Seasonality and the effectiveness of mass vaccination

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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

Abstract
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Under a Creative Commons license

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), 467-484. doi: 10.1111/j.1461-0248.2005.00879.x.
[2]	R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, United Kingdom, 1991.
[3]	J. L. Aron and I. B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model, J Theor Biol, 110 (1984), 665-679. doi: 10.1016/S0022-5193(84)80150-2.
[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), 1066-1080. doi: 10.4269/ajtmh.13-0321.
[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), vol. 379, Springer-Verlag, Berlin, 2014, 195-209. doi: 10.1007/82_2013_307.
[6]	C. T. Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir, BMC Infect Dis, 1 (2001), p1.
[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), 344-347. doi: 10.1097/EDE.0b013e31819d1092.
[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), 365-382. doi: 10.1007/BF00178324.
[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), e3343. doi: 10.1371/journal.pntd.0003343.
[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), 2775-2782. doi: 10.1098/rspb.2010.0536.
[11]	P. Fine, K. Eames and D. L. Heymann, "Herd immunity'': A rough guide, Clin Infect Dis, 52 (2011), 911-916. doi: 10.1093/cid/cir007.
[12]	D. Fisman, Seasonality of viral infections: Mechanisms and unknowns, Clin Microbiol Infect, 18 (2012), 946-954. doi: 10.1111/j.1469-0691.2012.03968.x.
[13]	D. N. Fisman, Seasonality of infectious diseases, Annu Rev Public Health, 28 (2007), 127-143. doi: 10.1146/annurev.publhealth.28.021406.144128.
[14]	J. P. Fox, Herd immunity and measles, Rev Infect Dis, 5 (1983), 463-466. doi: 10.1093/clinids/5.3.463.
[15]	N. C. Grassly and C. Fraser, Seasonal infectious disease epidemiology, Proc Biol Sci, 273 (2006), 2541-2550. doi: 10.1098/rspb.2006.3604.
[16]	S. B. Halstead, Dengue virus-mosquito interactions, Annu Rev Entomol, 53 (2008), 273-291. doi: 10.1146/annurev.ento.53.103106.093326.
[17]	H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653. doi: 10.1137/S0036144500371907.
[18]	M. J. Keeling and B. T. Grenfell, Understanding the persistence of measles: Reconciling theory, simulation and observation, Proc Biol Sci, 269 (2002), 335-343. doi: 10.1098/rspb.2001.1898.
[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), 700-721.
[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), 7460-7465.
[21]	D. Ludwig, Final size distribution for epidemics, Math Biosci, 23 (1975), 33-46. doi: 10.1016/0025-5564(75)90119-4.
[22]	G. Macdonald, The epidemiology and control of malaria, Oxford University Press, Oxford, United Kingdom, 1957.
[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), 20132438. doi: 10.1098/rspb.2013.2438.
[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), 17-27. doi: 10.1016/j.epidem.2015.06.001.
[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), 1007-1013. doi: 10.1086/511825.
[26]	M. G. Roberts and R. R. Kao, The dynamics of an infectious disease in a population with birth pulses, Math Biosci, 149 (1998), 23-36. doi: 10.1016/S0025-5564(97)10016-5.
[27]	L. A. Rvachev and I. M. Longini Jr., A mathematical model for the global spread of influenza, Math Biosci, 75 (1985), 3-22. doi: 10.1016/0025-5564(85)90064-1.
[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), 295-306.
[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), 1081-1088. doi: 10.3201/eid1407.071412.
[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), 207-215. doi: 10.1016/S0895-7177(00)00040-6.
[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), 29-48. doi: 10.1016/S0025-5564(02)00108-6.
[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), 399-409. doi: 10.1016/j.worlddev.2008.04.002.

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), 467-484. doi: 10.1111/j.1461-0248.2005.00879.x.
[2]	R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, United Kingdom, 1991.
[3]	J. L. Aron and I. B. Schwartz, Seasonality and period-doubling bifurcations in an epidemic model, J Theor Biol, 110 (1984), 665-679. doi: 10.1016/S0022-5193(84)80150-2.
[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), 1066-1080. doi: 10.4269/ajtmh.13-0321.
[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), vol. 379, Springer-Verlag, Berlin, 2014, 195-209. doi: 10.1007/82_2013_307.
[6]	C. T. Codeço, Endemic and epidemic dynamics of cholera: The role of the aquatic reservoir, BMC Infect Dis, 1 (2001), p1.
[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), 344-347. doi: 10.1097/EDE.0b013e31819d1092.
[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), 365-382. doi: 10.1007/BF00178324.
[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), e3343. doi: 10.1371/journal.pntd.0003343.
[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), 2775-2782. doi: 10.1098/rspb.2010.0536.
[11]	P. Fine, K. Eames and D. L. Heymann, "Herd immunity'': A rough guide, Clin Infect Dis, 52 (2011), 911-916. doi: 10.1093/cid/cir007.
[12]	D. Fisman, Seasonality of viral infections: Mechanisms and unknowns, Clin Microbiol Infect, 18 (2012), 946-954. doi: 10.1111/j.1469-0691.2012.03968.x.
[13]	D. N. Fisman, Seasonality of infectious diseases, Annu Rev Public Health, 28 (2007), 127-143. doi: 10.1146/annurev.publhealth.28.021406.144128.
[14]	J. P. Fox, Herd immunity and measles, Rev Infect Dis, 5 (1983), 463-466. doi: 10.1093/clinids/5.3.463.
[15]	N. C. Grassly and C. Fraser, Seasonal infectious disease epidemiology, Proc Biol Sci, 273 (2006), 2541-2550. doi: 10.1098/rspb.2006.3604.
[16]	S. B. Halstead, Dengue virus-mosquito interactions, Annu Rev Entomol, 53 (2008), 273-291. doi: 10.1146/annurev.ento.53.103106.093326.
[17]	H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653. doi: 10.1137/S0036144500371907.
[18]	M. J. Keeling and B. T. Grenfell, Understanding the persistence of measles: Reconciling theory, simulation and observation, Proc Biol Sci, 269 (2002), 335-343. doi: 10.1098/rspb.2001.1898.
[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), 700-721.
[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), 7460-7465.
[21]	D. Ludwig, Final size distribution for epidemics, Math Biosci, 23 (1975), 33-46. doi: 10.1016/0025-5564(75)90119-4.
[22]	G. Macdonald, The epidemiology and control of malaria, Oxford University Press, Oxford, United Kingdom, 1957.
[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), 20132438. doi: 10.1098/rspb.2013.2438.
[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), 17-27. doi: 10.1016/j.epidem.2015.06.001.
[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), 1007-1013. doi: 10.1086/511825.
[26]	M. G. Roberts and R. R. Kao, The dynamics of an infectious disease in a population with birth pulses, Math Biosci, 149 (1998), 23-36. doi: 10.1016/S0025-5564(97)10016-5.
[27]	L. A. Rvachev and I. M. Longini Jr., A mathematical model for the global spread of influenza, Math Biosci, 75 (1985), 3-22. doi: 10.1016/0025-5564(85)90064-1.
[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), 295-306.
[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), 1081-1088. doi: 10.3201/eid1407.071412.
[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), 207-215. doi: 10.1016/S0895-7177(00)00040-6.
[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), 29-48. doi: 10.1016/S0025-5564(02)00108-6.
[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), 399-409. doi: 10.1016/j.worlddev.2008.04.002.

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