Coxiella burnetii: Dose Response Models

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Coxiella burnetii

Yin Huang

General overview of Coxiella burnetii and Q fever

Coxiella burnetii (C. burnetii), an obligate intracellular gram-negative bacterium, is the causative agent of Q fever. C. burnetii multiplies only within the phagolysosomal vacuoles, particularly the macrophages of the host. During natural infections, the organism grows to high numbers in placental tissues of animals such as goats, sheep, and cows. The U.S. Centers for Disease Control and Prevention (CDC) has classified C. burnetii as a category B biological terrorist agent because it consistently causes disability, can be manufactured on a large scale, remains stable under production, storage, and transportation conditions, can be efficiently disseminated and remains viable for years after dissemination.

Q fever, a zoonotic disease found worldwide, may manifest as acute or chronic disease. The acute form is generally not fatal and manifests as self-controlled febrile illness. Chronic Q fever is usually characterized by endocarditis. Many mamalian models, including humans, have been studied for Q fever infection through various exposure routes.

Humans are infected primarily through inhalation of aerosolized C. burnetii. Aerosols, or airborne particles, easily cause infection even without contact with infected animals, whereas person-to-person infection is rare. Ingestion of contaminated dairy products or bites from infected ticks may also lead to infection but these modes of transmission are very rare. However, there have been some recorded cases of human Q fever caused by the consumption of unpasteurized goat's milk products [1]

Williams and Cantrell (1982)[2] intraperitoneally inoculated groups of C57BL/10ScN male mice by C. burnetii phase I Ohio strain to develop a vaccine against Q fever.

Scott and Williams (1987) [3]examined the susceptibility of inbred mice to infection by C. burnetii Nine mile phase I strain. As many as 47 strains of inbred mice were evaluated. Groups of resistant C57BL/6J mice were inoculated with mean doses ranging from 10−1.3 to 107 organisms. The mortalities at various doses were recorded.

The apparent difference of LD50 between the experiment 28 (4.93x108) and experiment 26 (1.22 x1010) routes while are similar may be associated with differences in susceptible hosts and pathogen strains.

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
28* [2] C57BL/1OScN mice phase I Ohio intraperitoneal 10 PFU death beta-Poisson α= 3.57E-01 , N50 = 4.93E+08 4.93E+08
26 [3] C57BL/6J mice Nine mile phase I intraperitoneal 13 PFU death exponential k = 5.7E-11 1.22E+10
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

*Recommended Model

It is recommended that experiment 28 should be used as the best dose-response model. A more virulent strain in experiment 28 can be more meaningful for emergency preparedness. Also, single host strain was used in experiment 28 instead of multiple strains as in experiment 26.

Exponential and betapoisson model.jpg
Mice/phase I Ohio strain model data [2]
Dose Dead Survived Total
0.7 0 30 30
7 0 20 20
70 0 30 30
7000 0 30 30
7E+05 0 30 30
7E+06 1 19 20
7E+07 6 24 30
7E+08 16 14 30
7E+09 23 7 30
7E+10 19 1 20

Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
Exponential 73.9 72.8 9 3.84
Beta Poisson 1.11 8 15.5
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 3.57E-01 1.91E-01 2.20E-01 2.38E-01 6.34E-01 7.08E-01 9.84E-01
N50 4.93E+08 1.89E+08 2.41E+08 2.73E+08 9.34E+08 1.06E+09 1.36E+09

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

Mice/Nine mile phase I model data [3]
Dose Dead Survived Total
0.05 0 10 10
0.5 0 10 10
5 0 10 10
50 0 10 10
501 0 10 10
5010 0 10 10
50100 0 10 10
501000 0 10 10
5010000 0 10 10
5.01E+07 0 10 10
5.01E+08 1 9 10
5.01E+09 3 7 10
5.01E+10 9 1 10

Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
Exponential 1.63 0.936 12 3.84
Beta Poisson 0.693 11 19.7
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 5.7E-11 2.31E-11 2.94E-11 3.33E-11 1.38E-10 1.61E-10 2.13E-10
ID50/LD50/ETC* 1.22E+10 3.25E+09 4.30E+09 5.02E+09 2.08E+10 2.36E+10 2.99E+10
*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


  1. Tamrakar SB, Haluska A, Haas CN and Bartrand BA (2011) Dose-Response Model of Coxiella burnetii (Q Fever). Risk Analysis. 31(1), 120-128.
  2. 2.0 2.1 2.2 Williams JC and Cantrell JL (1982) Biological and immunological properties of Coxiella burnetii vaccines in C57BL/1OScN endotoxin-nonresponder mice. Infection and Immunity 35(3), 1091–1102.
  3. 3.0 3.1 3.2 Scott G, Williams JC, Stephenson EH (1987) Animal models in Q fever: pathological responses of inbred mice to phase I Coxiella Burnetii. Journal of General Microbiology. 133(3), 691–700. Cite error: Invalid <ref> tag; name "Scott_et_al.2C_1987" defined multiple times with different content