Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic
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The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits a vaccine-induced backward bifurcation when the associated reproduction number is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the reproduction number is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model. For the case where the vaccine is perfect, it is shown that having the reproduction number less than unity is necessary and sufficient for effective control of H1N1 in the population (in such a case, the associated disease-free equilibrium is globally asymptotically stable). The model has a unique endemic equilibrium when the reproduction number exceeds unity. Numerical simulations of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a mass vaccination program together with the size of the Manitoban population that have preexisting infection-acquired immunity (from the first wave) are crucial to the magnitude of the expected burden of disease associated with the second wave of the H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally, it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and that the second wave would last until the end of January or early February, 2010.
KeywordsSwine flu H1N1 Model
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- Boëlle, P. Y., Bernillon, P., & Desenclos, J. C. (2000). A preliminary estimation of the reproduction ratio for new influenza A(H1N1) from the outbreak in Mexico. Euro Surveill., 14(19), 19205. Google Scholar
- Canada Enters Second Wave of H1N1. http://www.cbc.ca/health/story/2009/10/23/h1n1-second-wave-canada.html. Accessed 04 November 2009.
- Castillo-Chavez, C., Cooke, K., Huang, W., & Levin, S. A. (1989b). The role of long incubation periods in the dynamics of HIV/AIDS. Part 2: Multiple group models). In C. Castillo-Chavez (Ed.), Lecture notes in biomathematics: Vol. 83. Mathematical and statistical approaches to AIDS epidemiology (p. 200). Berlin: Springer. Google Scholar
- Centers for Disease Control and Prevention (2009a). http://www.cdc.gov/h1n1flu/background.htm. Accessed 27 October 2009.
- Centers for Disease Control and Prevention (2009b). http://www.cdc.gov/h1n1flu/recommendations.htm. Accessed 27 October 2009.
- Centers for Disease Control and Prevention (2009c). http://www.cdc.gov/media/pressrel/2009/r090729b.htm. Accessed 27 October 2009.
- Centers for Disease Control and Prevention (2009d). Outbreak of swine-origin influenza A (H1N1) virus infection-Mexico, March–April 2009. Morb. Mort. Wkly. Rep., 58, 1–3. Google Scholar
- Centers for Disease Control and Prevention (2009e). http://www.cdc.gov/h1n1flu/identifyingpatients.htm#incubationperiod. Accessed 27 October 2009.
- Cox, N., Bridges, C., Levandowski, R., & Katz, J. (2008). Influenza vaccine (inactivated). In S. Plotkin, W. Orenstein, & P. Offit (Eds.), Vaccines (pp. 259–290). Amsterdam: Elsevier. Google Scholar
- Demicheli, V., Di Pietrantonj, C., Jefferson, T., Rivetti, A., & Rivetti, D. (2009). Vaccines for preventing influenza in healthy adults (review). The Cochrane collaboration. New York: Wiley. Google Scholar
- El Universal, 6 April 2009. http://www.eluniversal.com.mx/hemeroteca/edicion_impresa_20090406.html. Accessed 27 October 2009.
- FluWatch (2010). Weekly reports 2009–2010 season. http://www.phac-aspc.gc.ca/fluwatch/index-eng.php. Accessed 11 January 2010.
- GenBank (2009). Sequences from 2009 H1N1 influenza outbreak. http://www.ncbi.nlm.nih.gov/genomes/FLU/SwineFlu.html. Accessed 27 October 2009.
- Greenberg, M. E., Lai, M. H., Hartel, G. F., Wichems, C. H., Gittleson, C., Bennet, J., Dawson, G., Hu, W., Leggio, C., Washington, D., & Basser, R. L. (2009). Response after one dose of a monovalent influenza A (H1N1) 2009 vaccine—preliminary report. N. Engl. J. Med., 361(25), 2405–2413. CrossRefGoogle Scholar
- Gumel, A. B., Nuno, M., & Chowell, G. (2008). Mathematical assessment of Canada’s pandemic preparedness plan. Can. J. Infect. Dis. Med. Microbiol., 19(2), 185–192. Google Scholar
- Mahmud, S. M., Becker, M., Keynan, Y., Elliot, L., et al. (2010, submitted). Serological survey of the pandemic influenza A H1N1 in Manitoba, Summer 2009. J. Infect. Dis. Google Scholar
- Manitoba Health (2009). Confirmed cases of H1N1 flu in Manitoba. http://www.gov.mb.ca/health/publichealth/sri/cases.html. Accessed 27 October 2009.
- Nishiura, H., Castillo-Chavez, C., Safan, M., & Chowell, G. (2009). Transmission potential of the new influenza A(H1N1) virus and its age-specificity in Japan. Euro Surveill., 14, 19227. Google Scholar
- Statistics Canada (2009a). Population urban and rural, by province and territory (Manitoba). http://www40.statcan.gc.ca/l01/cst01/demo62h-eng.htm. Accessed 27 October 2009.
- Statistics Canada (2009b). Life expectancy at birth, by sex, by province. http://www40.statcan.gc.ca/l01/cst01/health26-eng.htm. Accessed 27 October 2009.
- United States Centers for Disease Control and Prevention (2009). Pregnant women and novel influenza A (H1N1): considerations for clinicians. http://www.cdc.gov/h1n1flu/clinician_pregnant.htm. Accessed 5 November 2009.
- United States Centers for Disease Control (2009). Information on people at high risk of developing flu-related complications. http://www.cdc.gov/h1n1flu/highrisk.htm. Accessed 5 November 2009.
- van der Vries, E., Jonges, M., Herfst, S., Maaskant, J., Van der Linden, A., Guldemeester, J., Aron, G.I., Bestebroer, T.M., Koopmans, M., Meijer, A., Fouchier, R.A., Osterhaus, A.D., Boucher, C.A., & Schutten, M. (2009). Evaluation of a rapid molecular algorithm for detection of pandemic influenza A (H1N1) 2009 virus and screening for a key oseltamivir resistance (H275Y) substitution in neuraminidase. Clin. Virol. doi:10.1016/j.jcv.2009.09.030. Google Scholar
- Winnipeg Regional Health Authority Report (2009). Outbreak of novel H1N1 influenza A virus in the Winnipeg health region. http://www.wrha.mb.ca/. Accessed 4 November 2009.
- World Health Organization (2009a). Pandemic (H1N1) (2009)—update 71. http://www.who.int/csr/don/2009_10_23/en/index.html. Accessed 27 October 2009.
- World Health Organization (2009b). Influenza A (H1N1)—update 49. Global Alert and Response (GAR). http://www.who.int/csr/don/2009_06_15/en/index.html. Accessed 27 October 2009.
- World Health Organization (2009c). Statement by Director-General. 11 June 2009. Google Scholar
- World Health Organization (2009d). Pandemic (H1N1) (2009)—update 72. http://www.who.int/csr/don/2009_10_30/en/index.html. Accessed 31 October 2009.
- World Health Organization (2009e). Human infection with pandemic A (H1N1) 2009 infuenza virus: clinical observations in hospitalized patients, Americas, July 2009—update. Wkly. Epidemiol. Rec. 84, 305–308. Google Scholar
- World Health Organization (2009f). Alert and response: http://www.who.int/csr/disease/swineflu/updates/en/index.html. Accessed 02 November 2009.