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General Overview

Coronaviruses cause acute and chronic respiratory, enteric, and central nervous system (CNS) diseases in humans and many species of animals. Coronaviruses are divided into three groups based on the genome sequences, including SARS-CoV (a member of group II) as well as murine hepatitis virus (MHV), bovine coronavirus, porcine hemagglutinating encephalomyelitis virus (HEV), equine coronavirus, and human coronavirues OC43 and NL63, which also cause respiratory infections. SARS-CoV, the causal pathogen of severe acute respiratory syndrome (SARS), caused a large outbreak of this severe pneumonia occurred in Hong Kong in 2003 and rapidly spread throughout the world. SARS-CoV can infect and replicate in mice, ferrets, hamsters, cats, and several species of nonhuman primates (cynomolgus and rhesus macaques, African green monkeys, and marmosets). MHV that infects both mice and rats often has been studied as a suitable model of human coronavirus diseases, according to Watanabe et al..

Summary of Data

DeDiego et al. challenged four groups of the transgenic mice intranasally with graded doses of rSARS-CoV and the survival was monitored for 13 days.

De Albuquerque et al. inoculated A/J mice with MHV-1 intranasally via intranasal route and monitored the survival for 21 days.

 

Exponential and betapoisson model.jpg

 

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
260 intranasal 4.00 rSARS-CoV PFU mice hACE-2 exponential 2.33E+02 k = 2.97E-03 death
Albuquerque, N. D., Baig, E. ., Ma, X. ., Zhang, J. ., He, W. ., Rowe, A. ., … Levy, G. A. (2006). Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice. Journal of Virology, 80, 21. https://doi.org/10.1128/JVI.00747-06
260, 261 intranasal 0.00 rSARS-CoV PFU mice hACE-2 and A/J exponential 2.82E+02 k = 2.46E-03 death
261 intranasal 4.00 MHV-1 PFU A/J mice exponential 3.24E+02 k = 2.14E-03 death
Albuquerque, N. D., Baig, E. ., Ma, X. ., Zhang, J. ., He, W. ., Rowe, A. ., … Levy, G. A. (2006). Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice. Journal of Virology, 80, 21. https://doi.org/10.1128/JVI.00747-06
Exposure Route:
intranasal
# of Doses:
4.00
Agent Strain:
rSARS-CoV
Dose Units:
PFU
Host type:
mice hACE-2
Μodel:
exponential
LD50/ID50:
2.33E+02
Optimized parameters: k = 2.97E-03
Response type:
death
Reference:
Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice
mice/rSARS-CoV strain model data [2]
Dose Dead Survived Total
240 1 2 3
800 3 0 3
2400 2 0 2
12000 6 0 6

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 0.968 -0.000923 3 3.84 
1 		7.81 
0.809
Beta Poisson 0.969 2 5.99 
0.616
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 2.97E-03 1.90E-03 1.90E-03 1.90E-03 2.97E-03 2.97E-03 2.97E-03
ID50/LD50/ETC* 2.33E+02 2.33E+02 2.33E+02 2.33E+02 3.64E+02 3.64E+02 3.64E+02
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

Highest quality
Exposure Route:
intranasal
# of Doses:
0.00
Agent Strain:
rSARS-CoV
Dose Units:
PFU
Host type:
mice hACE-2 and A/J
Μodel:
exponential
LD50/ID50:
2.82E+02
Optimized parameters: k = 2.46E-03
Response type:
death
Reference:
Pooled dose response model data [1]
Dose Dead Survived Total
5 0 5 5
50 1 4 5
240 1 2 3
500 3 2 5
800 3 0 3
2400 2 0 2
5000 5 0 5
12000 6 0 6

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 1.75 -0.00181 7 3.84 
1 		14.1 
0.972
Beta Poisson 1.75 6 12.6 
0.941
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 2.46E-03 1.07E-03 1.28E-03 1.35E-03 4.59E-03 5.27E-03 6.80E-03
ID50/LD50/ETC* 2.82E+02 1.02E+02 1.32E+02 1.51E+02 5.13E+02 5.43E+02 6.47E+02
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

Exposure Route:
intranasal
# of Doses:
4.00
Agent Strain:
MHV-1
Dose Units:
PFU
Host type:
A/J mice
Μodel:
exponential
LD50/ID50:
3.24E+02
Optimized parameters: k = 2.14E-03
Response type:
death
Reference:
Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice
Mice/MHV-1 strains model data [3]
Dose Dead Survived Total
5 0 5 5
50 1 4 5
500 3 2 5
5000 5 0 5

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 0.606 0.0689 3 3.84 
0.793 		7.81 
0.895
Beta Poisson 0.537 2 5.99 
0.765
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

 

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 2.14E-03 6.25E-04 6.55E-04 9.06E-04 6.58E-03 6.58E-03 9.86E-03
ID50/LD50/ETC* 3.24E+02 7.03E+01 1.05E+02 1.05E+02 7.65E+02 1.06E+03 1.11E+03
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

 

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

References

  • Watanabe, T. ., Bartrand, T. A., Weir, M. H., Omura, T. ., & Haas, C. N. (2010). Development of a Dose-Response Model for SARS Coronavirus. Risk Analysis: An International Journal, 30(7), 1129–1138. https://doi.org/10.1111/j.1539-6924.2010.01427 (Original work published 2010)
  • DeDiego, M. L., Pewe, L. ., Alvarez, E. ., Rejas, M. T., Perlman, S. ., & Enjuanes, L. . (2008). Pathogenicity of severe acute respiratory coronavirus deletion mutants in hACE-2 transgenic mice. Virology., 376, 2. https://doi.org/10.1016/j.virol.2008.03.005
  • Albuquerque, N. D., Baig, E. ., Ma, X. ., Zhang, J. ., He, W. ., Rowe, A. ., … Levy, G. A. (2006). Murine Hepatitis Virus Strain 1 Produces a Clinically Relevant Model of Severe Acute Respiratory Syndrome in A/J Mice. Journal of Virology, 80, 21. https://doi.org/10.1128/JVI.00747-06