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Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks
Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza
1. | Department of Mathematics, University of Florida, Gainesville, FL 32611, United States |
2. | Department of Mathematics, Texas A&M University, College Station, TX 77843, United States |
3. | Department of Mathematics, Spelman College, Atlanta, GA 30314, United States |
4. | School of Human Evolution and Social Change, Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ 85287, United States, United States |
5. | Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287 |
References:
[1] |
L. Altman, "Many Swine Flu Cases Have no Fever," New York Times, 2009. |
[2] |
R. M. Anderson and R. M. May, "Infectious Diseases of Humans," Oxford University Press, Oxford, 1991. |
[3] |
I. G. Barr, J. McCauley, N. Cox, R. Daniels, O. G. Engelhardt, K. Fukuda, G. Grohmann, A. Hay, A. Kelso, A. Klimov, T. Odagiri, D. Smith, C. Russell, M. Tashiro, R. Webby, J. Wood, Z. Ye and W. Zhang, Epidemiological, antigenic and genetic characteristics of seasonal influenzaA(H1N1), A(H3N2) and B influenza viruses: Basis for the WHO recommendation on the composition of influenza vaccines for use in the 2009–2010 Northern Hemisphere season, Vaccine, 28 (2010), 1156-1167.
doi: 10.1016/j.vaccine.2009.11.043. |
[4] |
H. Behnke, Optimal control of deterministic epidemics, Optimal Control Application Methods, 21 (2000), 269-285.
doi: 10.1002/oca.678. |
[5] |
W. I. B. Beveridge, "Influenza: The Last Great Plague. An Unfinished Story of Discovery," Prodist, 1977. |
[6] |
F. Brauer, Z. Feng and C. Castillo-Chavez, Discrete epidemic models, Mathematical Biosciences and Engineering, 7 (2010), 1-15.
doi: 10.3934/mbe.2010.7.1. |
[7] |
C. Castillo-Chavez, H. Hethcote, V. Andreason, S. A. Levin and W. M. Liu, Cross-immunity in the dynamics of homogeneous and heterogeneous populations, Mathematical Ecology, (1988), 303-316. |
[8] |
Centers for Disease Control and Prevention (CDC), Key facts about seasonal influenza, http://www.cdc.gov/flu/keyfacts.htm. |
[9] |
Centers for Disease Control and Prevention (CDC), Monitoring influenza activity, including 2009 H1N1, (2009), Monitoring Influenza Activity, Including 2009 h1n1. |
[10] |
Centers for Disease Control and Prevention (CDC), Serum cross-reactive antibody response to a novel influenza A(H1N1) virus after vaccination with seasonal influenza vaccine, MMWR Morb Mortal Wkly Rep, 58 (2009), 521-524. |
[11] |
G. Chowell, M. A. Miller and C. Viboud, Seasonal influenza in the United States, France, and Australia: Transmission an prospects for control, Epidem. Infect., 136 (2008), 852-864.
doi: 10.1017/S0950268807009144. |
[12] |
G. Chowell, S. M. Bertozzi, M. A. Colchero, H. Lopez-Gatell, C. Alpuche-Aranda, M. Hernandez and M. A. Miller, Severe respiratory disease concurrent with the circulation of H1N1 influenza, The New England Journal of Medicine, 361 (2009), 674-679.
doi: 10.1056/NEJMoa0904023. |
[13] |
Brian Coburn, "Multi-species Influenza Models with Recombination," Ph.D thesis, University of Miami in Coral Gables,FL, 2009. |
[14] |
R. Couch and J. Kasel, Immunity to influenza in man, Annual Reviews in Microbiology, 37 (2002), 529-549.
doi: 10.1146/annurev.mi.37.100183.002525. |
[15] |
O. Diekmann and J. A. P. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation," John Wiley & Sons, Ltd., Chichester, 2000. |
[16] |
D. J. D. Earn, J. Dushoff and S. A. Levin, Ecology and evolution of the flu, Trends Ecol. Evol., 17 (2002), 334-340.
doi: 10.1016/S0169-5347(02)02502-8. |
[17] |
S. Echevarría-Zuno, J. M. Mejía-Aranguré, A. V. Mar-Obeso, C. Grajales-Muñiz, E. Robles-Pérez, M. González-León, M. C. Ortega-Alvarez, C. Gonzalez-Bonilla, R. A. Rascón-Pacheco and V. H. Borja-Aburto, Infection and death from influenza A H1N1 virus in Mexico: A retrospective analysis, Lancet, 374 (2009), 2072-2079.
doi: 10.1016/S0140-6736(09)61638-X. |
[18] |
A. Esteves-Jaramillo, S. B. Omer and E. Gonzalez-Diaz, Acceptance of a vaccine against novel influenza A (H1N1) virus among health care workers in two major cities in Mexico, Archives of Medical Research, 40 (2009), 705-711.
doi: 10.1016/j.arcmed.2010.01.004. |
[19] |
W. H. Fleming and R. W. Rishel, "Deterministic and Stochasitic Optimal Control," Springer-Verlag, New York, 1994. |
[20] |
FLU. GOV, 2009 H1N1 vaccine doses allocated, ordered, and shipped by project area, (2010), http://www.flu.gov/individualfamily/vaccination/supply.html. |
[21] |
M. A. Herrera-Valdez, M. Cruz-Aponte and C. Castillo-Chavez, Multiple waves for the same pandemic: Local transportation and social distancing explain the dynamics of the A/H1N1 epidemic during 2009 in Mexico, (2010). |
[22] |
E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473-482.
doi: 10.3934/dcdsb.2002.2.473. |
[23] |
P. Y. Lee, D. B. Matchar, D. A. Clements, J. Huber, J. D. Hamilton and E. D. Peterson, Economic analysis of influenza vaccination and antiviral treatment for healthy working adults, Ann. Intern. Med., 137 (2002), 225-231. |
[24] |
S. Lee, G. Chowell and C. Castillo-Chavez, Optimal control of influenza pandemics: the role of antiviral treatment and isolation, Journal of Theoretical Biology, 265 (2010), 136-150.
doi: 10.1016/j.jtbi.2010.04.003. |
[25] |
S. Lenhart and J. T. Workman, "Optimal Control Applied to Biological Models," Chapman & Hall/CRC Mathematical and Computational Biology Series, 2007. |
[26] |
E. Malkin, Flu? What flu?, The New York Times, http://www.nytimes.com/2009/05/09/business/global/09peso.html. |
[27] |
H. Nishiura, C. Castillo-Chavez, M. Safan and G. Chowell, Transmission potential of the new Influenza A(H1N1) virus and its age-specificity in Japan, Eurosurveillance, 14 (2009), 1-4. |
[28] |
M. Nuno, G. Chowell and A. B. Gumel, Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: Scenarios for the US, UK and the Netherlands, Journal of The Royal Society Interface, 4 (2007), 505-521.
doi: 10.1098/rsif.2006.0186. |
[29] |
J. Plotkin, J. Dushoff and S. Levin, Hemagglutinin sequence clusters and the antigenic evolution of influenza A virus, Proceedings of the National Academy of Sciences, 99 (2002), 6263-6268.
doi: 10.1073/pnas.082110799. |
[30] |
L. S. Pontryagin, R. V. Boltyanski, R. V. Gamkrelidge and E. F. Mischenko, "The Mathematical Theory of Optimal Processes," John Wiley and Sons, N.Y., 1962. |
[31] |
Prevent Influenza Now! Sponsored by the National Influenza Vaccine Summit, Influenza vaccine availability tracking system (IVATS), http://www.preventinfluenza.org/ivats/. |
[32] |
C. E. Shoichet, Mexico still waiting for most swine flu vaccines, (2010), http://www.boston.com/business/articles/2010/01/13/mexico_still_waiting_for_most_swine _flu_vaccines. |
[33] |
E. Spackman, D. Stallknecht, R. Slemons, K. Winker, D. L. Suarez, M. Scott and D. E. Swayne, Phylogenetic analyses of type A influenza genes in natural reservoir species in North America reveals genetic variation, Virus research, 114 (2005), 89-100.
doi: 10.1016/j.virusres.2005.05.013. |
[34] |
R. Stengel, Optimal control and estimation, http://www.princeton.edu/ stengel/MAE546.html. |
[35] |
T. Suess, U. Buchholz, S. Dupke, R. Grunow, M. an der Heiden, A. Heider, B. Biere, B. Schweiger, W. Haas and G. Krause, Shedding and transmission of novel influenza virus A/H1N1 infection in households—Germany, 2009, American Journal of Epidemiology, 171 (2010), 1157-1164.
doi: 10.1093/aje/kwq071. |
[36] |
J. K. Taubenberger, D. M. Morens, 1918 influenza: the mother of all pandemics, Emerging Infectious Diseases, (2009), http://www.cdc.gov/ncidod/EID/vol12no01/05-0979.htm. |
[37] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[38] |
World Health Organization, Recommended composition of influenza of influenza virus vaccines for use in the 2001-2002 season, Wkly. Epidemiol. Rec., 76 (2001), 58-61. |
show all references
References:
[1] |
L. Altman, "Many Swine Flu Cases Have no Fever," New York Times, 2009. |
[2] |
R. M. Anderson and R. M. May, "Infectious Diseases of Humans," Oxford University Press, Oxford, 1991. |
[3] |
I. G. Barr, J. McCauley, N. Cox, R. Daniels, O. G. Engelhardt, K. Fukuda, G. Grohmann, A. Hay, A. Kelso, A. Klimov, T. Odagiri, D. Smith, C. Russell, M. Tashiro, R. Webby, J. Wood, Z. Ye and W. Zhang, Epidemiological, antigenic and genetic characteristics of seasonal influenzaA(H1N1), A(H3N2) and B influenza viruses: Basis for the WHO recommendation on the composition of influenza vaccines for use in the 2009–2010 Northern Hemisphere season, Vaccine, 28 (2010), 1156-1167.
doi: 10.1016/j.vaccine.2009.11.043. |
[4] |
H. Behnke, Optimal control of deterministic epidemics, Optimal Control Application Methods, 21 (2000), 269-285.
doi: 10.1002/oca.678. |
[5] |
W. I. B. Beveridge, "Influenza: The Last Great Plague. An Unfinished Story of Discovery," Prodist, 1977. |
[6] |
F. Brauer, Z. Feng and C. Castillo-Chavez, Discrete epidemic models, Mathematical Biosciences and Engineering, 7 (2010), 1-15.
doi: 10.3934/mbe.2010.7.1. |
[7] |
C. Castillo-Chavez, H. Hethcote, V. Andreason, S. A. Levin and W. M. Liu, Cross-immunity in the dynamics of homogeneous and heterogeneous populations, Mathematical Ecology, (1988), 303-316. |
[8] |
Centers for Disease Control and Prevention (CDC), Key facts about seasonal influenza, http://www.cdc.gov/flu/keyfacts.htm. |
[9] |
Centers for Disease Control and Prevention (CDC), Monitoring influenza activity, including 2009 H1N1, (2009), Monitoring Influenza Activity, Including 2009 h1n1. |
[10] |
Centers for Disease Control and Prevention (CDC), Serum cross-reactive antibody response to a novel influenza A(H1N1) virus after vaccination with seasonal influenza vaccine, MMWR Morb Mortal Wkly Rep, 58 (2009), 521-524. |
[11] |
G. Chowell, M. A. Miller and C. Viboud, Seasonal influenza in the United States, France, and Australia: Transmission an prospects for control, Epidem. Infect., 136 (2008), 852-864.
doi: 10.1017/S0950268807009144. |
[12] |
G. Chowell, S. M. Bertozzi, M. A. Colchero, H. Lopez-Gatell, C. Alpuche-Aranda, M. Hernandez and M. A. Miller, Severe respiratory disease concurrent with the circulation of H1N1 influenza, The New England Journal of Medicine, 361 (2009), 674-679.
doi: 10.1056/NEJMoa0904023. |
[13] |
Brian Coburn, "Multi-species Influenza Models with Recombination," Ph.D thesis, University of Miami in Coral Gables,FL, 2009. |
[14] |
R. Couch and J. Kasel, Immunity to influenza in man, Annual Reviews in Microbiology, 37 (2002), 529-549.
doi: 10.1146/annurev.mi.37.100183.002525. |
[15] |
O. Diekmann and J. A. P. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation," John Wiley & Sons, Ltd., Chichester, 2000. |
[16] |
D. J. D. Earn, J. Dushoff and S. A. Levin, Ecology and evolution of the flu, Trends Ecol. Evol., 17 (2002), 334-340.
doi: 10.1016/S0169-5347(02)02502-8. |
[17] |
S. Echevarría-Zuno, J. M. Mejía-Aranguré, A. V. Mar-Obeso, C. Grajales-Muñiz, E. Robles-Pérez, M. González-León, M. C. Ortega-Alvarez, C. Gonzalez-Bonilla, R. A. Rascón-Pacheco and V. H. Borja-Aburto, Infection and death from influenza A H1N1 virus in Mexico: A retrospective analysis, Lancet, 374 (2009), 2072-2079.
doi: 10.1016/S0140-6736(09)61638-X. |
[18] |
A. Esteves-Jaramillo, S. B. Omer and E. Gonzalez-Diaz, Acceptance of a vaccine against novel influenza A (H1N1) virus among health care workers in two major cities in Mexico, Archives of Medical Research, 40 (2009), 705-711.
doi: 10.1016/j.arcmed.2010.01.004. |
[19] |
W. H. Fleming and R. W. Rishel, "Deterministic and Stochasitic Optimal Control," Springer-Verlag, New York, 1994. |
[20] |
FLU. GOV, 2009 H1N1 vaccine doses allocated, ordered, and shipped by project area, (2010), http://www.flu.gov/individualfamily/vaccination/supply.html. |
[21] |
M. A. Herrera-Valdez, M. Cruz-Aponte and C. Castillo-Chavez, Multiple waves for the same pandemic: Local transportation and social distancing explain the dynamics of the A/H1N1 epidemic during 2009 in Mexico, (2010). |
[22] |
E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473-482.
doi: 10.3934/dcdsb.2002.2.473. |
[23] |
P. Y. Lee, D. B. Matchar, D. A. Clements, J. Huber, J. D. Hamilton and E. D. Peterson, Economic analysis of influenza vaccination and antiviral treatment for healthy working adults, Ann. Intern. Med., 137 (2002), 225-231. |
[24] |
S. Lee, G. Chowell and C. Castillo-Chavez, Optimal control of influenza pandemics: the role of antiviral treatment and isolation, Journal of Theoretical Biology, 265 (2010), 136-150.
doi: 10.1016/j.jtbi.2010.04.003. |
[25] |
S. Lenhart and J. T. Workman, "Optimal Control Applied to Biological Models," Chapman & Hall/CRC Mathematical and Computational Biology Series, 2007. |
[26] |
E. Malkin, Flu? What flu?, The New York Times, http://www.nytimes.com/2009/05/09/business/global/09peso.html. |
[27] |
H. Nishiura, C. Castillo-Chavez, M. Safan and G. Chowell, Transmission potential of the new Influenza A(H1N1) virus and its age-specificity in Japan, Eurosurveillance, 14 (2009), 1-4. |
[28] |
M. Nuno, G. Chowell and A. B. Gumel, Assessing the role of basic control measures, antivirals and vaccine in curtailing pandemic influenza: Scenarios for the US, UK and the Netherlands, Journal of The Royal Society Interface, 4 (2007), 505-521.
doi: 10.1098/rsif.2006.0186. |
[29] |
J. Plotkin, J. Dushoff and S. Levin, Hemagglutinin sequence clusters and the antigenic evolution of influenza A virus, Proceedings of the National Academy of Sciences, 99 (2002), 6263-6268.
doi: 10.1073/pnas.082110799. |
[30] |
L. S. Pontryagin, R. V. Boltyanski, R. V. Gamkrelidge and E. F. Mischenko, "The Mathematical Theory of Optimal Processes," John Wiley and Sons, N.Y., 1962. |
[31] |
Prevent Influenza Now! Sponsored by the National Influenza Vaccine Summit, Influenza vaccine availability tracking system (IVATS), http://www.preventinfluenza.org/ivats/. |
[32] |
C. E. Shoichet, Mexico still waiting for most swine flu vaccines, (2010), http://www.boston.com/business/articles/2010/01/13/mexico_still_waiting_for_most_swine _flu_vaccines. |
[33] |
E. Spackman, D. Stallknecht, R. Slemons, K. Winker, D. L. Suarez, M. Scott and D. E. Swayne, Phylogenetic analyses of type A influenza genes in natural reservoir species in North America reveals genetic variation, Virus research, 114 (2005), 89-100.
doi: 10.1016/j.virusres.2005.05.013. |
[34] |
R. Stengel, Optimal control and estimation, http://www.princeton.edu/ stengel/MAE546.html. |
[35] |
T. Suess, U. Buchholz, S. Dupke, R. Grunow, M. an der Heiden, A. Heider, B. Biere, B. Schweiger, W. Haas and G. Krause, Shedding and transmission of novel influenza virus A/H1N1 infection in households—Germany, 2009, American Journal of Epidemiology, 171 (2010), 1157-1164.
doi: 10.1093/aje/kwq071. |
[36] |
J. K. Taubenberger, D. M. Morens, 1918 influenza: the mother of all pandemics, Emerging Infectious Diseases, (2009), http://www.cdc.gov/ncidod/EID/vol12no01/05-0979.htm. |
[37] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[38] |
World Health Organization, Recommended composition of influenza of influenza virus vaccines for use in the 2001-2002 season, Wkly. Epidemiol. Rec., 76 (2001), 58-61. |
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