American Institute of Mathematical Sciences

Advanced
2016, 13(2): 249-259. doi: 10.3934/mbe.2015001

Seasonality and the effectiveness of mass vaccination

Dennis L. Chao 1, and  Dobromir T. Dimitrov 1,

1. 

Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N, Seattle, WA 98109, United States, United States

Received  March 2015 Revised  September 2015 Published  November 2015

Many infectious diseases have seasonal outbreaks, which may be driven by cyclical environmental conditions (e.g., an annual rainy season) or human behavior (e.g., school calendars or seasonal migration). If a pathogen is only transmissible for a limited period of time each year, then seasonal outbreaks could infect fewer individuals than expected given the pathogen's in-season transmissibility. Influenza, with its short serial interval and long season, probably spreads throughout a population until a substantial fraction of susceptible individuals are infected. Dengue, with a long serial interval and shorter season, may be constrained by its short transmission season rather than the depletion of susceptibles. Using mathematical modeling, we show that mass vaccination is most efficient, in terms of infections prevented per vaccine administered, at high levels of coverage for pathogens that have relatively long epidemic seasons, like influenza, and at low levels of coverage for pathogens with short epidemic seasons, like dengue. Therefore, the length of a pathogen's epidemic season may need to be considered when evaluating the costs and benefits of vaccination programs.
Keywords: epidemics, infectious disease, vaccination, Mathematical model, seasonality..
Mathematics Subject Classification: Primary: 92D30; Secondary: 34C60, 92B0.
Citation: Dennis L. Chao, Dobromir T. Dimitrov. Seasonality and the effectiveness of mass vaccination. Mathematical Biosciences & Engineering, 2016, 13 (2) : 249-259. doi: 10.3934/mbe.2015001
References:
[1]

S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual and P. Rohani, Seasonality and the dynamics of infectious diseases,, Ecol Lett, 9 (2006), 467.  doi: 10.1111/j.1461-0248.2005.00879.x.  Google Scholar

[2]

R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control,, Oxford University Press, (1991).   Google Scholar

[3]

J. L. Aron and I. B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model,, J Theor Biol, 110 (1984), 665.  doi: 10.1016/S0022-5193(84)80150-2.  Google Scholar

[4]

K. M. Campbell, C. D. Lin, S. Iamsirithaworn and T. W. Scott, The complex relationship between weather and dengue virus transmission in Thailand,, Am J Trop Med Hyg, 89 (2013), 1066.  doi: 10.4269/ajtmh.13-0321.  Google Scholar

[5]

D. L. Chao, I. M. Longini Jr. and J. G. Morris Jr., Modeling cholera outbreaks,, in Current Topics in Microbiology and Immunology: Cholera Outbreaks (eds. G. B. Nair and Y. Takeda), (2014), 195.  doi: 10.1007/82_2013_307.  Google Scholar

[6]

C. T. Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir,, BMC Infect Dis, 1 (2001).   Google Scholar

[7]

B. J. Cowling, V. J. Fang, S. Riley, J. S. Malik Peiris and G. M. Leung, Estimation of the serial interval of influenza,, Epidemiology, 20 (2009), 344.  doi: 10.1097/EDE.0b013e31819d1092.  Google Scholar

[8]

O. Diekmann, J. A. Heesterbeek and J. A. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations,, J Math Biol, 28 (1990), 365.  doi: 10.1007/BF00178324.  Google Scholar

[9]

D. T. Dimitrov, C. Troeger, M. E. Halloran, I. M. Longini and D. L. Chao, Comparative effectiveness of different strategies of oral cholera vaccination in {Bangladesh}: A modeling study,, PLoS Negl Trop Dis, 8 (2014).  doi: 10.1371/journal.pntd.0003343.  Google Scholar

[10]

M. J. Ferrari, A. Djibo, R. F. Grais, N. Bharti, B. T. Grenfell and O. N. Bjornstad, Rural-urban gradient in seasonal forcing of measles transmission in Niger,, Proc Biol Sci, 277 (2010), 2775.  doi: 10.1098/rspb.2010.0536.  Google Scholar

[11]

P. Fine, K. Eames and D. L. Heymann, "Herd immunity'': A rough guide,, Clin Infect Dis, 52 (2011), 911.  doi: 10.1093/cid/cir007.  Google Scholar

[12]

D. Fisman, Seasonality of viral infections: Mechanisms and unknowns,, Clin Microbiol Infect, 18 (2012), 946.  doi: 10.1111/j.1469-0691.2012.03968.x.  Google Scholar

[13]

D. N. Fisman, Seasonality of infectious diseases,, Annu Rev Public Health, 28 (2007), 127.  doi: 10.1146/annurev.publhealth.28.021406.144128.  Google Scholar

[14]

J. P. Fox, Herd immunity and measles,, Rev Infect Dis, 5 (1983), 463.  doi: 10.1093/clinids/5.3.463.  Google Scholar

[15]

N. C. Grassly and C. Fraser, Seasonal infectious disease epidemiology,, Proc Biol Sci, 273 (2006), 2541.  doi: 10.1098/rspb.2006.3604.  Google Scholar

[16]

S. B. Halstead, Dengue virus-mosquito interactions,, Annu Rev Entomol, 53 (2008), 273.  doi: 10.1146/annurev.ento.53.103106.093326.  Google Scholar

[17]

H. W. Hethcote, The mathematics of infectious diseases,, SIAM Review, 42 (2000), 599.  doi: 10.1137/S0036144500371907.  Google Scholar

[18]

M. J. Keeling and B. T. Grenfell, Understanding the persistence of measles: Reconciling theory, simulation and observation,, Proc Biol Sci, 269 (2002), 335.  doi: 10.1098/rspb.2001.1898.  Google Scholar

[19]

W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics,, Proceedings of the Royal Society of London. Series A, 115 (1927), 700.   Google Scholar

[20]

L. Lambrechts, K. P. Paaijmans, T. Fansiri, L. B. Carrington, L. D. Kramer, M. B. Thomas and T. W. Scott, Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti,, Proc Natl Acad Sci U S A, 108 (2011), 7460.   Google Scholar

[21]

D. Ludwig, Final size distribution for epidemics,, Math Biosci, 23 (1975), 33.  doi: 10.1016/0025-5564(75)90119-4.  Google Scholar

[22]

G. Macdonald, The epidemiology and control of malaria,, Oxford University Press, (1957).   Google Scholar

[23]

M. Martinez-Bakker, K. M. Bakker, A. A. King and P. Rohani, Human birth seasonality: Latitudinal gradient and interplay with childhood disease dynamics,, Proc Biol Sci, 281 (2014).  doi: 10.1098/rspb.2013.2438.  Google Scholar

[24]

L. Matrajt, T. Britton, M. E. Halloran and I. M. Longini Jr., One versus two doses: What is the best use of vaccine in an influenza pandemic?,, Epidemics, 13 (2015), 17.  doi: 10.1016/j.epidem.2015.06.001.  Google Scholar

[25]

H. Nishiura and S. B. Halstead, Natural history of dengue virus (DENV)-1 and DENV-4 infections: reanalysis of classic studies,, J Infect Dis, 195 (2007), 1007.  doi: 10.1086/511825.  Google Scholar

[26]

M. G. Roberts and R. R. Kao, The dynamics of an infectious disease in a population with birth pulses,, Math Biosci, 149 (1998), 23.  doi: 10.1016/S0025-5564(97)10016-5.  Google Scholar

[27]

L. A. Rvachev and I. M. Longini Jr., A mathematical model for the global spread of influenza,, Math Biosci, 75 (1985), 3.  doi: 10.1016/0025-5564(85)90064-1.  Google Scholar

[28]

D. L. Schanzer, J. M. Langley, T. Dummer, C. Viboud and T. W. S. Tam, A composite epidemic curve for seasonal influenza in Canada with an international comparison,, Influenza Other Respir Viruses, 4 (2010), 295.   Google Scholar

[29]

E. Schwartz, L. H. Weld, A. Wilder-Smith, F. von Sonnenburg, J. S. Keystone, K. C. Kain, J. Torresi and D. O. Freedman, Seasonality, annual trends, and characteristics of dengue among ill returned travelers, 1997-2006,, Emerg Infect Dis, 14 (2008), 1081.  doi: 10.3201/eid1407.071412.  Google Scholar

[30]

L. Stone, B. Shulgin and Z. Agur, Theoretical examination of the pulse vaccination policy in the SIR epidemic model,, Math and Comp Mod, 31 (2000), 207.  doi: 10.1016/S0895-7177(00)00040-6.  Google Scholar

[31]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math Biosci, 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[32]

D. Whittington, D. Sur, J. Cook, S. Chatterjee, B. Maskery, M. Lahiri, C. Poulos, S. Boral, A. Nyamete, J. Deen, L. Ochiai and S. K. Bhattacharya, Rethinking cholera and typhoid vaccination policies for the poor: Private demand in Kolkata, India,, World Development, 37 (2009), 399.  doi: 10.1016/j.worlddev.2008.04.002.  Google Scholar

show all references

References:
[1]

S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual and P. Rohani, Seasonality and the dynamics of infectious diseases,, Ecol Lett, 9 (2006), 467.  doi: 10.1111/j.1461-0248.2005.00879.x.  Google Scholar

[2]

R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control,, Oxford University Press, (1991).   Google Scholar

[3]

J. L. Aron and I. B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model,, J Theor Biol, 110 (1984), 665.  doi: 10.1016/S0022-5193(84)80150-2.  Google Scholar

[4]

K. M. Campbell, C. D. Lin, S. Iamsirithaworn and T. W. Scott, The complex relationship between weather and dengue virus transmission in Thailand,, Am J Trop Med Hyg, 89 (2013), 1066.  doi: 10.4269/ajtmh.13-0321.  Google Scholar

[5]

D. L. Chao, I. M. Longini Jr. and J. G. Morris Jr., Modeling cholera outbreaks,, in Current Topics in Microbiology and Immunology: Cholera Outbreaks (eds. G. B. Nair and Y. Takeda), (2014), 195.  doi: 10.1007/82_2013_307.  Google Scholar

[6]

C. T. Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir,, BMC Infect Dis, 1 (2001).   Google Scholar

[7]

B. J. Cowling, V. J. Fang, S. Riley, J. S. Malik Peiris and G. M. Leung, Estimation of the serial interval of influenza,, Epidemiology, 20 (2009), 344.  doi: 10.1097/EDE.0b013e31819d1092.  Google Scholar

[8]

O. Diekmann, J. A. Heesterbeek and J. A. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations,, J Math Biol, 28 (1990), 365.  doi: 10.1007/BF00178324.  Google Scholar

[9]

D. T. Dimitrov, C. Troeger, M. E. Halloran, I. M. Longini and D. L. Chao, Comparative effectiveness of different strategies of oral cholera vaccination in {Bangladesh}: A modeling study,, PLoS Negl Trop Dis, 8 (2014).  doi: 10.1371/journal.pntd.0003343.  Google Scholar

[10]

M. J. Ferrari, A. Djibo, R. F. Grais, N. Bharti, B. T. Grenfell and O. N. Bjornstad, Rural-urban gradient in seasonal forcing of measles transmission in Niger,, Proc Biol Sci, 277 (2010), 2775.  doi: 10.1098/rspb.2010.0536.  Google Scholar

[11]

P. Fine, K. Eames and D. L. Heymann, "Herd immunity'': A rough guide,, Clin Infect Dis, 52 (2011), 911.  doi: 10.1093/cid/cir007.  Google Scholar

[12]

D. Fisman, Seasonality of viral infections: Mechanisms and unknowns,, Clin Microbiol Infect, 18 (2012), 946.  doi: 10.1111/j.1469-0691.2012.03968.x.  Google Scholar

[13]

D. N. Fisman, Seasonality of infectious diseases,, Annu Rev Public Health, 28 (2007), 127.  doi: 10.1146/annurev.publhealth.28.021406.144128.  Google Scholar

[14]

J. P. Fox, Herd immunity and measles,, Rev Infect Dis, 5 (1983), 463.  doi: 10.1093/clinids/5.3.463.  Google Scholar

[15]

N. C. Grassly and C. Fraser, Seasonal infectious disease epidemiology,, Proc Biol Sci, 273 (2006), 2541.  doi: 10.1098/rspb.2006.3604.  Google Scholar

[16]

S. B. Halstead, Dengue virus-mosquito interactions,, Annu Rev Entomol, 53 (2008), 273.  doi: 10.1146/annurev.ento.53.103106.093326.  Google Scholar

[17]

H. W. Hethcote, The mathematics of infectious diseases,, SIAM Review, 42 (2000), 599.  doi: 10.1137/S0036144500371907.  Google Scholar

[18]

M. J. Keeling and B. T. Grenfell, Understanding the persistence of measles: Reconciling theory, simulation and observation,, Proc Biol Sci, 269 (2002), 335.  doi: 10.1098/rspb.2001.1898.  Google Scholar

[19]

W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics,, Proceedings of the Royal Society of London. Series A, 115 (1927), 700.   Google Scholar

[20]

L. Lambrechts, K. P. Paaijmans, T. Fansiri, L. B. Carrington, L. D. Kramer, M. B. Thomas and T. W. Scott, Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti,, Proc Natl Acad Sci U S A, 108 (2011), 7460.   Google Scholar

[21]

D. Ludwig, Final size distribution for epidemics,, Math Biosci, 23 (1975), 33.  doi: 10.1016/0025-5564(75)90119-4.  Google Scholar

[22]

G. Macdonald, The epidemiology and control of malaria,, Oxford University Press, (1957).   Google Scholar

[23]

M. Martinez-Bakker, K. M. Bakker, A. A. King and P. Rohani, Human birth seasonality: Latitudinal gradient and interplay with childhood disease dynamics,, Proc Biol Sci, 281 (2014).  doi: 10.1098/rspb.2013.2438.  Google Scholar

[24]

L. Matrajt, T. Britton, M. E. Halloran and I. M. Longini Jr., One versus two doses: What is the best use of vaccine in an influenza pandemic?,, Epidemics, 13 (2015), 17.  doi: 10.1016/j.epidem.2015.06.001.  Google Scholar

[25]

H. Nishiura and S. B. Halstead, Natural history of dengue virus (DENV)-1 and DENV-4 infections: reanalysis of classic studies,, J Infect Dis, 195 (2007), 1007.  doi: 10.1086/511825.  Google Scholar

[26]

M. G. Roberts and R. R. Kao, The dynamics of an infectious disease in a population with birth pulses,, Math Biosci, 149 (1998), 23.  doi: 10.1016/S0025-5564(97)10016-5.  Google Scholar

[27]

L. A. Rvachev and I. M. Longini Jr., A mathematical model for the global spread of influenza,, Math Biosci, 75 (1985), 3.  doi: 10.1016/0025-5564(85)90064-1.  Google Scholar

[28]

D. L. Schanzer, J. M. Langley, T. Dummer, C. Viboud and T. W. S. Tam, A composite epidemic curve for seasonal influenza in Canada with an international comparison,, Influenza Other Respir Viruses, 4 (2010), 295.   Google Scholar

[29]

E. Schwartz, L. H. Weld, A. Wilder-Smith, F. von Sonnenburg, J. S. Keystone, K. C. Kain, J. Torresi and D. O. Freedman, Seasonality, annual trends, and characteristics of dengue among ill returned travelers, 1997-2006,, Emerg Infect Dis, 14 (2008), 1081.  doi: 10.3201/eid1407.071412.  Google Scholar

[30]

L. Stone, B. Shulgin and Z. Agur, Theoretical examination of the pulse vaccination policy in the SIR epidemic model,, Math and Comp Mod, 31 (2000), 207.  doi: 10.1016/S0895-7177(00)00040-6.  Google Scholar

[31]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math Biosci, 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[32]

D. Whittington, D. Sur, J. Cook, S. Chatterjee, B. Maskery, M. Lahiri, C. Poulos, S. Boral, A. Nyamete, J. Deen, L. Ochiai and S. K. Bhattacharya, Rethinking cholera and typhoid vaccination policies for the poor: Private demand in Kolkata, India,, World Development, 37 (2009), 399.  doi: 10.1016/j.worlddev.2008.04.002.  Google Scholar

[1]

Bruno Buonomo, Giuseppe Carbone, Alberto d'Onofrio. Effect of seasonality on the dynamics of an imitation-based vaccination model with public health intervention. Mathematical Biosciences & Engineering, 2018, 15 (1) : 299-321. doi: 10.3934/mbe.2018013
[2]

Martin Luther Mann Manyombe, Joseph Mbang, Jean Lubuma, Berge Tsanou. Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers. Mathematical Biosciences & Engineering, 2016, 13 (4) : 813-840. doi: 10.3934/mbe.2016019
[3]

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
[4]

C. Connell McCluskey. Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 381-400. doi: 10.3934/mbe.2015008
[5]

Min Zhu, Xiaofei Guo, Zhigui Lin. The risk index for an SIR epidemic model and spatial spreading of the infectious disease. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1565-1583. doi: 10.3934/mbe.2017081
[6]

W. E. Fitzgibbon, J. J. Morgan. Analysis of a reaction diffusion model for a reservoir supported spread of infectious disease. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 6239-6259. doi: 10.3934/dcdsb.2019137
[7]

Ionel S. Ciuperca, Matthieu Dumont, Abdelkader Lakmeche, Pauline Mazzocco, Laurent Pujo-Menjouet, Human Rezaei, Léon M. Tine. Alzheimer's disease and prion: An in vitro mathematical model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5225-5260. doi: 10.3934/dcdsb.2019057
[8]

Xinli Hu. Threshold dynamics for a Tuberculosis model with seasonality. Mathematical Biosciences & Engineering, 2012, 9 (1) : 111-122. doi: 10.3934/mbe.2012.9.111
[9]

Roberto A. Saenz, Herbert W. Hethcote. Competing species models with an infectious disease. Mathematical Biosciences & Engineering, 2006, 3 (1) : 219-235. doi: 10.3934/mbe.2006.3.219
[10]

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
[11]

Tinevimbo Shiri, Winston Garira, Senelani D. Musekwa. A two-strain HIV-1 mathematical model to assess the effects of chemotherapy on disease parameters. Mathematical Biosciences & Engineering, 2005, 2 (4) : 811-832. doi: 10.3934/mbe.2005.2.811
[12]

Horst R. Thieme. Distributed susceptibility: A challenge to persistence theory in infectious disease models. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 865-882. doi: 10.3934/dcdsb.2009.12.865
[13]

Cruz Vargas-De-León, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1019-1033. doi: 10.3934/mbe.2017053
[14]

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
[15]

Karyn L. Sutton, H.T. Banks, Carlos Castillo-Chávez. Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia. Mathematical Biosciences & Engineering, 2008, 5 (1) : 175-204. doi: 10.3934/mbe.2008.5.175
[16]

Shangbin Cui, Meng Bai. Mathematical analysis of population migration and its effects to spread of epidemics. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 2819-2858. doi: 10.3934/dcdsb.2015.20.2819
[17]

Islam A. Moneim, David Greenhalgh. Use Of A Periodic Vaccination Strategy To Control The Spread Of Epidemics With Seasonally Varying Contact Rate. Mathematical Biosciences & Engineering, 2005, 2 (3) : 591-611. doi: 10.3934/mbe.2005.2.591
[18]

Qingkai Kong, Zhipeng Qiu, Zi Sang, Yun Zou. Optimal control of a vector-host epidemics model. Mathematical Control & Related Fields, 2011, 1 (4) : 493-508. doi: 10.3934/mcrf.2011.1.493
[19]

Bruno Buonomo, Eleonora Messina. Impact of vaccine arrival on the optimal control of a newly emerging infectious disease: A theoretical study. Mathematical Biosciences & Engineering, 2012, 9 (3) : 539-552. doi: 10.3934/mbe.2012.9.539
[20]

Hiroshi Nishiura. Time variations in the generation time of an infectious disease: Implications for sampling to appropriately quantify transmission potential. Mathematical Biosciences & Engineering, 2010, 7 (4) : 851-869. doi: 10.3934/mbe.2010.7.851

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (21)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences