2011, 8(1): 123-139. doi: 10.3934/mbe.2011.8.123

Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks

1. 

Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1, Hungary

2. 

Analysis and Stochastics Research Group, Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1.

Received  March 2010 Revised  September 2010 Published  January 2011

Finding optimal policies to reduce the morbidity and mortality of the ongoing pandemic is a top public health priority. Using a compartmental model with age structure and vaccination status, we examined the effect of age specific scheduling of vaccination during a pandemic influenza outbreak, when there is a race between the vaccination campaign and the dynamics of the pandemic. Our results agree with some recent studies on that age specificity is paramount to vaccination planning. However, little is known about the effectiveness of such control measures when they are applied during the outbreak. Comparing five possible strategies, we found that age specific scheduling can have a huge impact on the outcome of the epidemic. For the best scheme, the attack rates were up to 10% lower than for other strategies. We demonstrate the importance of early start of the vaccination campaign, since ten days delay may increase the attack rate by up to 6%. Taking into account the delay between developing immunity and vaccination is a key factor in evaluating the impact of vaccination campaigns. We provide a general framework which will be useful for the next pandemic waves as well.
Citation: Diána H. Knipl, Gergely Röst. Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks. Mathematical Biosciences & Engineering, 2011, 8 (1) : 123-139. doi: 10.3934/mbe.2011.8.123
References:
[1]

M. E. Alexander, C. S. Bowman, Z. Feng, M. Gardam, S. M. Moghadas, G. Röst, J. Wu and P. Yan, Emergence of drug-resistance: Implications for antiviral control of pandemic influenza,, P. Roy. Soc. B - Biol. Sci., 274 (2007), 1675.

[2]

M. E. Alexander, S. M. Moghadas, G. Röst and J. Wu, A delay differential model for pandemic influenza with antiviral treatment,, Bulletin of Mathematical Biology, 70 (2008), 382. doi: 10.1007/s11538-007-9257-2.

[3]

J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, Simple models for containment of a pandemic,, J. R. Soc. Interface, 3 (2006), 453. doi: 10.1098/rsif.2006.0112.

[4]

P. Baccam, C. Beauchemin, C. A. Macken, F. G. Hayden and A. S. Perelson, Kinetics of influenza A virus infection in humans,, J. Virol., 80 (2006), 7590. doi: 10.1128/JVI.01623-05.

[5]

D. Balcan et al., Seasonal transmission potential and activity peaks of the new influenza A(H1N1): A Monte Carlo likelihood analysis based on human mobility,, BMC Medicine, 7 (2009). doi: 10.1186/1741-7015-7-45.

[6]

N. E. Basta, E. M. Halloran, L. Matrajt and I. M. Longini Jr., Estimating influenza vaccine efficacy from challenge and community-based study data,, Am. J. Epidemiol., 168 (2008), 1343. doi: 10.1093/aje/kwn259.

[7]

G. Chowell, C. E. Ammon, N. W. Hengartner and J. M. Hyman, Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions,, J. Theor. Biol., 241 (2006), 193. doi: 10.1016/j.jtbi.2005.11.026.

[8]

G. Chowell, M. A. Miller and C. Viboud, Seasonal influenza in the United States, France and Australia: Transmission and prospects for control,, Epidemiol. Infect., 136 (2007), 852.

[9]

G. Chowell, C. Viboud, X. Wang, S. Bertozzi and M. Miller, Adaptive vaccination strategies to mitigate pandemic influenza - Mexico as a case study,, PLoS ONE, 4 (2009). doi: 10.1371/journal.pone.0008164.

[10]

CDC, Prevention and control of influenza: Recommendations of the advisory committee on immunization practices (ACIP),, July 17, (2008), 1.

[11]

CDC, "Key Facts About Seasonal Flu Vaccine,", \url{http://www.cdc.gov/Flu/protect/keyfacts.htm}, (2009).

[12]

O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models,, J. R. Soc. Interface, 7 (2010), 873. doi: 10.1098/rsif.2009.0386.

[13]

L. J. Donaldson, P. D. Rutter, B. M. Ellis, F. E. C. Greaves, O. T. Mytton, R. G. Pebody and I. E. Yardley, Mortality from pandemic A/H1N1 2009 influenza in England: Public health surveillance study,, British Medical Journal, 339 (2009).

[14]

European CDC Risk Assessment, "Pandemic H1N1,", Version 6, (2009).

[15]

Eurostat, "Population Statistics 2006 Edition,", Official Publications of the European Communities (Luxembourg), (2006).

[16]

F. Falus and B. Oroszi, "National Chief Medical Officer's Office,", Hungary, (2009).

[17]

N. M. Ferguson, D. A. Cummings, C. Fraser, J. C. Cajka and P. C. Cooley, Strategies for mitigating an influenza pandemic,, Nature, 442 (2006), 448. doi: 10.1038/nature04795.

[18]

D. M. Fleming and A. J. Elliot, Estimating the risk population in relation to influenza vaccination policy,, Vaccine, 24 (2006), 4378. doi: 10.1016/j.vaccine.2006.02.053.

[19]

M. Z. Gojovic, B. Sander, D. Fisman, M. D. Krahn and C. T. Bauch, Modelling mitigation strategies for pandemic (H1N1) 2009,, Can. Med. Assoc. J., 181 (2009). doi: 10.1503/cmaj.091641.

[20]

E. Goldstein, A. Apolloni, B. Lewis, J. C. Miller, M. Macauley, S. Eubank, M. Lipsitch and J. Wallinga, Distribution of vaccine/antivirals and the least spread line in a stratified population,, J. R. Soc. Interface, 7 (2009), 755. doi: 10.1098/rsif.2009.0393.

[21]

M. E. Greenberg, M. H. Lai, G. F. Hartel, C. H. Wichems, C. Gittleson, J. Bennet, G. Dawson, W. Hu, C. Leggio, D. Washington and R. L. Basser, Response to a monovalent influenza a (H1N1) 2009 vaccine,, N. Eng. J. Med., 361 (2009), 2405. doi: 10.1056/NEJMoa0907413.

[22]

K. Hancock, V. Veguilla, X. Lu, et al., Cross-reactive antibody responses to the 2009 pandemic H1N1 influenza virus,, N. Engl. J. Med., 361 (2009), 1945. doi: 10.1056/NEJMoa0906453.

[23]

J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio,, J. R. Soc. Interface, 2 (2005), 281. doi: 10.1098/rsif.2005.0042.

[24]

K. Johansen, A. Nicoll, B. C. Ciancio and P. Kramarz, Pandemic influenza A(A(H1N1)v) 2009 vaccines in the European Union,, Euro Surveill, 14 (2009).

[25]

I. M. Longini Jr and M. E. Halloran, Strategy for distribution of influenza vaccine to high-risk groups and children,, Am. J. Epidemiol., 161 (2005). doi: 10.1093/aje/kwi053.

[26]

L. Matrajt and I. M. Longini, "Optimizing Vaccine Allocation at Different Points in Time During an Epidemic,", UW Biostatistics Working Paper Series 363, (2010).

[27]

J. Medlock and A. P. Galvani, Optimizing influenza vaccine distribution,, Science, 325 (2009), 1705. doi: 10.1126/science.1175570.

[28]

J. Medlock, L. A. Meyers and A. P. Galvani, "Optimizing Allocation for a Delayed Influenza Vaccine Campaign,", PLOS Curr Influenza, (2010).

[29]

S. Merler, M. Ajelli and C. Rizzo, Age-prioritized use of antivirals during an influenza pandemic,, BMC Infectious Diseases, 9 (2009). doi: 10.1186/1471-2334-9-117.

[30]

E. Miller, K. Hoschler, P. Hardelid, E. Stanford, N. Andrews and M. Zambon, Incidence of 2009 pandemic influenza A H1N1 infection in England: a cross-sectional serological study,, The Lancet, 375 (2010), 1100. doi: 10.1016/S0140-6736(09)62126-7.

[31]

S. M. Moghadas, C. S. Bowman, G. Röst and J. Wu, Population-wide emergence of antiviral resistance during pandemic influenza,, PLOS ONE, 3 (2008).

[32]

S. M. Moghadas, C. S. Bowman, G. Röst, D. Fisman and J. Wu, Post-exposure prophylaxis during pandemic outbreaks,, BMC Medicine, 3 (2009).

[33]

S. Moghadas, T. Day, C. Bauch, S. M. Driedger, F. Brauer, A. L. Greer, P. Yan, J. Wu, N. Pizzi and D. N. Fisman, Modelling an influenza pandemic: A guide for the perplexed,, Can. Med. Assoc. J., 181 (2009), 171.

[34]

J. Mossong, N. Hens, M. Nit et al., Social contacts and mixing patterns relevant to the spread of infectious diseases,, PLOS Medicine, 5 (2008). doi: 10.1371/journal.pmed.0050074.

[35]

S. D. Mylius, T. J. Hagenaars, A. K. Lugnér and J. Wallinga, Optimal allocation of pandemic influenza vaccine depends on age, risk and timing,, Vaccine, 26 (2008), 3742. doi: 10.1016/j.vaccine.2008.04.043.

[36]

K. L. Nichol, Efficacy/clinical effectiveness of inactivated influenza virus vaccines in adults 1998,, In: Nicholson KG, (1998), 358.

[37]

H. Nishiura and K. Iwata, A simple mathematical approach to deciding the dosage of vaccine against pandemic H1N1 influenza,, Euro. Surveill, 14 (2009).

[38]

A. M. Presanis, D. De Angelis, A. Hagy, C. Reed, S. Riley, et al., The severity of pandemic H1N1 influenza in the United States, from April to July 2009: A Bayesian analysis,, PLoS Med., 6 (2009). doi: 10.1371/journal.pmed.1000207.

[39]

R. Robinson, "A(H1N1)v Vaccine Products and Production, ACIP July 2009 Meeting,", www.cdc.gov/vaccines/recs/acip/downloads/mtg-slides-jul09-flu/05-Flu-Robinson.pdf., ().

[40]

R. E. Serfling, I. L. Sherman and W. J. Houseworth, Excess pneumonia-influenza mortality by age and sex in three major influenza A2 epidemics, United States, 1957-58, 1960 and 1963,, Am. J. Epidemiol., 86 (1967), 433.

[41]

V. Sypsa, I. Pavlopoulou and A. Hatzakis, "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).

[42]

A. R. Tuite, D. N. Fisman, J. C. Kwong and A. L. Greer, Optimal pandemic influenza vaccine allocation strategies for the Canadian population,, PLOS ONE, 5 (2010). doi: 10.1371/journal.pone.0010520.

[43]

A. R. Tuite, A. L. Greer, M. Whelan, A. L. Winter, B. Lee, P. Yan, J. Wu, S. M. Moghadas, D. Buckeridge, B. Pourbohloul and D. N. Fisman, Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza,, Can. Med. Assoc. J., 182 (2009). doi: 10.1503/cmaj.091807.

[44]

L. Vaillant, G. La Ruche, P. Barboza, for the epidemic intelligence team at InVS, Epidemiology of fatal cases associated with pandemic H1N1 influenza 2009,, Euro., 14 (2009).

[45]

Z. Vajo, J. Wood, L. Kosa, I. Szilvasy, Gy. Paragh, Zs. Pauliny, K. Bartha, I. Visontay, A. Kis and I. Jankovics, A single-dose influenza A (H5N1) vaccine safe and immunogenic in adult and elderly patients - an approach to pandemic vaccine development,, J. Virol., 84 (2009), 1237. doi: 10.1128/JVI.01894-09.

[46]

Y. Yang, J. D. Sugimoto, M. E. Halloran, N. E. Basta, D. L. Chao, L. Matrajt, G. Potter, E. Kenah and I. M. Longini Jr., The transmissibility and control of pandemic influenza A (H1N1) virus,, Science, 326 (2009), 729. doi: 10.1126/science.1177373.

show all references

References:
[1]

M. E. Alexander, C. S. Bowman, Z. Feng, M. Gardam, S. M. Moghadas, G. Röst, J. Wu and P. Yan, Emergence of drug-resistance: Implications for antiviral control of pandemic influenza,, P. Roy. Soc. B - Biol. Sci., 274 (2007), 1675.

[2]

M. E. Alexander, S. M. Moghadas, G. Röst and J. Wu, A delay differential model for pandemic influenza with antiviral treatment,, Bulletin of Mathematical Biology, 70 (2008), 382. doi: 10.1007/s11538-007-9257-2.

[3]

J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, Simple models for containment of a pandemic,, J. R. Soc. Interface, 3 (2006), 453. doi: 10.1098/rsif.2006.0112.

[4]

P. Baccam, C. Beauchemin, C. A. Macken, F. G. Hayden and A. S. Perelson, Kinetics of influenza A virus infection in humans,, J. Virol., 80 (2006), 7590. doi: 10.1128/JVI.01623-05.

[5]

D. Balcan et al., Seasonal transmission potential and activity peaks of the new influenza A(H1N1): A Monte Carlo likelihood analysis based on human mobility,, BMC Medicine, 7 (2009). doi: 10.1186/1741-7015-7-45.

[6]

N. E. Basta, E. M. Halloran, L. Matrajt and I. M. Longini Jr., Estimating influenza vaccine efficacy from challenge and community-based study data,, Am. J. Epidemiol., 168 (2008), 1343. doi: 10.1093/aje/kwn259.

[7]

G. Chowell, C. E. Ammon, N. W. Hengartner and J. M. Hyman, Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: Assessing the effects of hypothetical interventions,, J. Theor. Biol., 241 (2006), 193. doi: 10.1016/j.jtbi.2005.11.026.

[8]

G. Chowell, M. A. Miller and C. Viboud, Seasonal influenza in the United States, France and Australia: Transmission and prospects for control,, Epidemiol. Infect., 136 (2007), 852.

[9]

G. Chowell, C. Viboud, X. Wang, S. Bertozzi and M. Miller, Adaptive vaccination strategies to mitigate pandemic influenza - Mexico as a case study,, PLoS ONE, 4 (2009). doi: 10.1371/journal.pone.0008164.

[10]

CDC, Prevention and control of influenza: Recommendations of the advisory committee on immunization practices (ACIP),, July 17, (2008), 1.

[11]

CDC, "Key Facts About Seasonal Flu Vaccine,", \url{http://www.cdc.gov/Flu/protect/keyfacts.htm}, (2009).

[12]

O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models,, J. R. Soc. Interface, 7 (2010), 873. doi: 10.1098/rsif.2009.0386.

[13]

L. J. Donaldson, P. D. Rutter, B. M. Ellis, F. E. C. Greaves, O. T. Mytton, R. G. Pebody and I. E. Yardley, Mortality from pandemic A/H1N1 2009 influenza in England: Public health surveillance study,, British Medical Journal, 339 (2009).

[14]

European CDC Risk Assessment, "Pandemic H1N1,", Version 6, (2009).

[15]

Eurostat, "Population Statistics 2006 Edition,", Official Publications of the European Communities (Luxembourg), (2006).

[16]

F. Falus and B. Oroszi, "National Chief Medical Officer's Office,", Hungary, (2009).

[17]

N. M. Ferguson, D. A. Cummings, C. Fraser, J. C. Cajka and P. C. Cooley, Strategies for mitigating an influenza pandemic,, Nature, 442 (2006), 448. doi: 10.1038/nature04795.

[18]

D. M. Fleming and A. J. Elliot, Estimating the risk population in relation to influenza vaccination policy,, Vaccine, 24 (2006), 4378. doi: 10.1016/j.vaccine.2006.02.053.

[19]

M. Z. Gojovic, B. Sander, D. Fisman, M. D. Krahn and C. T. Bauch, Modelling mitigation strategies for pandemic (H1N1) 2009,, Can. Med. Assoc. J., 181 (2009). doi: 10.1503/cmaj.091641.

[20]

E. Goldstein, A. Apolloni, B. Lewis, J. C. Miller, M. Macauley, S. Eubank, M. Lipsitch and J. Wallinga, Distribution of vaccine/antivirals and the least spread line in a stratified population,, J. R. Soc. Interface, 7 (2009), 755. doi: 10.1098/rsif.2009.0393.

[21]

M. E. Greenberg, M. H. Lai, G. F. Hartel, C. H. Wichems, C. Gittleson, J. Bennet, G. Dawson, W. Hu, C. Leggio, D. Washington and R. L. Basser, Response to a monovalent influenza a (H1N1) 2009 vaccine,, N. Eng. J. Med., 361 (2009), 2405. doi: 10.1056/NEJMoa0907413.

[22]

K. Hancock, V. Veguilla, X. Lu, et al., Cross-reactive antibody responses to the 2009 pandemic H1N1 influenza virus,, N. Engl. J. Med., 361 (2009), 1945. doi: 10.1056/NEJMoa0906453.

[23]

J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio,, J. R. Soc. Interface, 2 (2005), 281. doi: 10.1098/rsif.2005.0042.

[24]

K. Johansen, A. Nicoll, B. C. Ciancio and P. Kramarz, Pandemic influenza A(A(H1N1)v) 2009 vaccines in the European Union,, Euro Surveill, 14 (2009).

[25]

I. M. Longini Jr and M. E. Halloran, Strategy for distribution of influenza vaccine to high-risk groups and children,, Am. J. Epidemiol., 161 (2005). doi: 10.1093/aje/kwi053.

[26]

L. Matrajt and I. M. Longini, "Optimizing Vaccine Allocation at Different Points in Time During an Epidemic,", UW Biostatistics Working Paper Series 363, (2010).

[27]

J. Medlock and A. P. Galvani, Optimizing influenza vaccine distribution,, Science, 325 (2009), 1705. doi: 10.1126/science.1175570.

[28]

J. Medlock, L. A. Meyers and A. P. Galvani, "Optimizing Allocation for a Delayed Influenza Vaccine Campaign,", PLOS Curr Influenza, (2010).

[29]

S. Merler, M. Ajelli and C. Rizzo, Age-prioritized use of antivirals during an influenza pandemic,, BMC Infectious Diseases, 9 (2009). doi: 10.1186/1471-2334-9-117.

[30]

E. Miller, K. Hoschler, P. Hardelid, E. Stanford, N. Andrews and M. Zambon, Incidence of 2009 pandemic influenza A H1N1 infection in England: a cross-sectional serological study,, The Lancet, 375 (2010), 1100. doi: 10.1016/S0140-6736(09)62126-7.

[31]

S. M. Moghadas, C. S. Bowman, G. Röst and J. Wu, Population-wide emergence of antiviral resistance during pandemic influenza,, PLOS ONE, 3 (2008).

[32]

S. M. Moghadas, C. S. Bowman, G. Röst, D. Fisman and J. Wu, Post-exposure prophylaxis during pandemic outbreaks,, BMC Medicine, 3 (2009).

[33]

S. Moghadas, T. Day, C. Bauch, S. M. Driedger, F. Brauer, A. L. Greer, P. Yan, J. Wu, N. Pizzi and D. N. Fisman, Modelling an influenza pandemic: A guide for the perplexed,, Can. Med. Assoc. J., 181 (2009), 171.

[34]

J. Mossong, N. Hens, M. Nit et al., Social contacts and mixing patterns relevant to the spread of infectious diseases,, PLOS Medicine, 5 (2008). doi: 10.1371/journal.pmed.0050074.

[35]

S. D. Mylius, T. J. Hagenaars, A. K. Lugnér and J. Wallinga, Optimal allocation of pandemic influenza vaccine depends on age, risk and timing,, Vaccine, 26 (2008), 3742. doi: 10.1016/j.vaccine.2008.04.043.

[36]

K. L. Nichol, Efficacy/clinical effectiveness of inactivated influenza virus vaccines in adults 1998,, In: Nicholson KG, (1998), 358.

[37]

H. Nishiura and K. Iwata, A simple mathematical approach to deciding the dosage of vaccine against pandemic H1N1 influenza,, Euro. Surveill, 14 (2009).

[38]

A. M. Presanis, D. De Angelis, A. Hagy, C. Reed, S. Riley, et al., The severity of pandemic H1N1 influenza in the United States, from April to July 2009: A Bayesian analysis,, PLoS Med., 6 (2009). doi: 10.1371/journal.pmed.1000207.

[39]

R. Robinson, "A(H1N1)v Vaccine Products and Production, ACIP July 2009 Meeting,", www.cdc.gov/vaccines/recs/acip/downloads/mtg-slides-jul09-flu/05-Flu-Robinson.pdf., ().

[40]

R. E. Serfling, I. L. Sherman and W. J. Houseworth, Excess pneumonia-influenza mortality by age and sex in three major influenza A2 epidemics, United States, 1957-58, 1960 and 1963,, Am. J. Epidemiol., 86 (1967), 433.

[41]

V. Sypsa, I. Pavlopoulou and A. Hatzakis, "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).

[42]

A. R. Tuite, D. N. Fisman, J. C. Kwong and A. L. Greer, Optimal pandemic influenza vaccine allocation strategies for the Canadian population,, PLOS ONE, 5 (2010). doi: 10.1371/journal.pone.0010520.

[43]

A. R. Tuite, A. L. Greer, M. Whelan, A. L. Winter, B. Lee, P. Yan, J. Wu, S. M. Moghadas, D. Buckeridge, B. Pourbohloul and D. N. Fisman, Estimated epidemiologic parameters and morbidity associated with pandemic H1N1 influenza,, Can. Med. Assoc. J., 182 (2009). doi: 10.1503/cmaj.091807.

[44]

L. Vaillant, G. La Ruche, P. Barboza, for the epidemic intelligence team at InVS, Epidemiology of fatal cases associated with pandemic H1N1 influenza 2009,, Euro., 14 (2009).

[45]

Z. Vajo, J. Wood, L. Kosa, I. Szilvasy, Gy. Paragh, Zs. Pauliny, K. Bartha, I. Visontay, A. Kis and I. Jankovics, A single-dose influenza A (H5N1) vaccine safe and immunogenic in adult and elderly patients - an approach to pandemic vaccine development,, J. Virol., 84 (2009), 1237. doi: 10.1128/JVI.01894-09.

[46]

Y. Yang, J. D. Sugimoto, M. E. Halloran, N. E. Basta, D. L. Chao, L. Matrajt, G. Potter, E. Kenah and I. M. Longini Jr., The transmissibility and control of pandemic influenza A (H1N1) virus,, Science, 326 (2009), 729. doi: 10.1126/science.1177373.

[1]

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

[2]

Rodolfo Acuňa-Soto, Luis Castaňeda-Davila, Gerardo Chowell. A perspective on the 2009 A/H1N1 influenza pandemic in Mexico. Mathematical Biosciences & Engineering, 2011, 8 (1) : 223-238. doi: 10.3934/mbe.2011.8.223

[3]

Raimund Bürger, Gerardo Chowell, Pep Mulet, Luis M. Villada. Modelling the spatial-temporal progression of the 2009 A/H1N1 influenza pandemic in Chile. Mathematical Biosciences & Engineering, 2016, 13 (1) : 43-65. doi: 10.3934/mbe.2016.13.43

[4]

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

[5]

Arni S.R. Srinivasa Rao. Modeling the rapid spread of avian influenza (H5N1) in India. Mathematical Biosciences & Engineering, 2008, 5 (3) : 523-537. doi: 10.3934/mbe.2008.5.523

[6]

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

[7]

Christopher S. Bowman, Julien Arino, S.M. Moghadas. Evaluation of vaccination strategies during pandemic outbreaks. Mathematical Biosciences & Engineering, 2011, 8 (1) : 113-122. doi: 10.3934/mbe.2011.8.113

[8]

Stephen C. Preston, Ralph Saxton. An $H^1$ model for inextensible strings. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 2065-2083. doi: 10.3934/dcds.2013.33.2065

[9]

Sunmi Lee, Romarie Morales, Carlos Castillo-Chavez. A note on the use of influenza vaccination strategies when supply is limited. Mathematical Biosciences & Engineering, 2011, 8 (1) : 171-182. doi: 10.3934/mbe.2011.8.171

[10]

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

[11]

Ruiling Tian, Dequan Yue, Wuyi Yue. Optimal balking strategies in an M/G/1 queueing system with a removable server under N-policy. Journal of Industrial & Management Optimization, 2015, 11 (3) : 715-731. doi: 10.3934/jimo.2015.11.715

[12]

Frédéric Vanhove. A geometric proof of the upper bound on the size of partial spreads in $H(4n+1,$q2$)$. Advances in Mathematics of Communications, 2011, 5 (2) : 157-160. doi: 10.3934/amc.2011.5.157

[13]

Linfang Liu, Xianlong Fu, Yuncheng You. Pullback attractor in $H^{1}$ for nonautonomous stochastic reaction-diffusion equations on $\mathbb{R}^n$. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3629-3651. doi: 10.3934/dcdsb.2017143

[14]

M. De Boeck, P. Vandendriessche. On the dual code of points and generators on the Hermitian variety $\mathcal{H}(2n+1,q^{2})$. Advances in Mathematics of Communications, 2014, 8 (3) : 281-296. doi: 10.3934/amc.2014.8.281

[15]

Alan J. Terry. Pulse vaccination strategies in a metapopulation SIR model. Mathematical Biosciences & Engineering, 2010, 7 (2) : 455-477. doi: 10.3934/mbe.2010.7.455

[16]

Shaojun Lan, Yinghui Tang, Miaomiao Yu. System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1435-1464. doi: 10.3934/jimo.2016.12.1435

[17]

Alexander A. Kovalevsky, Andrey Shishkov. To the memory of Professor Igor V. Skrypnik. Communications on Pure & Applied Analysis, 2013, 12 (4) : i-v. doi: 10.3934/cpaa.2013.12.4i

[18]

Sherry Towers, Katia Vogt Geisse, Chia-Chun Tsai, Qing Han, Zhilan Feng. The impact of school closures on pandemic influenza: Assessing potential repercussions using a seasonal SIR model. Mathematical Biosciences & Engineering, 2012, 9 (2) : 413-430. doi: 10.3934/mbe.2012.9.413

[19]

C.M. Elliott, S. A. Smitheman. Analysis of the TV regularization and $H^{-1}$ fidelity model for decomposing animage into cartoon plus texture. Communications on Pure & Applied Analysis, 2007, 6 (4) : 917-936. doi: 10.3934/cpaa.2007.6.917

[20]

Markus Thäter, Kurt Chudej, Hans Josef Pesch. Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth. Mathematical Biosciences & Engineering, 2018, 15 (2) : 485-505. doi: 10.3934/mbe.2018022

2016 Impact Factor: 1.035

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]