2011, 8(1): 21-48. doi: 10.3934/mbe.2011.8.21

Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different "waves" of A-H1N1pdm cases observed in México during 2009

1. 

Mathematical, Computational, and Modeling Sciences Center, Physical Sciences A, P.O. Box, 871904, Tempe, AZ 85287-1904, United States, United States

Received  June 2010 Revised  September 2010 Published  January 2011

Influenza outbreaks have been of relatively limited historical interest in México. The 2009 influenza pandemic not only changed México's health priorities but also brought to the forefront some of the strengths and weaknesses of México's epidemiological surveillance and public health system. A year later, México's data show an epidemic pattern characterized by three "waves''. The reasons this three-wave patterns are theoretically investigated via models that incorporate México's general trends of land transportation, public health measures, and the regular opening and closing of schools during 2009. The role of vaccination is also studied taking into account delays in access and limitations in the total and daily numbers of vaccines available. The research in this article supports the view that the thee epidemic "waves" are the result of the synergistic interactions of three factors: regional movement patterns of Mexicans, the impact and effectiveness of dramatic social distancing measures imposed during the first outbreak, and the summer release of school children followed by their subsequent return to classes in the fall. The three "waves" cannot be explained by the transportation patterns alone but only through the combination of transport patterns and changes in contact rates due to the use of explicit or scheduled social distancing measures. The research identifies possible vaccination schemes that account for the school calendar and whose effectiveness are enhanced by social distancing measures. The limited impact of the late arrival of the vaccine is also analyzed.
Citation: Marco Arieli Herrera-Valdez, Maytee Cruz-Aponte, Carlos Castillo-Chavez. Multiple outbreaks for the same pandemic: Local transportation and social distancing explain the different "waves" of A-H1N1pdm cases observed in México during 2009. Mathematical Biosciences & Engineering, 2011, 8 (1) : 21-48. doi: 10.3934/mbe.2011.8.21
References:
[1]

R. Acuña-Soto, "Historical and Epidemiological Patterns of Influenza in México,", In, (2009).

[2]

R. Acuna-Soto, Death records from historical archives: A valuable source of epidemiological information,, Mathematical and Statistical Estimation Approaches in Epidemiology, (2009), 189.

[3]

F. S. Albright, P. Orlando, A. T. Pavia, G. G. Jackson and L. A. C. Albright, Evidence for a heritable predisposition to death due to influenza,, The Journal of Infectious Diseases, 197 (2008), 18. doi: 10.1086/524064.

[4]

L. K. Altman, "Many Swine Flu Cases Have no Fever,", New York Times, (2009).

[5]

V. Andreasen, J. Lin and S. A. Levin, The dynamics of co-circulating influenza strains conferring partial cross-immunity,, Journal of Mathematical Biology, 35 (1997), 825.

[6]

L. A. Angelova, Long-term immunity to influenza A (H1N1) in humans,, In Annales de l'Institut Pasteur. Virologie, 133 (1982), 267.

[7]

J. Arino and P. van den Driessche, A multi-city epidemic model,, Mathematical Population Studies, 10 (2003), 175. doi: 10.1080/08898480306720.

[8]

J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, A model for influenza with vaccination and antiviral treatment,, Journal of Theoretical Biology, 253 (2008), 118. doi: 10.1016/j.jtbi.2008.02.026.

[9]

O. V. Baroyan and L. A. Rvachev, Deterministic models of epidemics for a territory with a transport network,, Cybernetics and Systems Analysis, 3 (1967), 55. doi: 10.1007/BF01120008.

[10]

S. Bertozzi, A. Kelso, M. Tashiro, V. Savy, J. Farrar, M. Osterholm, S. Jameel and C. P. Muller, Pandemic flu: From the front lines. Interviewed by Declan Butler,, Nature, 461 (2009).

[11]

F. Brauer, Compartmental models in epidemiology,, Mathematical Epidemiology, (2008), 19.

[12]

F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Springer Verlag, (2001).

[13]

F. Brauer and C. Kribs-Zaleta, "An Introduction to Dynamical Systems for Biological Modeling" (series: chapman & hall/crc mathematical & computational biology),, 2010., ().

[14]

R. M. Bush, C. A. Bender, K. Subbarao, N. J. Cox and W. M. Fitch, Predicting the evolution of human influenza A,, Science, 286 (1999). doi: 10.1126/science.286.5446.1921.

[15]

P. Caley, D. J. Philp and K. McCracken, Quantifying social distancing arising from pandemic influenza,, Journal of The Royal Society Interface, 5 (2008). doi: 10.1098/rsif.2007.1197.

[16]

C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. Liu, "Cross-Immunity in the Dynamics of Homogeneous and Heterogeneous Populations,", Mathematical Ecology, (1988).

[17]

C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. M. Liu, Epidemiological models with age structure, proportionate mixing, and cross-immunity,, Journal of Mathematical Biology, 27 (1989), 233.

[18]

C. Castillo-Chavez, B. Song and J. Zhang, An epidemic model with virtual mass transportation: the case of smallpox in a large city,, Bioterrorism: Mathematical Modeling Applications in Homeland Security, (2003).

[19]

M. Chan, "Influenza A(H1N1),", Technical report, (2009).

[20]

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). doi: 10.1056/NEJMoa0904023.

[21]

G. Chowell, C. Viboud, X. Wang, S. M. Bertozzi and M. A. Miller, Adaptive vaccination strategies to mitigate pandemic influenza: Mexico as a case study,, 2009., ().

[22]

G. Chowell, C. Viboud, L. Simonsen, M. A. Miller and R. Acuna-Soto, Mortality patterns associated with the 1918 influenza pandemic in Mexico: Evidence for a spring herald wave and lack of preexistingiImmunity in older populations,, The Journal of Infectious Diseases, (2010).

[23]

V. Colizza, A. Barrat, M. Barthelemy, A. Valleron and A. Vespignani, Modeling the worldwide spread of pandemic influenza: Baseline case and containment interventions,, PLoS Medicine, 4 (2007). doi: 10.1371/journal.pmed.0040013.

[24]

J. A. Córdova-Villalobos, Lessons learned and preparing for the future: Influenza a/h1n1 in méxico,, Plenary 1, (2009).

[25]

R. B. Couch and J. A. Kasel, Immunity to influenza in man,, Annual Reviews in Microbiology, 37 (1983), 529. doi: 10.1146/annurev.mi.37.100183.002525.

[26]

G. Del Giudice, K. J. Stittelaar, G. van Amerongen, J. Simon, A. D. M. E. Osterhaus, K. Stöhr and R. Rappuoli, Seasonal influenza vaccine provides priming for A/H1N1 immunization,, Science Translational Medicine, 1 (2009).

[27]

Instituto Mexicano del Transporte, North american transportation statistics database, 2006-., URL , ().

[28]

M. Falco, Cdc: Production of h1n1 flu lagging, 2009., URL , ().

[29]

Z. Feng, W. Huang and C. Castillo-Chavez, On the role of variable latent periods in mathematical models for tuberculosis,, Journal of Dynamics and Differential Equations, 13 (2001), 425.

[30]

A. Flahault, X. De Lamballerie and T. Hanslik, Symptomatic infections less frequent with H1N1pdm than with seasonal strains,, 2009., ().

[31]

T. Garske, J. Legrand, C. A. Donnelly, H. Ward, S. Cauchemez, C. Fraser, N. M. Ferguson and A. C. Ghani, Assessing the severity of the novel influenza A/H1N1 pandemic,, British Medical Journal, 339 (2009).

[32]

Mexico City guide, "Transport," 2010., URL , ().

[33]

M. Haber, I. R. A. M. Longini JR and M. E. Halloran, Measures of the effects of vaccination in a randomly mixing population,, International Journal of Epidemiology, 20 (1991). doi: 10.1093/ije/20.1.300.

[34]

K. Hadeler and C. Castillo-Chavez, A core group model for disease transmission,, Mathematical Biosciences, 128 (1995), 41. doi: 10.1016/0025-5564(94)00066-9.

[35]

M. E. Halloran, M. Haber, I. M. Longini Jr and C. J. Struchiner, Direct and indirect effects in vaccine efficacy and effectiveness,, American Journal of Epidemiology, 133 (1991).

[36]

W. Huang, K. L. Cooke and C. Castillo-Chavez, Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission,, SIAM Journal on Applied Mathematics, (1992), 835.

[37]

J. Hunter, D. Dale and M. Droettboom, "Matplotlib: A Python 2d Plotting Library," 2008-., URL , ().

[38]

A. C. Hurt, J. Ernest, Y. M. Deng, P. Iannello, T. G. Besselaar, C. Birch, P. Buchy, M. Chittaganpitch, S. C. Chiu, D. Dwyer, et al., "Emergence and spread of oseltamivir-resistant A (H1N1) influenza viruses in Oceania, South East Asia and South Africa,", Antiviral Research, (2009).

[39]

E. S. Hurwitz, M. Haber, A. Chang, T. Shope, S. Teo, M. Ginsberg, N. Waecker and N. J. Cox, Effectiveness of influenza vaccination of day care children in reducing influenza-related morbidity among household contacts,, The Journal of the American Medical Association, 284 (2000).

[40]

J. M. Hyman and T. Laforce, Modeling the spread of in fluecnza among cities,, Biomathematical Modeling Applications for Homeland Security, (2003), 215.

[41]

E. Jones, T. Oliphant, P. Peterson, et al., "SciPy: Open Source Scientific Tools for Python," 2001-., URL , ().

[42]

W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-I,, Proceedings of the Royal Society, 115A (1927), 700.

[43]

K. Khan, J. Arino, W. Hu, P. Raposo, J. Sears, F. Calderon, C. Heidebrecht, M. Macdonald, J. Liauw, A. Chan, et al., Spread of a novel influenza A (H1N1) virus via global airline transportation,, The New England Journal of Medicine, 361 (2009). doi: 10.1056/NEJMc0904559.

[44]

C. D. Kozul, K. H. Ely, R. I. Enelow and J. W. Hamilton, Low-dose arsenic compromises the immune response to influenza a infection in vivo,, Environ Health Perspect. PubMed, 117 (2009), 1441.

[45]

R. J. Kurukulaaratchy, S. Matthews and S. H. Arshad, Does environment mediate earlier onset of the persistent childhood asthma phenotype?,, Pediatrics, 113 (2004). doi: 10.1542/peds.113.2.345.

[46]

P. R. S. Lagacé-Wiens, E. Rubinstein and A. Gumel, "Influenza Epidemiology: Past, Present, and Future,", Critical Care Medicine, (2010).

[47]

M. A. Lezana-Fernández, "A/h1n1 Epidemic in México: Lessons Learned,", Talk at, (2009).

[48]

F. Libenson, "Llegaron al Edomex 66 mil Vacunas Contra AH1N1," 2009., http://elinformantemexico.com/index.php/noticias/llegaron-al-edomex-66-mil-v acunas-contra-ah1n1-franklin-libenson-violante.html., ().

[49]

H. C. Lin, M. J. Chen, S. J. Chang, M. T. Liu, H. S. Wu, J. H. Chuang, J. H. Chou, H. S. Kuo and S. C. Chang, Investigation of the first two cases of oseltamivir-resistant pandemic (H1N1) 2009 virus in Taiwan,, Taiwan Epidemiology Bulletin, (2009), 815.

[50]

M. López-Cervantes, A. Venado, A. Moreno, R. L. Pacheco-Domínguez and G. Ortega-Pierres, On the spread of the novel influenza A (H1N1) virus in Mexico,, The Journal of Infection in Developing Countries, 3 (2009).

[51]

Mexicocity.com.mx, "Taxi Cabs," 2010., URL , ().

[52]

M. A. Miller, C. Viboud, M. Balinska and L. Simonsen, The signature features of influenza pandemics-implications for policy,, The New England Journal of Medicine, 360 (2009).

[53]

A. S. Monto, Interrupting the transmission of respiratory tract infections: Theory and practice,, Clinical Infectious Diseases, 28 (1999), 200.

[54]

A. Moscona, Global transmission of oseltamivir-resistant influenza,, The New England Journal of Medicine, (2009).

[55]

M. R. Moser, T. R. Bender, H. S. Margolis, G. R. Noble, A. P. Kendal and D. G. Ritter, An outbreak of influenza aboard a commercial airliner,, American Journal of Epidemiology, 110 (1979).

[56]

M. I. Nelson and E. C. Holmes, The evolution of epidemic influenza,, Nature Reviews Genetics, 8 (2007), 196.

[57]

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,, Euro Surveill, 14 (2009).

[58]

SSA Notimex, "Este Lunes Llegan las Vacunas Contra Influenza AH1N1,", Notimex, (2009).

[59]

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). doi: 10.1098/rsif.2006.0186.

[60]

M. Nuno, G. Chowell, X. Wang and C. Castillo-Chavez, On the role of cross-immunity and vaccines on the survival of less fit flu-strains,, Theoretical Population Biology, 71 (2007), 20. doi: 10.1016/j.tpb.2006.07.002.

[61]

A. Pedroza, J. G. Huerta, M. de la Luz Garcia, A. Rojas, I. López-Martínez, M. Penagos, C. Franco-Paredes, C. Deroche and C. Mascareñas, The safety and immunogenicity of influenza vaccine in children with asthma in Mexico,, International Journal of Infectious Diseases, 13 (2009), 469. doi: 10.1016/j.ijid.2008.08.015.

[62]

J. B. Plotkin, J. Dushoff and S. A. Levin, Hemagglutinin sequence clusters and the antigenic evolution of influenza A virus,, Proceedings of the National Academy of Sciences, 99 (2002). doi: 10.1073/pnas.082110799.

[63]

L. A. Rvachev and I. M. Jr. Longini, A mathematical model for the global spread of influenza,, Mathematical Biosciences, 75 (1985), 3.

[64]

A. N. Slepushkin, E. I. Bourtseva, A. L. Belyaev, L. N. Vlassova and E. L. Feodoritova, Influenza morbidity and some peculiarities of antiinfluenza immunity and prevention during influenza pandemics,, In International Congress Series, 1263 (2004), 787.

[65]

E. Spackman, D. E. Stallknecht, R. D. 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. doi: 10.1016/j.virusres.2005.05.013.

[66]

SSA, "Situación Actual de la Epidemia [Current Epidemic Situation]," January 2010., URL , ().

[67]

C. Sun and Y. H. Hsieh, Global analysis of an SEIR model with varying population size and vaccination,, Applied Mathematical Modelling, (2009).

[68]

R. A. Trammell and L. A. Toth, Genetic susceptibility and resistance to influenza infection and disease in humans and mice,, Expert Review of Molecular Diagnostics, 8 (2008), 515. doi: 10.1586/14737159.8.4.515.

[69]

B. Valadez, "Aplicadas, Solo 10/100 de las Dosis Contra el A/H1N1," 2010., URL , ().

[70]

C. Viboud, P. Y. Boélle, S. Cauchemez, A. Lavenu, A. J. Valleron, A. Flahault and F. Carrat, Risk factors of influenza transmission in households,, In International Congress Series, 1263 (2004), 291.

[71]

C. Viboud, O. N. Bjornstad, D. L. Smith, L. Simonsen, M. A. Miller and B. T. Grenfell, Synchrony, waves, and spatial hierarchies in the spread of influenza,, Science, 312 (2006). doi: 10.1126/science.1125237.

[72]

D. Weycker, J. Edelsberg, M. Elizabeth Halloran, I. M. Longini, et al., Population-wide benefits of routine vaccination of children against influenza,, Vaccine, 23 (2005), 1284. doi: 10.1016/j.vaccine.2004.08.044.

[73]

T. White, S. Lavoie and M. D. Nettleman, Potential cost savings attributable to influenza vaccination of school-aged children,, Pediatrics, 103 (1999). doi: 10.1542/peds.103.6.e73.

[74]

Wikipedia, "World Population 1800-2100," 2010-., URL , (): 1800.

show all references

References:
[1]

R. Acuña-Soto, "Historical and Epidemiological Patterns of Influenza in México,", In, (2009).

[2]

R. Acuna-Soto, Death records from historical archives: A valuable source of epidemiological information,, Mathematical and Statistical Estimation Approaches in Epidemiology, (2009), 189.

[3]

F. S. Albright, P. Orlando, A. T. Pavia, G. G. Jackson and L. A. C. Albright, Evidence for a heritable predisposition to death due to influenza,, The Journal of Infectious Diseases, 197 (2008), 18. doi: 10.1086/524064.

[4]

L. K. Altman, "Many Swine Flu Cases Have no Fever,", New York Times, (2009).

[5]

V. Andreasen, J. Lin and S. A. Levin, The dynamics of co-circulating influenza strains conferring partial cross-immunity,, Journal of Mathematical Biology, 35 (1997), 825.

[6]

L. A. Angelova, Long-term immunity to influenza A (H1N1) in humans,, In Annales de l'Institut Pasteur. Virologie, 133 (1982), 267.

[7]

J. Arino and P. van den Driessche, A multi-city epidemic model,, Mathematical Population Studies, 10 (2003), 175. doi: 10.1080/08898480306720.

[8]

J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, A model for influenza with vaccination and antiviral treatment,, Journal of Theoretical Biology, 253 (2008), 118. doi: 10.1016/j.jtbi.2008.02.026.

[9]

O. V. Baroyan and L. A. Rvachev, Deterministic models of epidemics for a territory with a transport network,, Cybernetics and Systems Analysis, 3 (1967), 55. doi: 10.1007/BF01120008.

[10]

S. Bertozzi, A. Kelso, M. Tashiro, V. Savy, J. Farrar, M. Osterholm, S. Jameel and C. P. Muller, Pandemic flu: From the front lines. Interviewed by Declan Butler,, Nature, 461 (2009).

[11]

F. Brauer, Compartmental models in epidemiology,, Mathematical Epidemiology, (2008), 19.

[12]

F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Springer Verlag, (2001).

[13]

F. Brauer and C. Kribs-Zaleta, "An Introduction to Dynamical Systems for Biological Modeling" (series: chapman & hall/crc mathematical & computational biology),, 2010., ().

[14]

R. M. Bush, C. A. Bender, K. Subbarao, N. J. Cox and W. M. Fitch, Predicting the evolution of human influenza A,, Science, 286 (1999). doi: 10.1126/science.286.5446.1921.

[15]

P. Caley, D. J. Philp and K. McCracken, Quantifying social distancing arising from pandemic influenza,, Journal of The Royal Society Interface, 5 (2008). doi: 10.1098/rsif.2007.1197.

[16]

C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. Liu, "Cross-Immunity in the Dynamics of Homogeneous and Heterogeneous Populations,", Mathematical Ecology, (1988).

[17]

C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin and W. M. Liu, Epidemiological models with age structure, proportionate mixing, and cross-immunity,, Journal of Mathematical Biology, 27 (1989), 233.

[18]

C. Castillo-Chavez, B. Song and J. Zhang, An epidemic model with virtual mass transportation: the case of smallpox in a large city,, Bioterrorism: Mathematical Modeling Applications in Homeland Security, (2003).

[19]

M. Chan, "Influenza A(H1N1),", Technical report, (2009).

[20]

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). doi: 10.1056/NEJMoa0904023.

[21]

G. Chowell, C. Viboud, X. Wang, S. M. Bertozzi and M. A. Miller, Adaptive vaccination strategies to mitigate pandemic influenza: Mexico as a case study,, 2009., ().

[22]

G. Chowell, C. Viboud, L. Simonsen, M. A. Miller and R. Acuna-Soto, Mortality patterns associated with the 1918 influenza pandemic in Mexico: Evidence for a spring herald wave and lack of preexistingiImmunity in older populations,, The Journal of Infectious Diseases, (2010).

[23]

V. Colizza, A. Barrat, M. Barthelemy, A. Valleron and A. Vespignani, Modeling the worldwide spread of pandemic influenza: Baseline case and containment interventions,, PLoS Medicine, 4 (2007). doi: 10.1371/journal.pmed.0040013.

[24]

J. A. Córdova-Villalobos, Lessons learned and preparing for the future: Influenza a/h1n1 in méxico,, Plenary 1, (2009).

[25]

R. B. Couch and J. A. Kasel, Immunity to influenza in man,, Annual Reviews in Microbiology, 37 (1983), 529. doi: 10.1146/annurev.mi.37.100183.002525.

[26]

G. Del Giudice, K. J. Stittelaar, G. van Amerongen, J. Simon, A. D. M. E. Osterhaus, K. Stöhr and R. Rappuoli, Seasonal influenza vaccine provides priming for A/H1N1 immunization,, Science Translational Medicine, 1 (2009).

[27]

Instituto Mexicano del Transporte, North american transportation statistics database, 2006-., URL , ().

[28]

M. Falco, Cdc: Production of h1n1 flu lagging, 2009., URL , ().

[29]

Z. Feng, W. Huang and C. Castillo-Chavez, On the role of variable latent periods in mathematical models for tuberculosis,, Journal of Dynamics and Differential Equations, 13 (2001), 425.

[30]

A. Flahault, X. De Lamballerie and T. Hanslik, Symptomatic infections less frequent with H1N1pdm than with seasonal strains,, 2009., ().

[31]

T. Garske, J. Legrand, C. A. Donnelly, H. Ward, S. Cauchemez, C. Fraser, N. M. Ferguson and A. C. Ghani, Assessing the severity of the novel influenza A/H1N1 pandemic,, British Medical Journal, 339 (2009).

[32]

Mexico City guide, "Transport," 2010., URL , ().

[33]

M. Haber, I. R. A. M. Longini JR and M. E. Halloran, Measures of the effects of vaccination in a randomly mixing population,, International Journal of Epidemiology, 20 (1991). doi: 10.1093/ije/20.1.300.

[34]

K. Hadeler and C. Castillo-Chavez, A core group model for disease transmission,, Mathematical Biosciences, 128 (1995), 41. doi: 10.1016/0025-5564(94)00066-9.

[35]

M. E. Halloran, M. Haber, I. M. Longini Jr and C. J. Struchiner, Direct and indirect effects in vaccine efficacy and effectiveness,, American Journal of Epidemiology, 133 (1991).

[36]

W. Huang, K. L. Cooke and C. Castillo-Chavez, Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission,, SIAM Journal on Applied Mathematics, (1992), 835.

[37]

J. Hunter, D. Dale and M. Droettboom, "Matplotlib: A Python 2d Plotting Library," 2008-., URL , ().

[38]

A. C. Hurt, J. Ernest, Y. M. Deng, P. Iannello, T. G. Besselaar, C. Birch, P. Buchy, M. Chittaganpitch, S. C. Chiu, D. Dwyer, et al., "Emergence and spread of oseltamivir-resistant A (H1N1) influenza viruses in Oceania, South East Asia and South Africa,", Antiviral Research, (2009).

[39]

E. S. Hurwitz, M. Haber, A. Chang, T. Shope, S. Teo, M. Ginsberg, N. Waecker and N. J. Cox, Effectiveness of influenza vaccination of day care children in reducing influenza-related morbidity among household contacts,, The Journal of the American Medical Association, 284 (2000).

[40]

J. M. Hyman and T. Laforce, Modeling the spread of in fluecnza among cities,, Biomathematical Modeling Applications for Homeland Security, (2003), 215.

[41]

E. Jones, T. Oliphant, P. Peterson, et al., "SciPy: Open Source Scientific Tools for Python," 2001-., URL , ().

[42]

W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-I,, Proceedings of the Royal Society, 115A (1927), 700.

[43]

K. Khan, J. Arino, W. Hu, P. Raposo, J. Sears, F. Calderon, C. Heidebrecht, M. Macdonald, J. Liauw, A. Chan, et al., Spread of a novel influenza A (H1N1) virus via global airline transportation,, The New England Journal of Medicine, 361 (2009). doi: 10.1056/NEJMc0904559.

[44]

C. D. Kozul, K. H. Ely, R. I. Enelow and J. W. Hamilton, Low-dose arsenic compromises the immune response to influenza a infection in vivo,, Environ Health Perspect. PubMed, 117 (2009), 1441.

[45]

R. J. Kurukulaaratchy, S. Matthews and S. H. Arshad, Does environment mediate earlier onset of the persistent childhood asthma phenotype?,, Pediatrics, 113 (2004). doi: 10.1542/peds.113.2.345.

[46]

P. R. S. Lagacé-Wiens, E. Rubinstein and A. Gumel, "Influenza Epidemiology: Past, Present, and Future,", Critical Care Medicine, (2010).

[47]

M. A. Lezana-Fernández, "A/h1n1 Epidemic in México: Lessons Learned,", Talk at, (2009).

[48]

F. Libenson, "Llegaron al Edomex 66 mil Vacunas Contra AH1N1," 2009., http://elinformantemexico.com/index.php/noticias/llegaron-al-edomex-66-mil-v acunas-contra-ah1n1-franklin-libenson-violante.html., ().

[49]

H. C. Lin, M. J. Chen, S. J. Chang, M. T. Liu, H. S. Wu, J. H. Chuang, J. H. Chou, H. S. Kuo and S. C. Chang, Investigation of the first two cases of oseltamivir-resistant pandemic (H1N1) 2009 virus in Taiwan,, Taiwan Epidemiology Bulletin, (2009), 815.

[50]

M. López-Cervantes, A. Venado, A. Moreno, R. L. Pacheco-Domínguez and G. Ortega-Pierres, On the spread of the novel influenza A (H1N1) virus in Mexico,, The Journal of Infection in Developing Countries, 3 (2009).

[51]

Mexicocity.com.mx, "Taxi Cabs," 2010., URL , ().

[52]

M. A. Miller, C. Viboud, M. Balinska and L. Simonsen, The signature features of influenza pandemics-implications for policy,, The New England Journal of Medicine, 360 (2009).

[53]

A. S. Monto, Interrupting the transmission of respiratory tract infections: Theory and practice,, Clinical Infectious Diseases, 28 (1999), 200.

[54]

A. Moscona, Global transmission of oseltamivir-resistant influenza,, The New England Journal of Medicine, (2009).

[55]

M. R. Moser, T. R. Bender, H. S. Margolis, G. R. Noble, A. P. Kendal and D. G. Ritter, An outbreak of influenza aboard a commercial airliner,, American Journal of Epidemiology, 110 (1979).

[56]

M. I. Nelson and E. C. Holmes, The evolution of epidemic influenza,, Nature Reviews Genetics, 8 (2007), 196.

[57]

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,, Euro Surveill, 14 (2009).

[58]

SSA Notimex, "Este Lunes Llegan las Vacunas Contra Influenza AH1N1,", Notimex, (2009).

[59]

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). doi: 10.1098/rsif.2006.0186.

[60]

M. Nuno, G. Chowell, X. Wang and C. Castillo-Chavez, On the role of cross-immunity and vaccines on the survival of less fit flu-strains,, Theoretical Population Biology, 71 (2007), 20. doi: 10.1016/j.tpb.2006.07.002.

[61]

A. Pedroza, J. G. Huerta, M. de la Luz Garcia, A. Rojas, I. López-Martínez, M. Penagos, C. Franco-Paredes, C. Deroche and C. Mascareñas, The safety and immunogenicity of influenza vaccine in children with asthma in Mexico,, International Journal of Infectious Diseases, 13 (2009), 469. doi: 10.1016/j.ijid.2008.08.015.

[62]

J. B. Plotkin, J. Dushoff and S. A. Levin, Hemagglutinin sequence clusters and the antigenic evolution of influenza A virus,, Proceedings of the National Academy of Sciences, 99 (2002). doi: 10.1073/pnas.082110799.

[63]

L. A. Rvachev and I. M. Jr. Longini, A mathematical model for the global spread of influenza,, Mathematical Biosciences, 75 (1985), 3.

[64]

A. N. Slepushkin, E. I. Bourtseva, A. L. Belyaev, L. N. Vlassova and E. L. Feodoritova, Influenza morbidity and some peculiarities of antiinfluenza immunity and prevention during influenza pandemics,, In International Congress Series, 1263 (2004), 787.

[65]

E. Spackman, D. E. Stallknecht, R. D. 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. doi: 10.1016/j.virusres.2005.05.013.

[66]

SSA, "Situación Actual de la Epidemia [Current Epidemic Situation]," January 2010., URL , ().

[67]

C. Sun and Y. H. Hsieh, Global analysis of an SEIR model with varying population size and vaccination,, Applied Mathematical Modelling, (2009).

[68]

R. A. Trammell and L. A. Toth, Genetic susceptibility and resistance to influenza infection and disease in humans and mice,, Expert Review of Molecular Diagnostics, 8 (2008), 515. doi: 10.1586/14737159.8.4.515.

[69]

B. Valadez, "Aplicadas, Solo 10/100 de las Dosis Contra el A/H1N1," 2010., URL , ().

[70]

C. Viboud, P. Y. Boélle, S. Cauchemez, A. Lavenu, A. J. Valleron, A. Flahault and F. Carrat, Risk factors of influenza transmission in households,, In International Congress Series, 1263 (2004), 291.

[71]

C. Viboud, O. N. Bjornstad, D. L. Smith, L. Simonsen, M. A. Miller and B. T. Grenfell, Synchrony, waves, and spatial hierarchies in the spread of influenza,, Science, 312 (2006). doi: 10.1126/science.1125237.

[72]

D. Weycker, J. Edelsberg, M. Elizabeth Halloran, I. M. Longini, et al., Population-wide benefits of routine vaccination of children against influenza,, Vaccine, 23 (2005), 1284. doi: 10.1016/j.vaccine.2004.08.044.

[73]

T. White, S. Lavoie and M. D. Nettleman, Potential cost savings attributable to influenza vaccination of school-aged children,, Pediatrics, 103 (1999). doi: 10.1542/peds.103.6.e73.

[74]

Wikipedia, "World Population 1800-2100," 2010-., URL , (): 1800.

[1]

Eunha Shim. Optimal strategies of social distancing and vaccination against seasonal influenza. Mathematical Biosciences & Engineering, 2013, 10 (5/6) : 1615-1634. doi: 10.3934/mbe.2013.10.1615

[2]

Kasia A. Pawelek, Anne Oeldorf-Hirsch, Libin Rong. Modeling the impact of twitter on influenza epidemics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1337-1356. doi: 10.3934/mbe.2014.11.1337

[3]

Xun-Yang Wang, Khalid Hattaf, Hai-Feng Huo, Hong Xiang. Stability analysis of a delayed social epidemics model with general contact rate and its optimal control. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1267-1285. doi: 10.3934/jimo.2016.12.1267

[4]

Olivia Prosper, Omar Saucedo, Doria Thompson, Griselle Torres-Garcia, Xiaohong Wang, Carlos Castillo-Chavez. Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 141-170. doi: 10.3934/mbe.2011.8.141

[5]

Plamen Stefanov, Yang Yang. Multiwave tomography with reflectors: Landweber's iteration. Inverse Problems & Imaging, 2017, 11 (2) : 373-401. doi: 10.3934/ipi.2017018

[6]

David Kinderlehrer, Adrian Tudorascu. Transport via mass transportation. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 311-338. doi: 10.3934/dcdsb.2006.6.311

[7]

Jacques Demongeot, Jean Gaudart, Julie Mintsa, Mustapha Rachdi. Demography in epidemics modelling. Communications on Pure & Applied Analysis, 2012, 11 (1) : 61-82. doi: 10.3934/cpaa.2012.11.61

[8]

Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209

[9]

Plamen Stefanov, Gunther Uhlmann. Instability of the linearized problem in multiwave tomography of recovery both the source and the speed. Inverse Problems & Imaging, 2013, 7 (4) : 1367-1377. doi: 10.3934/ipi.2013.7.1367

[10]

Vikram Krishnamurthy, William Hoiles. Information diffusion in social sensing. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 365-411. doi: 10.3934/naco.2016017

[11]

Werner Creixell, Juan Carlos Losada, Tomás Arredondo, Patricio Olivares, Rosa María Benito. Serendipity in social networks. Networks & Heterogeneous Media, 2012, 7 (3) : 363-371. doi: 10.3934/nhm.2012.7.363

[12]

Pradeep Dubey, Rahul Garg, Bernard De Meyer. Competing for customers in a social network. Journal of Dynamics & Games, 2014, 1 (3) : 377-409. doi: 10.3934/jdg.2014.1.377

[13]

Oren Barnea, Rami Yaari, Guy Katriel, Lewi Stone. Modelling seasonal influenza in Israel. Mathematical Biosciences & Engineering, 2011, 8 (2) : 561-573. doi: 10.3934/mbe.2011.8.561

[14]

Shu Liao, Jin Wang, Jianjun Paul Tian. A computational study of avian influenza. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1499-1509. doi: 10.3934/dcdss.2011.4.1499

[15]

G.S. Liu, J.Z. Zhang. Decision making of transportation plan, a bilevel transportation problem approach. Journal of Industrial & Management Optimization, 2005, 1 (3) : 305-314. doi: 10.3934/jimo.2005.1.305

[16]

Hal L. Smith, Horst R. Thieme. Chemostats and epidemics: Competition for nutrients/hosts. Mathematical Biosciences & Engineering, 2013, 10 (5/6) : 1635-1650. doi: 10.3934/mbe.2013.10.1635

[17]

Cristina Cross, Alysse Edwards, Dayna Mercadante, Jorge Rebaza. Dynamics of a networked connectivity model of epidemics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3379-3390. doi: 10.3934/dcdsb.2016102

[18]

Folashade B. Agusto, Abba B. Gumel. Theoretical assessment of avian influenza vaccine. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 1-25. doi: 10.3934/dcdsb.2010.13.1

[19]

Eunha Shim. Prioritization of delayed vaccination for pandemic influenza. Mathematical Biosciences & Engineering, 2011, 8 (1) : 95-112. doi: 10.3934/mbe.2011.8.95

[20]

Lorenzo Brasco, Filippo Santambrogio. An equivalent path functional formulation of branched transportation problems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 845-871. doi: 10.3934/dcds.2011.29.845

2016 Impact Factor: 1.035

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (0)

[Back to Top]