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General Overview

Rocky Mountain spotted fever is a disease endemic to North America is caused by Rickettsia rickettsi. The bacterium is delivered to the victim by a tick bite, and is the most lethal disease of all Rickettsial illnesses, especially in the United States. While the main vector for the disease is via an insect (most typically a tick), there has been evidence cited in Saslaw and Carlisle (1966) that aerosol dissemination and infection can be possible as well. This form of exposure to the bacterium can still develop into the lethal form of the disease, therefore, aerosol animal models were needed.

Typically rocky mountain spotted fever (RMSF) can be a misnomer, as the disease neither originated from this area of America and Canada, nor is it isolated to just this region or these countries. As the bacterium has been known to cause RMSF in south and central America as well. RMSF presents with sudden onset of flu-like symptoms, followed by the onset of a spotty rash, similar to pox, yet not raised above the skin as a pox is. Patients often require hospitalization from infection and can be fatal is not treated immediately and aggressively.

Summary Data

Saslaw and Carlisle in 1966 studied the aerosol infectivity of R. rickettsii in monkeys. Rhesus monkeys were challenged with aerosolized pathogens and morbidity as well as mortality was observed (Saslaw and Carlisle 1966). Dupont et al. carried out a study of R. rickettsii (Sheila Smith) in human volunteers via the intradermal route(Dupont, Hornick et al. 1973). Sammons et al. exposed Macaca mulatta (Rhesus monkey) to R. rickettsii (strain Sheila Smith) via different routes to find the changes in blood serum constituents(Sammons, Kenyon et al. 1976).

Recommended Model

The pooled model of human exposed intradermally and aerosol exposed rhesus monkey is the recommended model. Intradermal route is the one of the natural routes of infection and aerosol route might be an accidental or intentional route. Moreover, the experiment 301 was conducted with human volunteers.

Exponential and betapoisson model.jpg

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
244 24 NA CFU rhesus monkey beta-Poisson a = 1.45E-01

LD50/ID50 = 5.01E+01
N50 = 5.01E+01
death Sammons, L. S., R. H. Kenyon, and C. E. Pedersen. "Effect of vaccination schedule on immune response of Macaca mulatta to cell culture-grown Rocky Mountain spotted fever vaccine." Journal of Clinical Microbiology. 4 (1976): 3.
245 5 KHW CFU C57BL/6 mice exponential
k = 3.18E-03
LD50/ID50 = 2.18E+02

infection Meynell, G. G., and E. W. Meynell. "The growth of micro-organisms in vivo with particular reference to the relation between dose and latent period." Epidemiology & Infection. 56 (1958).
300 24 R1 CFU rhesus monkey beta-Poisson a = 8.58E-01

LD50/ID50 = 1.88E+01
N50 = 1.88E+01
morbidity Saslaw, S., and H. N. Carlisle. "Aerosol infection of monkeys with Rickettsia rickettsii." Bacteriological Reviews. 30 (1966): 3.
300 and 301 27 R1 and Sheila Smith CFU pooled beta-Poisson a = 7.77E-01

LD50/ID50 = 2.13E+01
N50 = 2.13E+01
morbidity Saslaw, S., and H. N. Carlisle. "Aerosol infection of monkeys with Rickettsia rickettsii." Bacteriological Reviews. 30 (1966): 3.
301 3 Sheila Smith CFU human beta-Poisson a = 6.75E-01

LD50/ID50 = 2.36E+01
N50 = 2.36E+01
clinical signs DuPont, HL, et al. "Rocky Mountain spotted fever: a comparative study of the active immunity induced by inactivated and viable pathogenic Rickettsia rickettsii." Journal of Infectious Diseases. 128 (1973): 340-344.
Experiment ID:
244
# of Doses:
24
Agent Strain:
NA
Dose Units:
CFU
Host type:
rhesus monkey
Μodel:
beta-Poisson
Optimized parameters: a = 1.45E-01

LD50/ID50 = 5.01E+01
N50 = 5.01E+01
Reference:
Rhesus monkey Data [4]
Dose Dead Survived Total
25 1 3 4
66 2 0 2
83 2 0 2
99 1 1 2
182 3 4 7
1111 1 1 2
1774 1 1 2
2287 1 1 2
2586 2 0 2
3166 1 1 2
5055 6 1 7
5519 2 0 2
5652 2 0 2
5669 1 0 1
7459 2 0 2
9199 1 1 2
10774 2 0 2
16790 1 1 2
41023 2 0 2
45498 1 2 3
53206 2 0 2
55195 2 0 2
131771 1 1 2
149175 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 137 113 23 3.84 
0
35.2 
0
Beta Poisson 24 22 33.9 
0.345
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 1.45E-01 1.82E-02 2.72E-02 4.15E-02 2.59E-01 2.87E-01 3.49E-01
N50 5.01E+01 6.71E-12 6.31E-07 2.86E-03 2.62E+02 3.28E+02 4.87E+02

 

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

Experiment ID:
245
# of Doses:
5
Agent Strain:
KHW
Dose Units:
CFU
Host type:
C57BL/6 mice
Μodel:
exponential
Optimized parameters:
k = 3.18E-03
LD50/ID50 = 2.18E+02

Reference:
C57BL/6 Mice KHW Strain Data[5]
Dose Infected Non-infected Total
5 0 3 3
45 1 5 6
450 6 2 8
4500 7 0 7
45000 7 0 7

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 0.155 0.0201 4 3.84 
0.887
9.49 
0.997
Beta Poisson 0.135 3 7.81 
0.987
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 3.18E-03 1.05E-03 1.41E-03 1.63E-03 7.50E-03 7.54E-03 1.46E-02
ID50/LD50/ETC* 2.18E+02 4.74E+01 9.19E+01 9.25E+01 4.25E+02 4.91E+02 6.63E+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

Experiment ID:
300
# of Doses:
24
Agent Strain:
R1
Dose Units:
CFU
Host type:
rhesus monkey
Μodel:
beta-Poisson
Optimized parameters: a = 8.58E-01

LD50/ID50 = 1.88E+01
N50 = 1.88E+01
Reference:
Rhesus monkey Data [6]
Dose MORBIDITY NOT MORBIDITY Total
25 1 3 4
66 2 0 2
83 2 0 2
99 2 0 2
182 7 0 7
1110 1 1 2
1770 2 0 2
2290 2 0 2
2590 2 0 2
3170 2 0 2
5060 7 0 7
5520 2 0 2
5650 2 0 2
5670 1 0 1
7460 2 0 2
9200 2 0 2
10800 2 0 2
16800 2 0 2
41000 2 0 2
45500 3 0 3
53200 2 0 2
55200 2 0 2
132000 2 0 2
149000 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 27.6 16.4 23 3.84 
5.12e-05
35.2 
0.232
Beta Poisson 11.2 22 33.9 
0.972
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 8.58E-01 9.77E-04 9.77E-04 9.78E-04 5.70E+06 1.41E+08 1.62E+11
N50 1.88E+01 3.58E-01 1.81E+00 7.74E+00 1.02E+03 4.02E+03 3.71E+04

 

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

Best Fit
Experiment ID:
300 and 301
# of Doses:
27
Agent Strain:
R1 and Sheila Smith
Dose Units:
CFU
Host type:
pooled
Μodel:
beta-Poisson
Optimized parameters: a = 7.77E-01

LD50/ID50 = 2.13E+01
N50 = 2.13E+01
Reference:
Pooled data (experiment no. 300 and 301) [6]
Dose MORBIDITY NOT MORBIDITY Total
13 2 4 6
25 1 3 4
66 2 0 2
83 2 0 2
99 2 0 2
126 6 1 7
182 7 0 7
1110 1 1 2
1260 17 1 18
1770 2 0 2
2290 2 0 2
2590 2 0 2
3170 2 0 2
5060 7 0 7
5520 2 0 2
5650 2 0 2
5670 1 0 1
7460 2 0 2
9200 2 0 2
10800 2 0 2
16800 2 0 2
41000 2 0 2
45500 3 0 3
53200 2 0 2
55200 2 0 2
132000 2 0 2
149000 2 0 2

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 42.2 30.5 26 3.84 
3.41e-08
38.9 
0.0235
Beta Poisson 11.7 25 37.7 
0.989
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 7.77E-01 3.82E-01 4.41E-01 4.90E-01 4.24E+00 3.59E+03 3.25E+04
N50 2.13E+01 5.70E+00 8.34E+00 1.01E+01 4.00E+01 4.16E+01 5.10E+01

 

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

Experiment ID:
301
# of Doses:
3
Agent Strain:
Sheila Smith
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
Optimized parameters: a = 6.75E-01

LD50/ID50 = 2.36E+01
N50 = 2.36E+01
Reference:
Human data( Rickettsia rickettsii) [6]
Dose CLINICAL SIGNS NOT CLINICAL SIGNS Total
13 2 4 6
126 6 1 7
1260 17 1 18

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom
χ20.95,1 
p-value
χ20.95,m-k 
p-value
Exponential 13.5 13.2 2 3.84 
0.000277
5.99 
0.00119
Beta Poisson 0.248 1 3.84 
0.618
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

 

Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
α 6.75E-01 1.17E-01 2.44E-01 3.31E-01 1.21E+03 3.74E+03 4.98E+03
N50 2.36E+01 2.56E-02 3.35E+00 7.30E+00 6.41E+01 8.91E+01 1.28E+02

 

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