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Evaluating vaccination effectiveness of group-specific fractional-dose strategies
1. | School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, China |
2. | Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, China |
3. | School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China |
In this paper, we formulate a multi-group SIR epidemic model with the consideration of proportionate mixing patterns between groups and group-specific fractional-dose vaccination to evaluate the effects of fractionated dosing strategies on disease control and prevention in a heterogeneously mixing population. The basic reproduction number $ \mathscr{R}_0 $, the final size of the epidemic, and the infection attack rate are used as three measures of population-level implications of fractionated dosing programs. Theoretically, we identify the basic reproduction number, $ \mathscr{R}_0 $, establish the existence and uniqueness of the final size and the final size relation with $ \mathscr{R}_0 $, and obtain explicit calculation expressions of the infection attack rate for each group and the whole population. Furthermore, the simulation results suggest that dose fractionation policies take positive effects in lowering the $ \mathscr{R}_0 $, decreasing the final size and reducing the infection attack rate only when the fractional-dose influenza vaccine efficacy is high enough rather than just similar to standard-dose. We find evidences that fractional-dose vaccination in response to influenza vaccine shortages take negative community-level effects. Our results indicate that the role of fractional dose vaccines should not be overestimated even though fractional dosing strategies could extend the vaccine coverage.
References:
[1] |
V. Andreasen,
The final size of an epidemic and its relation to the basic reproduction number, Bull. Math. Biol., 73 (2011), 2305-2321.
doi: 10.1007/s11538-010-9623-3. |
[2] |
A. C. Campi-Azevedo, P. de Almeida Estevam, J. G. Coelho-Dos-Reis and et al., Subdoses of 17DD yellow fever vaccine elicit equivalent virological/immunological kinetics timeline, BMC Infect. Dis., 14 (2014), 1-12.
doi: 10.1186/1471-2334-14-391. |
[3] |
Z. Chen, K. Liu, X. Liu and Y. Lou, Modelling epidemic with fractional-dose vaccination in response to limited vaccine supply, J. Theor. Biol., 468 (2020), 110085, 10pp.
doi: 10.1016/j.jtbi.2019.110085. |
[4] |
L. Chow, M. Fan and Z. Feng,
Dynamics of a multigroup epidemiological model with group-targeted vaccination strategies, J. Theor. Biol., 291 (2011), 56-64.
doi: 10.1016/j.jtbi.2011.09.020. |
[5] |
J. Cui, Y. Zhang and Z. Feng,
Influence of non-homogeneous mixing on final epidemic size in a meta-population model, J. Biol. Dyn., 13 (2019), 31-46.
doi: 10.1080/17513758.2018.1484186. |
[6] |
D. Ding and X. Ding,
Global stability of multi-group vaccination epidemic models with delays, Nonlinear Anal. Real World Appl., 12 (2011), 1991-1997.
doi: 10.1016/j.nonrwa.2010.12.015. |
[7] |
S. Gandon, M. J. Mackinnon, S. Nee and A. F. Read,
Imperfect vaccines and the evolution of pathogen virulence, Nature, 414 (2001), 751-755.
|
[8] |
P. Guerin, L. Næss, C. Fogg and et al., Immunogenicity of fractional doses of tetravalent A/C/Y/W135 meningococcal polysaccharide vaccine: Results from a randomized non-inferiority controlled trial in uganda, PLoS Negl. Trop. Dis., 2 (2008), e342.
doi: 10.1371/journal.pntd.0000342. |
[9] |
P. Haldar, P. Agrawal, P. Bhatnagar and et al., Fractional-dose inactivated poliovirus vaccine, India, Bull. World Health Organ., 97 (2019), 328-334.
doi: 10.2471/BLT.18.218370. |
[10] |
J. K. Hale, Ordinary Differential Equations, New York: Robert E. Krieger Publishing Company, Inc., Huntington, 1980. |
[11] |
M. E. Halloran, C. J. Struchiner and I. M. Longini Jr,
Study designs for evaluating different efficacy and effectiveness aspects of vaccines, Am. J. Epidemiol., 146 (1997), 789-803.
doi: 10.1093/oxfordjournals.aje.a009196. |
[12] |
I. F. Hung, Y. Levin, K. K. To and et al., Dose sparing intradermal trivalent influenza (2010/2011) vaccination overcomes reduced immunogenicity of the 2009 H1N1 strain, Vaccine, 30 (2012), 6427-6435.
doi: 10.1016/j.vaccine.2012.08.014. |
[13] |
E. Jonkera, M. van Ravenhorstbs, G. Berbersb and L. Visser,
Safety and immunogenicity of fractional dose intradermal injection of two quadrivalent conjugated meningococcal vaccines, Vaccine, 36 (2018), 3727-3732.
doi: 10.1016/j.vaccine.2018.05.064. |
[14] |
U. Joseph, M. Linster, Y. Suzuki and et al., Adaptation of pandemic H2N2 influenza a viruses in humans, J. Virol., 89 (2015), 2442-2447.
doi: 10.1128/JVI.02590-14. |
[15] |
W. O. Kermack and A. G. McKendrick,
A contribution to the mathematical theory of epidemics, Proc. Math. Phys. Eng. Sci., 15 (1927), 700-721.
|
[16] |
V. Künzi, J. M. Klap, M. K. Seiberling and et al., Immunogenicity and safety of low dose virosomal adjuvanted influenza vaccine administered intradermally compared to intramuscular full dose administration, Vaccine, 27 (2009), 3561-3567. |
[17] |
S. Lee, R. Morales and C. Castillo-Chavez,
A note on the use of influenza vaccination strategies when supply is limited, Math. Biosci. Eng., 8 (2011), 171-182.
doi: 10.3934/mbe.2011.8.171. |
[18] |
I. M. Longini, M. E. Halloran, A. Nizam and Y. Yang,
Containing pandemic influenza with antiviral agents, Am. J. Epidemiol., 159 (2004), 623-633.
doi: 10.1093/aje/kwh092. |
[19] |
J. Ma and D. J. D. Earn,
Generality of the final size formula for an epidemic of a newly invading infectious disease, Bull. Math. Biol., 68 (2006), 679-702.
doi: 10.1007/s11538-005-9047-7. |
[20] |
P. Magal, O. Seydi and G. Webb,
Final size of an epidemic for a two-group SIR model, SIAM J. Appl. Math., 76 (2016), 2042-2059.
doi: 10.1137/16M1065392. |
[21] |
P. Magal, O. Seydi and G. Webb,
Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission, Math. Biosci., 301 (2018), 59-67.
doi: 10.1016/j.mbs.2018.03.020. |
[22] |
R. M. Martins, M. D. Maia, R. H. Farias, L. A. Camacho, M. S. Freire, R. Galler and et al., 7dd yellow fever vaccine: A double blind, randomized clinical trial of immunogenicity and safety on a dose-response study, Hum. Vaccin. Immunother., 9 (2013), 879-888. |
[23] |
A. J. Mohammed, S. Alawaidy, S. Bawikar and et al., Fractional doses of inactivated poliovirus vaccine in Oman, N. Engl. J. Med., 362 (2010), 2351-2359.
doi: 10.1056/NEJMoa0909383. |
[24] |
J. Mossong, N. Hens, M. Jit and et al., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med., 5 (2008), e74.
doi: 10.1371/journal.pmed.0050074. |
[25] |
W. Qin, S. Tang and R. A. Cheke,
Nonlinear pulse vaccination in an SIR epidemic model with resource limitation, Abstr. Appl. Anal., 2013 (2013), 1-13.
doi: 10.1155/2013/670263. |
[26] |
L. Rass and J. Radclie, Spatial Deterministic Epidemics, Rhode Island: Mathematical Surveys and Monographs, 2003.
doi: 10.1090/surv/102. |
[27] |
Z. B. Reneer and T. M. Ross,
H2 influenza viruses: Designing vaccines against future H2 pandemics, Biochem. Soc. Trans., 47 (2019), 251-264.
doi: 10.1042/BST20180602. |
[28] |
S. Resik, A. Tejeda, R. W. Sutter and et al., Priming after a fractional dose of inactivated poliovirus vaccine, N. Engl. J. Med., 368 (2013), 416-424.
doi: 10.1056/NEJMoa1202541. |
[29] |
S. Riley, J. T. Wu and G. M. Leung, Optimizing the dose of pre-pandemic influenza vaccines to reduce the infection attack rate, PLoS Med., 4 (2007), e218.
doi: 10.1371/journal.pmed.0040218. |
[30] |
A. H. Roukens, K. van Halem, A. W. de Visser and L. G. Visser,
Long-term protection after fractional-dose yellow fever vaccination: Follow-up study of a randomized, controlled, noninferiority trial, Ann. Intern. Med., 169 (2018), 1761-1765.
doi: 10.7326/M18-1529. |
[31] |
A. H. Roukens, A. C. Vossen, P. J. Bredenbeek, J. T. van Dissel and L. G. Visser, Intradermally administered yellow fever vaccine at reduced dose induces a protective immune response: A randomized controlled non-inferiority trial, PLoS One, 3 (2008), e1993.
doi: 10.1371/journal.pone.0001993. |
[32] |
H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, New York, 1995.
doi: 10.1017/CBO9780511530043.![]() ![]() ![]() |
[33] |
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. |
[34] |
J. T. Wu, C. M. Peak, G. M. Leung and M. Lipsitch,
Fractional dosing of yellow fever vaccine of extend supply: A modelling study, Lancet, 388 (2016), 2904-2911.
doi: 10.1016/S0140-6736(16)31838-4. |
[35] |
K. N. Wyatt, G. J. Ryan and K. A. Sheerin,
Reduced-dose influenza vaccine, Ann. Pharmacother, 40 (2006), 1635-1639.
doi: 10.1345/aph.1G645. |
[36] |
T. Yu, D. Cao and S. Liu,
Epidemic model with group mixing: Stability and optimal control based on limited vaccination resources, Commun. Nonlinear Sci. Numer. Simul., 61 (2018), 54-70.
doi: 10.1016/j.cnsns.2018.01.011. |
show all references
References:
[1] |
V. Andreasen,
The final size of an epidemic and its relation to the basic reproduction number, Bull. Math. Biol., 73 (2011), 2305-2321.
doi: 10.1007/s11538-010-9623-3. |
[2] |
A. C. Campi-Azevedo, P. de Almeida Estevam, J. G. Coelho-Dos-Reis and et al., Subdoses of 17DD yellow fever vaccine elicit equivalent virological/immunological kinetics timeline, BMC Infect. Dis., 14 (2014), 1-12.
doi: 10.1186/1471-2334-14-391. |
[3] |
Z. Chen, K. Liu, X. Liu and Y. Lou, Modelling epidemic with fractional-dose vaccination in response to limited vaccine supply, J. Theor. Biol., 468 (2020), 110085, 10pp.
doi: 10.1016/j.jtbi.2019.110085. |
[4] |
L. Chow, M. Fan and Z. Feng,
Dynamics of a multigroup epidemiological model with group-targeted vaccination strategies, J. Theor. Biol., 291 (2011), 56-64.
doi: 10.1016/j.jtbi.2011.09.020. |
[5] |
J. Cui, Y. Zhang and Z. Feng,
Influence of non-homogeneous mixing on final epidemic size in a meta-population model, J. Biol. Dyn., 13 (2019), 31-46.
doi: 10.1080/17513758.2018.1484186. |
[6] |
D. Ding and X. Ding,
Global stability of multi-group vaccination epidemic models with delays, Nonlinear Anal. Real World Appl., 12 (2011), 1991-1997.
doi: 10.1016/j.nonrwa.2010.12.015. |
[7] |
S. Gandon, M. J. Mackinnon, S. Nee and A. F. Read,
Imperfect vaccines and the evolution of pathogen virulence, Nature, 414 (2001), 751-755.
|
[8] |
P. Guerin, L. Næss, C. Fogg and et al., Immunogenicity of fractional doses of tetravalent A/C/Y/W135 meningococcal polysaccharide vaccine: Results from a randomized non-inferiority controlled trial in uganda, PLoS Negl. Trop. Dis., 2 (2008), e342.
doi: 10.1371/journal.pntd.0000342. |
[9] |
P. Haldar, P. Agrawal, P. Bhatnagar and et al., Fractional-dose inactivated poliovirus vaccine, India, Bull. World Health Organ., 97 (2019), 328-334.
doi: 10.2471/BLT.18.218370. |
[10] |
J. K. Hale, Ordinary Differential Equations, New York: Robert E. Krieger Publishing Company, Inc., Huntington, 1980. |
[11] |
M. E. Halloran, C. J. Struchiner and I. M. Longini Jr,
Study designs for evaluating different efficacy and effectiveness aspects of vaccines, Am. J. Epidemiol., 146 (1997), 789-803.
doi: 10.1093/oxfordjournals.aje.a009196. |
[12] |
I. F. Hung, Y. Levin, K. K. To and et al., Dose sparing intradermal trivalent influenza (2010/2011) vaccination overcomes reduced immunogenicity of the 2009 H1N1 strain, Vaccine, 30 (2012), 6427-6435.
doi: 10.1016/j.vaccine.2012.08.014. |
[13] |
E. Jonkera, M. van Ravenhorstbs, G. Berbersb and L. Visser,
Safety and immunogenicity of fractional dose intradermal injection of two quadrivalent conjugated meningococcal vaccines, Vaccine, 36 (2018), 3727-3732.
doi: 10.1016/j.vaccine.2018.05.064. |
[14] |
U. Joseph, M. Linster, Y. Suzuki and et al., Adaptation of pandemic H2N2 influenza a viruses in humans, J. Virol., 89 (2015), 2442-2447.
doi: 10.1128/JVI.02590-14. |
[15] |
W. O. Kermack and A. G. McKendrick,
A contribution to the mathematical theory of epidemics, Proc. Math. Phys. Eng. Sci., 15 (1927), 700-721.
|
[16] |
V. Künzi, J. M. Klap, M. K. Seiberling and et al., Immunogenicity and safety of low dose virosomal adjuvanted influenza vaccine administered intradermally compared to intramuscular full dose administration, Vaccine, 27 (2009), 3561-3567. |
[17] |
S. Lee, R. Morales and C. Castillo-Chavez,
A note on the use of influenza vaccination strategies when supply is limited, Math. Biosci. Eng., 8 (2011), 171-182.
doi: 10.3934/mbe.2011.8.171. |
[18] |
I. M. Longini, M. E. Halloran, A. Nizam and Y. Yang,
Containing pandemic influenza with antiviral agents, Am. J. Epidemiol., 159 (2004), 623-633.
doi: 10.1093/aje/kwh092. |
[19] |
J. Ma and D. J. D. Earn,
Generality of the final size formula for an epidemic of a newly invading infectious disease, Bull. Math. Biol., 68 (2006), 679-702.
doi: 10.1007/s11538-005-9047-7. |
[20] |
P. Magal, O. Seydi and G. Webb,
Final size of an epidemic for a two-group SIR model, SIAM J. Appl. Math., 76 (2016), 2042-2059.
doi: 10.1137/16M1065392. |
[21] |
P. Magal, O. Seydi and G. Webb,
Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission, Math. Biosci., 301 (2018), 59-67.
doi: 10.1016/j.mbs.2018.03.020. |
[22] |
R. M. Martins, M. D. Maia, R. H. Farias, L. A. Camacho, M. S. Freire, R. Galler and et al., 7dd yellow fever vaccine: A double blind, randomized clinical trial of immunogenicity and safety on a dose-response study, Hum. Vaccin. Immunother., 9 (2013), 879-888. |
[23] |
A. J. Mohammed, S. Alawaidy, S. Bawikar and et al., Fractional doses of inactivated poliovirus vaccine in Oman, N. Engl. J. Med., 362 (2010), 2351-2359.
doi: 10.1056/NEJMoa0909383. |
[24] |
J. Mossong, N. Hens, M. Jit and et al., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med., 5 (2008), e74.
doi: 10.1371/journal.pmed.0050074. |
[25] |
W. Qin, S. Tang and R. A. Cheke,
Nonlinear pulse vaccination in an SIR epidemic model with resource limitation, Abstr. Appl. Anal., 2013 (2013), 1-13.
doi: 10.1155/2013/670263. |
[26] |
L. Rass and J. Radclie, Spatial Deterministic Epidemics, Rhode Island: Mathematical Surveys and Monographs, 2003.
doi: 10.1090/surv/102. |
[27] |
Z. B. Reneer and T. M. Ross,
H2 influenza viruses: Designing vaccines against future H2 pandemics, Biochem. Soc. Trans., 47 (2019), 251-264.
doi: 10.1042/BST20180602. |
[28] |
S. Resik, A. Tejeda, R. W. Sutter and et al., Priming after a fractional dose of inactivated poliovirus vaccine, N. Engl. J. Med., 368 (2013), 416-424.
doi: 10.1056/NEJMoa1202541. |
[29] |
S. Riley, J. T. Wu and G. M. Leung, Optimizing the dose of pre-pandemic influenza vaccines to reduce the infection attack rate, PLoS Med., 4 (2007), e218.
doi: 10.1371/journal.pmed.0040218. |
[30] |
A. H. Roukens, K. van Halem, A. W. de Visser and L. G. Visser,
Long-term protection after fractional-dose yellow fever vaccination: Follow-up study of a randomized, controlled, noninferiority trial, Ann. Intern. Med., 169 (2018), 1761-1765.
doi: 10.7326/M18-1529. |
[31] |
A. H. Roukens, A. C. Vossen, P. J. Bredenbeek, J. T. van Dissel and L. G. Visser, Intradermally administered yellow fever vaccine at reduced dose induces a protective immune response: A randomized controlled non-inferiority trial, PLoS One, 3 (2008), e1993.
doi: 10.1371/journal.pone.0001993. |
[32] |
H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, New York, 1995.
doi: 10.1017/CBO9780511530043.![]() ![]() ![]() |
[33] |
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. |
[34] |
J. T. Wu, C. M. Peak, G. M. Leung and M. Lipsitch,
Fractional dosing of yellow fever vaccine of extend supply: A modelling study, Lancet, 388 (2016), 2904-2911.
doi: 10.1016/S0140-6736(16)31838-4. |
[35] |
K. N. Wyatt, G. J. Ryan and K. A. Sheerin,
Reduced-dose influenza vaccine, Ann. Pharmacother, 40 (2006), 1635-1639.
doi: 10.1345/aph.1G645. |
[36] |
T. Yu, D. Cao and S. Liu,
Epidemic model with group mixing: Stability and optimal control based on limited vaccination resources, Commun. Nonlinear Sci. Numer. Simul., 61 (2018), 54-70.
doi: 10.1016/j.cnsns.2018.01.011. |








Compartment | Definition | Initial Value |
Total number of susceptible individuals in the |
||
Total number of individuals in the |
||
Total number of susceptible individuals in the |
||
Total number of individuals in the |
||
Total number of individuals in the |
||
Total number of recovered individuals at time |
Compartment | Definition | Initial Value |
Total number of susceptible individuals in the |
||
Total number of individuals in the |
||
Total number of susceptible individuals in the |
||
Total number of individuals in the |
||
Total number of individuals in the |
||
Total number of recovered individuals at time |
Parameter | Definition | Range |
Number of individuals in the total population | ||
Proportion of population that standard-dose vaccines can coverage for the total population | ||
Vaccine coverage achievable with standard-dose vaccines for |
||
Fractionation number by each standard-dose vaccine for |
||
Number of contacts per unit time an individual in the |
||
Probability of infection given contact between a susceptible individual in the |
||
Recovery rate of infective individuals without vaccine protection in the |
||
Probability that a standard-dose vaccine takes effects for individuals in the |
||
The ratio of the probability that a |
||
Probability that a successfully vaccinated individual with a standard-dose vaccine gains full protection in the |
||
The ratio of the probability that a successfully vaccinated individual in the |
||
The ratio of the transmissibility of a vaccinated individual with a standard-dose vaccine in the |
||
The ratio of the transmissibility of a vaccinated individual with an |
||
The ratio of susceptibility of a vaccinated individual in the |
||
The ratio of the susceptibility of a vaccinated individual with an |
||
The ratio of the recoverability of a vaccinated individual in the |
||
The ratio of the recoverability of a vaccinated individual with an |
Parameter | Definition | Range |
Number of individuals in the total population | ||
Proportion of population that standard-dose vaccines can coverage for the total population | ||
Vaccine coverage achievable with standard-dose vaccines for |
||
Fractionation number by each standard-dose vaccine for |
||
Number of contacts per unit time an individual in the |
||
Probability of infection given contact between a susceptible individual in the |
||
Recovery rate of infective individuals without vaccine protection in the |
||
Probability that a standard-dose vaccine takes effects for individuals in the |
||
The ratio of the probability that a |
||
Probability that a successfully vaccinated individual with a standard-dose vaccine gains full protection in the |
||
The ratio of the probability that a successfully vaccinated individual in the |
||
The ratio of the transmissibility of a vaccinated individual with a standard-dose vaccine in the |
||
The ratio of the transmissibility of a vaccinated individual with an |
||
The ratio of susceptibility of a vaccinated individual in the |
||
The ratio of the susceptibility of a vaccinated individual with an |
||
The ratio of the recoverability of a vaccinated individual in the |
||
The ratio of the recoverability of a vaccinated individual with an |
Symbol | Description | Value | Unit | Reference |
Total population | Individuals | Estimated | ||
Children aged 0–17 years (group |
Individuals | Estimated | ||
Young adults aged 18–60 years (group |
Individuals | Estimated | ||
Older adults aged more than |
Individuals | Estimated | ||
Susceptible persons in group |
Individuals | Estimated | ||
Susceptible persons in group |
Individuals | Estimated | ||
Susceptible persons in group |
Individuals | Estimated | ||
Infected persons in group |
Individuals | [24] | ||
Infected persons in group |
Individuals | [24] | ||
Infected persons in group |
Individuals | [24] | ||
Vaccine coverage for the total population | Dimensionless | Estimated | ||
Average recover rate for overall population ( |
days |
[18] |
Symbol | Description | Value | Unit | Reference |
Total population | Individuals | Estimated | ||
Children aged 0–17 years (group |
Individuals | Estimated | ||
Young adults aged 18–60 years (group |
Individuals | Estimated | ||
Older adults aged more than |
Individuals | Estimated | ||
Susceptible persons in group |
Individuals | Estimated | ||
Susceptible persons in group |
Individuals | Estimated | ||
Susceptible persons in group |
Individuals | Estimated | ||
Infected persons in group |
Individuals | [24] | ||
Infected persons in group |
Individuals | [24] | ||
Infected persons in group |
Individuals | [24] | ||
Vaccine coverage for the total population | Dimensionless | Estimated | ||
Average recover rate for overall population ( |
days |
[18] |
Symbol | Value | Unit |
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless |
Symbol | Value | Unit |
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless | ||
Dimensionless |
Symbol | Value | Unit | Reference |
Dimensionless | Estimated | ||
Dimensionless | [16] | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | [18] | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | [18] | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated |
Symbol | Value | Unit | Reference |
Dimensionless | Estimated | ||
Dimensionless | [16] | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | [18] | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | [18] | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated | ||
Dimensionless | Estimated |
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