influenza. baseline case and containment interventions. PLoS Med. 2007, 4(1):e13.
7. Couzin J. Ethicists to guide rationing of flu vaccine. Science 2004, 306(5698):960-961.
8. Cropper M.L., Aydede S.K., Portney P.R. Preferences for life-saving programs. how the public discounts time and age. J. Risk Uncertain. 1994, 8:243-265.
9. Dushoff J., Plotkin J.B., Levin S.A., Earn D.J.D. Dynamical resonance can account for seasonality of influenza epidemics. Proc. Natl. Aacd. Sci. 2004, 101(November 30 (48)):16915-16916.
10. Emanuel E.J., Wertheimer A. Who should get influenza vaccine when not all can?. Science 2006, 312(5775):854-855.
11. Felippe de Souza, J.A.M., Caetano, M.A.L., Yonoyama, T., 2000. Optimal control theory applied to the anti-viral treatment of AIDS. In: Proceedings of the 39th IEEE Conference, vol. 5. Decision and Control, 2000. IEEE, pp. 4839-4844.
12. Ferguson N.M., Cummings D.A.T., Cauchemez S., Fraser C., Riley S., Meeyai A., Iamsirithaworn S., Burke D.S. Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 2005, 437:209-214.
13. Fleming W.H., Rishel R.W. Deterministic and Stochastic Optimal Control 1975, Springer-Verlag, New York.
14. Gaff H., Schaefer E. Optimal control applied to vaccination and treatment strategies for various epidemiological models. Math. Biosci. Eng. 2009, 6(July (3)):469-492.
15. Gani R., Hughes H., Griffin T., Medlock J., Leach S. Potential impact of antiviral use on hospitalizations during influenza pandemic. Emerg. Infect. Dis. 2005, 11:1355-1362.
16. Gojovic M.Z., Sander B., Fisman D., Krahn M.D., Bauch C.T. Modelling mitigation strategies for pandemic (H1N1) 2009. Can. Med. Assoc. J. 2009, 181:673-680.
17. Goldstein E., Apolloni A., Lewis B., Miller J.C., Macauley M. Distribution of vaccine/antivirals and the least spread line in a stratified population. J. R. Soc. Interface 2010, 7:755-764.
18. Gunzburger M.D. Perspectives in Flow Control and Optimization 2003, SIAM, Philadelphia.
19. Haddix, A.C., Teutsch, S.M., Shaffer, P.A., Dunet, D.O. (Eds.), 1996. Prevention Effectiveness: A Guide to Decision Analysis and Economic Evaluation. Oxford University Press, New York.
20. Hethcote H.W. A thousand and one epidemic models. Frontiers in Theoretical Biology 1994, 504-515. Springer-Verlag. S.A. Levin (Ed.).
21. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 2000, 42:599-653.
22. Joshi H.R. Optimal control of an HIV immunology model. Optimal Control Appl. Meth. 2002, 23:199-213.
23. Jung E., Lenhart S., Feng Z. Optimal control of treatments in a two-strain tuberculosis. Discrete Contin. Dyn. Syst. Ser. B 2002, 2:473-482.
24. Ledzewicz, U., Schaettler, H., 2002. On optimal controls for a general mathematical model for chemotherapy of HIV. In: Proceedings of the 2002 American Control Conference, An-chorage, Alaska, pp. 3454-3459.
25. Lipsitch M. Does aneuploidy or mutation start cancer?. Science 2005, 307(5706):41-42.
26. Longini I.M., Halloran M.E., Nizam A., Yang Y. Containing pandemic influenza with antiviral agents. Am. J. Epidemiol. 2004, 159:623-633.
27. Longini I.M., Nizam A., Xu S., Ungchusak K., Hanshaoworakul W., Cummings D.A.T., Halloran M.E. Containing pandemic influenza at the source. Science 2005, 309:1083-1087.
28. Medlock, J., Meyers, L.A., 2009. Optimizing allocation for a delayed influenza vaccination campaign. PLoS Curr. Influenza. pp RRN,1134.
29. Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko E.F. The Mathematical Theory of Optimal Processes 1962, Interscience Publishers John Wiley and Sons, Inc., New York, London, p. 28.
30. Sypsa V., Pavlopoulou I., Hatzakis A. Use of an inactivated vaccine in mitigating pandemic influenza A(H1N1) spread. a modelling study to assess the impact of vaccination timing and prioritisation strategies. Euro Surveill. 2009, 14(41):235-238.
31. Tuite, A., Fisman, D.N., Kwong, J.C., Greer, A., 2010. Optimal pandemic influenza vaccine allocation strategies for the Canadian population. PLoS Curr Influenza. pp RRN,1144.
32. Van den Driessche P., Watmough J. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 2002, 180:29-48.
33. World Health Organization (WHO), 2010. Pandemic (H1N1) 2009-update 112, August 6. Available from: URL: http://www.who.int/csr/don/20100806/en/index.html.
34. World Health Organization (WHO), 2009a. Influenza-like illness in the United States and Mexico, April 24. Available from: URL. http://www.who.int/csr/don/20090424/en/index.html.
35. World Health Organization (WHO), 2009b. World now at the start of 2009 influenza pandemic, June 11. Available from. http://www.who.int/mediacentre/news/statements/2009/h1n1.pandemic.phase6.20090611/en/index.html.
36. Wu J.T., Riley S., Fraser C., Leung G.M. Reducing the impact of the next influenza pandemic using household-based public health interventions. PLoS Med. 2007, 3(9):e361.