General Overview
According to Kitajima et al.^{[1]} and Watanabe et al.^{[2]} influenza A viruses are members of the family Orthomyxoviridae, which is comprised of enveloped viruses with segmented, negativesense RNA genomes. Based on the antigenicity of the two surface glycoproteins, hemagglutinin (HA) and neuraminidase (NA), influenza A viruses are currently divided into 16 HA and 9 NA subtypes, designated as H1H16 and N1N9. Over the past century, viruses of the H1N1, H2N2, H3N2, and H1N2 subtypes have circulated in humans. Additionally, new subtypes such as H5N1 and H7N9 have been recently isolated from human as well as poultry. Influenza A virus is one of the most common causes of human respiratory infections and the most significant because they cause high morbidity and mortality. Transmission of influenza can be achieved via environmental reservoirs or humantohuman communication.
Summary Data
Murphy et al. ^{[3]} intranasally challenged adult human volunteers with influenza A (H1N1) California/10/78 coldadapted viruses. Infection was defined as virus recovery and/or antibody response.
Murphy et al.^{[4]} challenged adult human volunteers with influenza A (H3N2) Washington/897/80 avianhuman reassortant viruses via the intranasal route. Infection was defined as virus isolation and/or antibody response.
Fan et al.^{[5]} exposed sixweekold SPF BALB/c mice (five mice/dose) intranasally with a highly pathogenic avian influenza A (H5N1) virus (DKGX/35 strain).
D  # of Doses  Agent Strain  Dose Units  Host type  Μodel  Optimized parameters  Response type  Reference 

257  4  H1N1,A/California/10/78 attenuated strain  TCID50  human  betaPoisson  a = 9.04E01
LD_{50}/ID_{50} = 1.25E+06 
infection  Murphy et al.^{[4]} 
257, 258  9  H1N1,A/California/10/78 attenuated strain,H3N2,A/Washington/897/80 attenuated strain  TCID50  human  betaPoisson  a = 5.81E01
LD_{50}/ID_{50} = 9.45E+05 
infection 
Murphy et al.^{[3]} 
258  5  H3N2,A/Washington/897/80 attenuated strain  TCID50  human  betaPoisson  a = 4.29E01
LD_{50}/ID_{50} = 6.66E+05 
infection  Fan et al.^{[5]} 
259  6  H5N1, DKGX/35 strain  EID50  mice  exponential 
k = 1.09E02 LD_{50}/ID_{50} = 6.38E+01 
death  DeDiego et al.^{[6]} 
Optimization Output for Exp. 257:
Experiment ID: 257
# of Doses: 4
Agent Strain: H1N1,A/California/10/78 attenuated strain
Dose Units: TCID50
Host type: human
Μodel: betaPoisson
Optimized parameters:
a = 9.04E01
LD_{50}/ID_{50} = 1.25E+06
N_{50} = 1.25E+06



Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
Optimization Output for Exp. 257, 258:
Best Fit
Experiment ID: 257, 258
# of Doses: 9
Agent Strain: H1N1,A/California/10/78 attenuated strain,H3N2,A/Washington/897/80 attenuated strain
Dose Units: TCID50
Host type: human
Μodel: betaPoisson
Optimized parameters:
a = 5.81E01
LD_{50}/ID_{50} = 9.45E+05
N_{50} = 9.45E+05



Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
Optimization Output for Exp. 258:
Experiment ID: 258
# of Doses: 5
Agent Strain: H3N2,A/Washington/897/80 attenuated strain
Dose Units: TCID50
Host type: human
Μodel: betaPoisson
Optimized parameters:
a = 4.29E01
LD_{50}/ID_{50} = 6.66E+05
N_{50} = 6.66E+05



Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.
beta Poisson model plot, with confidence bounds around optimized model
Optimization Output for Exp. 259:
Experiment ID: 259
# of Doses: 6
Agent Strain: H5N1, DKGX/35 strain
Dose Units: EID50
Host type: mice
Μodel: exponential
Optimized parameters:
k = 1.09E02
LD_{50}/ID_{50} = 6.38E+01



Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model
Recommended Model
It is recommended that the pooled experiments 257 and 258 should be used as the best doseresponse model. Both strains are common in human outbreaks. The pooling narrows the range of the confidence region of the parameter estimates and enhances the statistical precision.
Advanced Dose Response Model
Incorporating the time postinoculation into the classical doseresponse models for microbial infection generates a class of timedoseresponse (TDR) models. The parameter k in the exponential doseresponse model (equation 1) and the parameter N50 in the betaPoisson model (equation 2) were set equal to functions of time that represent in vivo bacterial kinetics. Equations 12 with candidate G(t; θ,…) were fit to the timedependent dose response data from experiment 259. The betaPoisson TDR model (equation 2) incorporating an exponentialinversepower distribution provided the best fit to the data. In the following figure, the best TDR models are plotted to compare with the observed mortalities, according to Kitajima et al. (under review)^{[1]}. As shown, the clear difference between the different times postinoculation gives a visible representation of the quantified results that the modification added to the classical models has a substantial effect on the dose response.
The bestfit TDR model (curves) compared to observed mortalities against doses (symbols) from experiment 259.
Summary
The pooling results indicate that the human responses to HIN1 and H3N2 viruses may have similar patterns.
References
 Kitajima, M.., Huang Y.., Watanabe T.., Katayama H.., & Haas C.. N. (2011). Dose–response time modelling for highly pathogenic avian influenza A (H5N1) virus infection. Letters in applied microbiology. 53, 438–444.
 Watanabe, T.., Bartrand T.. A., Omura T.., & Haas C.. N. (2012). DoseResponse Assessment for Influenza A Virus Based on Data Sets of Infection with its Live Attenuated Reassortants. Risk Analysis. 32, 555–565.
 Murphy, B. R., Clements M. L., Madore H. P., Steinberg J., O'Donnell S., Betts R., et al. (1984). Dose Response of ColdAdapted, Reassortant Influenza A/California/10/78 Virus (H1N1) in Adult Volunteers. Journal of Infectious Diseases. 149, 5.
 Murphy, B. R., Clements M. L., Tierney E. L., Black R. E., Stienberg J., & Chanock R. M. (1985). Dose Response of Influenza A/Washington/897/80 (H3N2) AvianHuman Reassortant Virus in Adult Volunteers. The Journal of Infectious Diseases. 152, 1.
 Fan, S., Deng G., Song J., Tian G., Suo Y., Jiang Y., et al. (2009). Two amino acid residues in the matrix protein M1 contribute to the virulence difference of H5N1 avian influenza viruses in mice. Virology.. 384, 1.
 DeDiego, M. L., Pewe L., Alvarez E., Rejas M. Teresa, Perlman S., & Enjuanes L. (2008). Pathogenicity of severe acute respiratory coronavirus deletion mutants in hACE2 transgenic mice. Virology. 376, 379–389.