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Modeling the spread of bird flu and predicting outbreak diversity. (English) Zbl 1154.92324

Summary: Avian influenza, commonly known as bird flu, is an epidemic caused by H5N1 virus that primarily affects birds like chickens, wild water birds, etc. On rare occasions, these can infect other species including pigs and humans. In the span of less than a year, the lethal strain of bird flu is spreading very fast across the globe mainly in South East Asia, parts of Central Asia, Africa and Europe. In order to study the patterns of spread of epidemic, we made an investigation of outbreaks of the epidemic in one week, that is from February 13-18, 2006, when the deadly virus surfaced in India. We have designed a statistical transmission model of bird flu taking into account the factors that affect the epidemic transmission such as source of infection, social and natural factors and various control measures are suggested. For modeling the general intensity coefficient \(f(r)\), we have implemented the recent ideas given by R. Howlett [Fitting the bill. Nature 439, 402 (2006)], which describes the geographical spread of epidemics due to transportation of poultry products. Our aim is to study the spread of avian influenza, both in time and space, to gain a better understanding of transmission mechanism. Our model yields satisfactory results as evidenced by the simulations and may be used for the prediction of future situations of epidemic for longer periods. We utilize real data at these various scales and our model allows one to generalize our predictions and make better suggestions for the control of this epidemic.

MSC:

92D30 Epidemiology
92C60 Medical epidemiology

References:

[1] Alexander, D. J., A review of avian influenza in different bird species, Vet. Microbiol., 74, 3-13 (2000)
[2] Anderson, R. M.; May, R. M., Infectious Diseases of Humans: Dynamics and Control (1991), Oxford University Press: Oxford University Press Oxford
[3] Canadian website on avian influenza. \( \langle;\) http://www.inspection.gc.ca/english/anima/heasan/disemala/avflu/situatione.html/\( \rangle;\); Canadian website on avian influenza. \( \langle;\) http://www.inspection.gc.ca/english/anima/heasan/disemala/avflu/situatione.html/\( \rangle;\)
[4] Centers for Disease Control and Prevention. Cases of influenza A (H5N1)—Thailand, 2004, MMWR Morbidity and Mortality Weekly Report 53 (2004) 100-103.; Centers for Disease Control and Prevention. Cases of influenza A (H5N1)—Thailand, 2004, MMWR Morbidity and Mortality Weekly Report 53 (2004) 100-103.
[5] Chen, H.; Smith, G. J.D.; Zhang, S. Y.; Qin, K.; Wang, J.; Li, K. S., Avian flu: H5N1 virus outbreak in migratory waterfowl, Nature, 436, 191-192 (2005)
[6] Chokephaibulkit, K.; Uiprasertkul, M.; Puthavathana, P.; Chearskul, P.; Auewarakul, P.; Dowell, S. F., A child with avian influenza A (H5N1) infection, Pediatr. Infect. Dis. J., 24, 162-166 (2005)
[7] Chotpitayasunondh, T.; Ungchusak, K.; Hanshaoworakul, W.; Chunsuthiwat, S.; Sawanpanyalert, P.; Kijphati, R., Human disease from influenza A (H5N1), Thailand, 2004, Emerg. Infect. Dis., 11, 201-209 (2005)
[8] Cox, N. J.; Subbarao, K., Global epidemiology of influenza: past and present, Annu. Rev. Med., 51, 407-421 (2000)
[9] Cyranoski, D., Bird flu spreads among Java’s pigs, Nature, 435, 390-391 (2005)
[10] De Jong, J. C.; Claas, E. C.; Osterhaus, A. D.; Webster, R. G.; Lim, W. L., A pandemic warning?, Nature, 389, 554 (1997)
[11] Earn, D. J.D.; Rohani, P.; Bolker, B. M.; Grenfell, B. T., A simple model for complex dynamical transitions in epidemics, Science, 287, 667-670 (2000)
[12] Ellis, T. M.; Bousfield, B. R.; Bissett, L. A.; Dyrting, K. C.; Luk, G. S.; Tsim, S. T., Investigation of outbreaks of highly pathogenic H5N1 avian influenza in waterfowl and wild birds in Hong Kong in late 2002, Avian Pathol., 33, 492-505 (2004)
[13] Fine, P., Applications of mathematical models to the epidemiology of influenza: a critique, (Selby, P., Influenza Models: Prospects for Developments and Use (1982), MTP Press: MTP Press Cambridge), 15-85
[14] Govorkova, E. A.; Rehg, J. E.; Krauss, S.; Yen, H.-L.; Guan, Y.; Peiris, M., Lethality to ferrets of H5N1 influenza viruses isolated from humans and poultry in 2004, J. Virol., 79, 2191-2198 (2005)
[15] Guan, Y.; Peiris, J. S.M.; Lipatov, A. S.; Ellis, T. M.; Dyrting, K. C.; Krauss, S., Emergence of multiple genotypes of H5N1 avian influenza viruses in Hong Kong SAR, Proc. Natl. Acad. Sci. USA, 99, 8950-8955 (2002)
[16] Guan, Y.; Zheng, B. J.; He, Y. Q.; Liu, X. L.; Zhuang, Z. X.; Cheung, C. L., Isolation and characterization of viruses related to the SARS coronavirus from animals in Southern China, Science, 302, 276-278 (2004)
[17] Hien, T. T.; De Jong, M.; Farrar, J., Avian influenza—a challenge to global health care structures, N. Engl. J. Med., 351, 2363-2365 (2004)
[18] Hope-Simpson, R. E., The Transmission of Epidemic Influenza (1992), Plenum Press
[19] Howlett, R., Fitting the bill, Nature, 439, 402 (2006)
[20] Hulse-Post, D. J.; Sturm-Ramirez, K. M.; Humbert, J.; Seiler, P.; Govorkova, E. A.; Krauss, S., Role of domestic ducks in the propagation and biological evolution of highly pathogenic H5N1 influenza viruses in Asia, Proc. Natl. Acad. Sci. USA, 102, 10682-10687 (2005)
[21] Jinping, Li, Qianlu, Ren, Y. Jianqin, Study on transmission model of avian influenza, IEEE (2004) 54-58.; Jinping, Li, Qianlu, Ren, Y. Jianqin, Study on transmission model of avian influenza, IEEE (2004) 54-58.
[22] Kermack, W. O.; McKendrick, A. G., A contribution to the mathematical theory of epidemics, Proc. R. Soc. London Ser. A, 115, 700-721 (1927) · JFM 53.0517.01
[23] Kuiken, T.; Rimmelzwaan, G.; Van Riel, D.; Van Amerongen, G.; Baars, M.; Fouchier, R., Avian H5N1 influenza in cats, Science, 306, 241 (2004)
[24] Kung, N. Y.; Guan, Y.; Perkins, N. R.; Bisset, L.; Ellis, T.; Sims, L., The impact of a monthly rest day on avian influenza virus isolation rates in retail live poultry markets in Hong Kong, Avian Dis., 47, 1037-1041 (2003)
[25] Lee, C. W.; Senne, D. A.; Suarez, D. L., Effect of vaccine use in the evolution of Mexican lineage H5N2 avian influenza virus, J. Virol., 78, 8372-8381 (2004)
[26] Li, K. S.; Guan, Y.; Wang, J.; Smith, G. J.; Xu, K. M.; Duan, L., Genesis of a highly pathogenic and potentially pandemic H5N1 influenza virus in eastern Asia, Nature, 430, 209-213 (2004)
[27] Liu, J.; Xiao, H.; Lei, F.; Zhu, Q.; Qin, K.; Zhang, X., Highly pathogenic H5N1 influenza virus infection in migratory birds, Science, 309, 1206 (2005)
[28] Liu, M.; He, S.; Walker, D.; Zhou, N. N.; Perez, D. R.; Mo, B., The influenza virus gene pool in a poultry market in South Central China, Virology, 305, 267-275 (2003)
[29] Longini, I. M.; Nizam, A.; Xu, S.; Ungchusak, K.; Hanshaoworakul, W.; Cummings, D. A., Containing pandemic influenza at the source, Science, 309, 1083-1087 (2005), (Epub 2005, August 3)
[30] Ludwig, S.; Haustein, A.; Kaleta, E. F.; Scholtissek, C., Recent influenza A (H1N1) infections of pigs and turkeys in northern Europe, Virology, 202, 281-286 (1994)
[31] Mase, M.; Tsukamoto, K.; Imada, T.; Imai, K.; Tanimura, N.; Nakamura, K., Characterization of H5N1 influenza A viruses isolated during the 2003-2004 influenza outbreaks in Japan, Virology, 332, 167-176 (2005)
[32] Mills, C. E.; Robins, J. M.; Lipsitch, M., Transmissibility of 1918 pandemic influenza, Nature, 432, 904-906 (2004)
[33] Peiris, J. S.M.; Yu, W. C.; Leung, C. W.; Cheung, C. Y.; Ng, W. F.; Nicholls, J. M.; Ng, T. K.; Chan, K. H.; Lai, S. T.; Lim, W. L.; Yuen, K. Y.; Guan, Y., Re-emergence of fatal human influenza A subtype H5N1 disease, Lancet, 363, 617-619 (2004)
[34] SARS: How a Global Epidemic Was Stopped, WHO, WHO Press, Geneva, Switzerland, 2006.; SARS: How a Global Epidemic Was Stopped, WHO, WHO Press, Geneva, Switzerland, 2006.
[35] Seo, S. H.; Peiris, M.; Webster, R. G., Protective cross-reactive cellular immunity to lethal A/Goose/Guangdong/1/96-like H5N1 influenza virus is correlated with the proportion of pulmonary CD8+ T cells expressing gamma interferon, J. Virol., 76, 4886-4890 (2002)
[36] Seo, S. H.; Webster, R. G., Cross-reactive, cell-mediated immunity and protection of chickens from lethal H5N1 influenza virus infection in Hong Kong poultry markets, J. Virol., 75, 2516-2525 (2001)
[37] Shortridge, K. F., Pandemic influenza: a zoonosis?, Semin. Respir. Infect., 7, 11-25 (1992)
[38] Shortridge, K. G.; Zhou, N. N.; Guan, Y.; Gao, P.; Ito, T.; Kawaoka, Y., Characterization of avian H5N1 influenza viruses from poultry in Hong Kong, Virology, 252, 331-342 (1998)
[39] Sims, L. D.; Ellis, T. M.; Liu, K. K.; Dyrting, K.; Wong, H.; Peiris, M., Avian influenza in Hong Kong 1997-2002, Avian Dis., 47, 832-838 (2003)
[40] O.J. Sonja, K. Ungchusak, L. Sovann, T.M. Uyeki, S.F. Dowell, N.J. Cox, W. Aldis, C. Suparnit, Family clustering of avian influenza, 2005, 11.; O.J. Sonja, K. Ungchusak, L. Sovann, T.M. Uyeki, S.F. Dowell, N.J. Cox, W. Aldis, C. Suparnit, Family clustering of avian influenza, 2005, 11.
[41] Stech, J.; Xiong, X.; Scholtissek, C.; Webster, R. G., Independence of evolutionary and mutational rates after transmission of avian influenza viruses to swine, J. Virol., 73, 1878-1884 (1999)
[42] Sturm-Ramirez, K. M.; Ellis, T.; Bousfield, B.; Bissett, L.; Dyrting, K.; Rehg, J. E., Re-emerging H5N1 influenza viruses in Hong Kong in 2002 are highly pathogenic to ducks, J. Virol., 78, 4892-4901 (2004)
[43] Sturm-Ramirez, K. M.; Hulse, D. J.; Govorkova, E.; Humberd, J.; Seiler, P.; Puthavathana, P., Are ducks contributing to the endemicity of highly pathogenic H5N1 influenza virus in Asia?, J. Virol., 79, 11269-11279 (2005)
[44] Subbarao, K.; Klimov, A.; Katz, J.; Regnery, H.; Lim, W.; Hall, H., Characterization of an avian influenza A (H5N1) virus isolated from a child with a fatal respiratory illness, Science, 279, 393-396 (1998)
[45] Tang, X.; Tian, G.; Zhao, J.; Zhou, K. Y., Isolation and characterization of prevalent strains of avian influenza viruses in China [article in Chinese], Chin. J. Anim. Poult. Infect. Dis., 20, 1-5 (1998)
[46] U.K. website avian influenza. \( \langle;\) http://www.defra.gov.uk/animalh/diseases/notifiable/disease/ai/index.htm/\( \rangle;\); U.K. website avian influenza. \( \langle;\) http://www.defra.gov.uk/animalh/diseases/notifiable/disease/ai/index.htm/\( \rangle;\)
[47] Ungchusak, K.; Auewarakul, P.; Dowell, S. F.; Kitphati, R.; Auwanit, W.; Puthavathana, P., Probable person-to-person transmission of avian influenza A (H5N1), N. Engl. J. Med., 352, 333-340 (2005)
[48] U.S. website avian influenza. \( \langle;\) http://www.usda.gov/wps/portal/usdahome?navtype=SU&navid=AVIAN_INFLUENZA/\( \rangle;\); U.S. website avian influenza. \( \langle;\) http://www.usda.gov/wps/portal/usdahome?navtype=SU&navid=AVIAN_INFLUENZA/\( \rangle;\)
[49] Webster, R. G.; Bean, W. J.; Gorman, O. T.; Chambers, T. M.; Kawaoka, Y., Evolution and ecology of influenza A viruses, Microbiol. Rev., 56, 152-179 (1992)
[50] Webster, R. G.; Hulse, D. J., Microbial adaptation and change: avian influenza, Rev. Sci. Tech. Off. Int. Epiz., 23, 453-465 (2004)
[51] Webster, R. G.; Malik, P.; Chen, H.; Guan, Y., H5N1 outbreaks and enzootic influenza, Emerg. Infect. Dis., 12, 3-8 (2006)
[52] World Health Organization, Cumulative number of confirmed human cases of avian influenza A/(H5N1) reported to WHO, vol. 2005. Geneva: The Organization, 2005 [cited 2005 September 22]. Available from \(\langle;\) http://www.who.int/csr/disease/avian_influenza/country/cases_table_2005_07_27/en/index.html/\( \rangle;\); World Health Organization, Cumulative number of confirmed human cases of avian influenza A/(H5N1) reported to WHO, vol. 2005. Geneva: The Organization, 2005 [cited 2005 September 22]. Available from \(\langle;\) http://www.who.int/csr/disease/avian_influenza/country/cases_table_2005_07_27/en/index.html/\( \rangle;\)
[53] World Health Organization, Evolution of H5N1 avian influenza viruses in Asia, Emerg. Infect. Dis. 11 (2005) 1515-1521.; World Health Organization, Evolution of H5N1 avian influenza viruses in Asia, Emerg. Infect. Dis. 11 (2005) 1515-1521.
[54] World Health Organization, Influenza pandemic preparedness and response, Geneva: The Organization, 2005 [cited 2005 September 22]. Available from \(\langle;\) http://www.who.int/gb/ebwha/pdf_files/EB115/B115_44-en.pdf/\( \rangle;\); World Health Organization, Influenza pandemic preparedness and response, Geneva: The Organization, 2005 [cited 2005 September 22]. Available from \(\langle;\) http://www.who.int/gb/ebwha/pdf_files/EB115/B115_44-en.pdf/\( \rangle;\)
[55] Wright, P. F.; Webster, R. G., Orthomyxoviruses, (Knipe, D. M.; Howley, P. M., Fields Virology (2001), Lippincott Williams & Wilkins: Lippincott Williams & Wilkins Philadelphia), 1533-1579
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