Francisella tularensis: Dose Response Models

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Francisella tularensis

Author: Yin Huang


General overview of Francisella tularensis and tularemia

Francisella tularensis is the causative agent of tularemia or rabbit fever. It is an intracellular pathogenic species of Gram-negative bacteria, replicating mainly in macrophages, and has also been reported in amoebae [1]. Interest in this pathogen grew due to its high infectivity, ease of dissemination and consequently its potential use as biological weapon [2] [3][4] It can be easily disseminated via aerosols that once inhaled may result in tularemia pneumonia, a severe form of disease with high mortality if untreated [5]. Known as one of the most infectious pathogens, only a few F. tularensis organisms may cause infection [6] [7]. The U.S. Centers for Disease Control and Prevention have classified F. tularensis as a Category A bioterrorism agent for public health preparedness.

http://www.cdc.gov/tularemia/


Summary Data

Day and Berendt[8] exposed 4-5 kg monkeys to aerosol particles of SCHU S-4 strain of F. tularensis. The aerosol particles were administered into different sizes to study the effect of size distribution.

A set of classical dose-response data for F. tularensis infection via oral exposure by Quan et al[9] were used in investigating the effects of inoculation route on the response. Albino mice were infected orally with drinking water contaminated with 104 to 108 organisms of a highly virulent Aa strain.



Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
274* [8] monkeys SCHU S-4 inhalation 4 CFU death exponential k = 4.73E-02 1.46E+01
275 [9] mice Aa strain oral 5 CFU death exponential k = 1.33E-07 5.22E+06
*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 274 should be used as the best dose response model for inhalation. Inhalation is much more infective than the oral exposure in this case so that it should receive more attention in terms of emergency preparedness and public intervention.

Exponential and betapoisson model.jpg

Optimization Output for experiment 274

Monkeys / SCHU S-4 model data [8]
Dose Dead Survived Total
5 1 5 6
11 3 3 6
32 4 2 6
65 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 1.26 -0.000367 3 3.84
1
7.81
0.738
Beta Poisson 1.26 2 5.99
0.531
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 4.73E-02 2.28E-02 2.72E-02 2.98E-02 7.81E-02 9.03E-02 1.11E-01
ID50/LD50/ETC* 1.46E+01 6.27E+00 7.67E+00 8.88E+00 2.33E+01 2.55E+01 3.04E+01
*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 experiment 275

Mice/ Aa strain model data [9]
Dose Dead Survived Total
1E+04 0 22 22
1E+05 1 21 22
1E+06 1 10 11
1E+07 16 6 22
1E+08 22 0 22


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 1.27 0.0341 4 3.84
0.854
9.49
0.867
Beta Poisson 1.23 3 7.81
0.745
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 1.33E-07 6.86E-08 7.91E-08 8.83E-08 2.06E-07 2.24E-07 2.75E-07
ID50/LD50/ETC* 5.22E+06 2.52E+06 3.10E+06 3.37E+06 7.85E+06 8.76E+06 1.01E+07
*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



Advanced Dose Response Model

Incorporating the time postinoculation into the classical dose-response models for microbial infection generates a class of time-dose-response (TDR) models. The parameter k in the exponential dose-response model (equation 1) and the parameter N50 in the beta-Poisson model (equation 2) were set equal to functions of time that represent in vivo bacterial kinetics. Equations 1-2 with candidate G(t; θ,…) were fit to the time-dependent dose response data from experiment 2. The exponential TDR model (equation 1) incorporating the Weibull distribution (equation 3), where k0 = 0.056, θ1 = 5.66, θ2 = 6.43, provided the best fit to the data. The probability density function of the best-fit model is compared with the observed densities of deaths at different dose levels.


The Weibull distribution based exponential TDR model (curves) compared with the observed percent mortalities (points) for monkeys exposed to 2.1-μm aerosols of the strain SCHU S4 at the dose of (a) 5, (b) 11, (c) 32 and (d) 65 organisms.
Equation Francisella tularensis.png



Summary

Noting the very different LD50 for these two exposure route (5.22E6 for oral route and 14.65 for inhalation), substantial variation of virulence with infection site is manifested.



References

  1. Titball, R. W. and A. Sjostedt (2003). "Francisella tularensis: an overview." American Society for Microbiology News 69(11): 558-563.
  2. World Health Organization (1970). Health Aspects of Chemical and Biological Weapons. Geneva, Switzerland, World Health Organization.
  3. Christopher, G. W., T. J. Cieslak, J. A. Pavlin and E. M. Eitzen (1997). "Biological warfare: a historical perspective." JAMA (Journal of the American Medical Association) 278: 412-417.
  4. Kaufmann, A. F., M. I. Meltzer and G. P. Schmid (1997). "The economic impact of a bioterrorist attack: are prevention and post-attack intervention programs justifiable?" Emerging Infectious Diseases 2: 83-94.
  5. Stuart, B. M. and R. L. Pullen (1945). "Tularemic pneumonia: Review of American literature and report of 15 additional cases." American Journal of the Medical Sciences 210: 223-236.
  6. Saslaw, S., H. T. Eigelsbach, J. A. Prior, H. E. Wilson and S. Carhart (1961). "Tularemia vaccine study. II. Respiratory challenge." Arch Intern Med. 107: 702-714.
  7. Saslaw, S., H. T. Eigelsbach, H. E. Wilson, J. A. Prior and S. Carhart (1961). "Tularemia vaccine study, I: intracutaneous challenge." Arch Intern Med 107: 121-133.
  8. 8.0 8.1 8.2 Day, W. C. and R. F. Berendt (1972). "Experimental Tularemia in Macaca mulatta: Relationship of Aerosol Particle Size to the Infectivity of Airborne Pasteurella tularensis." Infection and Immunity 5(1): 77-82.
  9. 9.0 9.1 9.2 Quan, S. F., A. G. McManus and H. von Fintel (1956). "Infectivity of Tularemia Applied to Intact Skin and Ingested in Drinking Water." Science 123: 942-943. Cite error: Invalid <ref> tag; name "Quan_et_al..2C1956" defined multiple times with different content Cite error: Invalid <ref> tag; name "Quan_et_al..2C1956" defined multiple times with different content