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General Overview

According to Stalkup and Chilukuri[1], enterovirus, a small (30 nm), nonenveloped, single-stranded RNA viruses, belongs to the family Picornaviridae. While most of the enterovirus infections are relatively mild and result in complete recovery of the patient, they can also cause severe and fatal diseases such as meningitis, encephalitis, myocarditis, neonatal sepsis, and polio like paralytic diseases. Infection occurs mainly via fecal-oral transmission and less commonly by respiratory droplets. While no known non-human reservoirs have been identified, water-borne, foodborne, and blood-borne transmissions have been reported.

Summary Data

Cliver[2] challenged pigs with Porcine enterovirus type 3 and 7 via oral exposure route.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
62 3 porcine, PE3-ECPO-6 PFU pig exponential k = 2.96E-04
LD50/ID50 = 2.34E+03
 		 infection

Cliver[2]
63 3 porcine, PE7-05i PFU pig exponential k = 3.74E-03
LD50/ID50 = 1.85E+02
 		 infection

Cliver[2]

Optimization Output for Exp. 62:

Experiment ID: 62

# of Doses: 3

Agent Strain: porcine, PE3-ECPO-6

Dose Units: PFU

Host type: pig

Μodel: exponential

Optimized parameters:
k = 2.96E-04
LD50/ID50 = 2.34E+03

Pigs/ Porcine enterovirus type 3 Strain model data [1]
Dose infected Non-infected Total
100 0 3 3
250 0 6 6
1000 2 4 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 1.24 -0.000314 2 3.84 
1		 5.99 
0.537
Beta Poisson 1.24 1 3.84 
0.265
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 2.96E-04 2.40E-17 2.40E-17 2.40E-17 7.19E-04 7.19E-04 1.02E-03
ID50/LD50/ETC* 2.34E+03 6.77E+02 9.64E+02 9.64E+02 2.89E+16 2.89E+16 2.89E+16
*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

Optimization Output for Exp. 63:

Best Fit

Experiment ID: 63

# of Doses: 3

Agent Strain: porcine, PE7-05i

Dose Units: PFU

Host type: pig

Μodel: exponential

Optimized parameters:
k = 3.74E-03
LD50/ID50 = 1.85E+02
 

pigs/ Porcine enterovirus type 7 [1]
Dose infected Non-infected Total
250 4 2 6
250 3 3 6
1000 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 0.614 -5.49e-05 2 3.84 
1		 5.99 
0.736
Beta Poisson 0.614 1 3.84 
0.433
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 3.74E-03 1.83E-03 2.19E-03 2.19E-03 5.62E-03 5.62E-03 5.62E-03
ID50/LD50/ETC* 1.85E+02 1.23E+02 1.23E+02 1.23E+02 3.16E+02 3.16E+02 3.79E+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

Recommended Model

It is recommended that experiment 63 should be used as the best dose-response model.

Summary

The different LD50 for these two experiments indicates that virulence varies between pathogen strains.

References

  1. Enterovirus infections: a review of clinical presentation, diagnosis, and treatment, Stalkup, J. R., and Chilukuri S. , Dermatologic clinics, Volume 20, p.217–223, (2002)
  2. Experimental infection by waterborne enteroviruses, CLIVER, DEAN O. , Journal of Food Protection, Volume 44, Number 11, p.861–865, (1981)
ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
62 3 porcine, PE3-ECPO-6 PFU pig exponential
k = 2.96E-04
LD50/ID50 = 2.34E+03

infection CLIVER, DEAN O.. "Experimental infection by waterborne enteroviruses." Journal of Food Protection. 44 (1981): 861-865.
63 3 porcine, PE7-05i PFU pig exponential
k = 3.74E-03
LD50/ID50 = 1.85E+02

infection CLIVER, DEAN O.. "Experimental infection by waterborne enteroviruses." Journal of Food Protection. 44 (1981): 861-865.
Experiment ID:
62
# of Doses:
3
Agent Strain:
porcine, PE3-ECPO-6
Dose Units:
PFU
Host type:
pig
Μodel:
exponential
Optimized parameters:
k = 2.96E-04
LD50/ID50 = 2.34E+03

Reference:
Pigs/ Porcine enterovirus type 3 Strain model data [1]
Dose infected Non-infected Total
100 0 3 3
250 0 6 6
1000 2 4 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 1.24 -0.000314 2 3.84 
1		 5.99 
0.537
Beta Poisson 1.24 1 3.84 
0.265
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 2.96E-04 2.40E-17 2.40E-17 2.40E-17 7.19E-04 7.19E-04 1.02E-03
ID50/LD50/ETC* 2.34E+03 6.77E+02 9.64E+02 9.64E+02 2.89E+16 2.89E+16 2.89E+16
*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

  1. Experimental infection by waterborne enteroviruses, Cliver, D. O. , Journal of Food Protection, Volume 44, p.861-865, (1981)
Best Fit
Experiment ID:
63
# of Doses:
3
Agent Strain:
porcine, PE7-05i
Dose Units:
PFU
Host type:
pig
Μodel:
exponential
Optimized parameters:
k = 3.74E-03
LD50/ID50 = 1.85E+02

Reference:
pigs/ Porcine enterovirus type 7 [1]
Dose infected Non-infected Total
250 4 2 6
250 3 3 6
1000 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 0.614 -5.49e-05 2 3.84 
1		 5.99 
0.736
Beta Poisson 0.614 1 3.84 
0.433
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 3.74E-03 1.83E-03 2.19E-03 2.19E-03 5.62E-03 5.62E-03 5.62E-03
ID50/LD50/ETC* 1.85E+02 1.23E+02 1.23E+02 1.23E+02 3.16E+02 3.16E+02 3.79E+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

References

  1. Experimental infection by waterborne enteroviruses, Cliver, D. O. , Journal of Food Protection, Volume 44, p.861-865, (1981)