General Overview

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 10to 108 organisms of a highly virulent Aa strain.

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

ID # of Doses Agent Strain Dose Units Host type Μodel Optimized parameters Response type Reference
274 4 SCHU S-4 CFU monkey exponential
k = 4.73E-02
LD50/ID50 = 1.46E+01

death Quan, S. F., A. G. McManus, and H. von Fintel. "Infectivity of Tularemia Applied to Intact Skin and Ingested in Drinking Water." Science. 123 (1956): 942-943.
275 5 Aa strain CFU mice exponential
k = 1.33E-07
LD50/ID50 = 5.22E+06

death John, D. T., and K. L. Hoppe. "Susceptibility of Wild Mammals to Infection with Naegleria fowleri." The Journal of Parasitology. 76 (1990): 6.
Best Fit
Experiment ID:
274
# of Doses:
4
Agent Strain:
SCHU S-4
Dose Units:
CFU
Host type:
monkey
Μodel:
exponential
Optimized parameters:
k = 4.73E-02
LD50/ID50 = 1.46E+01

Reference:

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

Experiment ID:
275
# of Doses:
5
Agent Strain:
Aa strain
Dose Units:
CFU
Host type:
mice
Μodel:
exponential
Optimized parameters:
k = 1.33E-07
LD50/ID50 = 5.22E+06

Reference:
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