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General Overview

Salmonella enterica, serovar Typhi (S. Typhi for short, but formerly known as Salmonella typhi or Salmonella typhosa) causes typhoid fever. Paratyphoid fever is a similar syndrome (but less common and less severe than typhoid fever) caused by Salmonella enterica, serovar Typhi (S. Paratyphi). Typhoid and paratyphoid fevers are also jointly known as enteric fever. Other Salmonella enterica serovars (e.g., Enteritidis, Typhimurium) cause a gastroenteritis known as salmonellosis. 

S. Typhi and S. Paratyphi only infect humans and are transmitted by the fecal-oral route.  Disease may include any combination of the following: cough, constipation, diarrhea, abdominal pain, anorexia, rose spots on the torso, or fever.  S. Typhi may also be shed asymptomatically for years in the feces of chronic carriers. 


http://www.cdc.gov/nczved/divisions/dfbmd/diseases/typhoid_fever/

Summary of data

There have been two feeding studiesin male prisoners of the Quailes strain of S. Typhi (which was named Salmonella typhosa at that time).

Other model fits to these data have been published.  However, these model fits exclude some of the experimental data for unclear reasons.

Recommended Model

The pooled model of experiment number 79 and 80 is the recommended model. Pooling is statistically accepted and it gives improvement in fits.

Exponential and betapoisson model.jpg

ID Exposure Route # of Doses Agent Strain Dose Units Host type Μodel LD50/ID50 Optimized parameters Response type Reference
79 oral (in milk) 3.00 Quailes CFU human beta-Poisson 3.45E+06" a = 1.11E-01 N50 = 3.45E+06 disease
Hornick, R. B., Greisman, S. ., Woodward, T. E., DuPont, H. L., Dawkins, A. T., & Snyder, M. J. (1970). Typhoid fever: pathogenesis and immunologic control. The New England Journal of Medicine, 283, 13.
79, 80 oral (in milk) 8.00 Quailes CFU human beta-Poisson 1.11E+06 a = 1.75E-01 N50 = 1.11E+06 disease
Hornick, R. ., Woodward, T. ., McCrumb, F. ., Snyder, M. ., Dawkins, A. ., Bulkeley, J. ., … Corozza, F. . (1966). Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness. Transactions of the Association of American Physicians, 79, 361-367. Retrieved from https://pubmed.ncbi.nlm.nih.gov/5929469/
80 oral (in milk) 5.00 Quailes CFU human beta-Poisson 8.53E+05 a = 2.03E-01 N50 = 8.53E+05 disease
Levine, M. M., DuPont, H. L., Formal, S. B., Hornick, R. B., Takeuchi, A. ., Gangarosa, E. J., … Libonati, J. P. (1973). Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery. Journal of Infectious Diseases, 127, 3.
Exposure Route:
oral (in milk)
# of Doses:
3.00
Agent Strain:
Quailes
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
3.45E+06"
Optimized parameters: a = 1.11E-01 N50 = 3.45E+06
Response type:
disease
Reference:
Typhoid fever: pathogenesis and immunologic control
Model data for S. Typhi (Quailes) in humans
Dose Disease No disease Total
1E+05 28 76 104
1E+07 15 15 30
1E+09 4 0 4

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 124 121 2 3.84 
0 		5.99 
0
Beta Poisson 2.87 1 3.84 
0.0905
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 1.11E-01 3.19E-02 4.80E-02 5.49E-02 1.96E-01 2.17E-01 2.59E-01
N50 3.45E+06 4.81E+05 6.95E+05 8.50E+05 9.53E+07 2.24E+08 4.19E+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

Highest quality
Exposure Route:
oral (in milk)
# of Doses:
8.00
Agent Strain:
Quailes
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
1.11E+06
Optimized parameters: a = 1.75E-01 N50 = 1.11E+06
Response type:
disease
Reference:
Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness
Model data for S. Typhi (Quailes) in humans
Dose Disease No disease Total
1000 0 14 14
1E+05 28 76 104
1E+05 32 84 116
1E+07 15 15 30
1E+07 16 16 32
1E+08 8 1 9
1E+09 4 0 4
1E+09 40 2 42

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 419 406 7 3.84 
0 		14.1 
0
Beta Poisson 13.8 6 12.6 
0.0321
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 1.75E-01 1.21E-01 1.32E-01 1.39E-01 2.23E-01 2.34E-01 2.58E-01
N50 1.11E+06 5.13E+05 6.10E+05 6.72E+05 2.00E+06 2.28E+06 2.95E+06

 

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

Exposure Route:
oral (in milk)
# of Doses:
5.00
Agent Strain:
Quailes
Dose Units:
CFU
Host type:
human
Μodel:
beta-Poisson
LD50/ID50:
8.53E+05
Optimized parameters: a = 2.03E-01 N50 = 8.53E+05
Response type:
disease
Reference:
Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery
 Model data for S. Typhi (Quailes) in humans 
Dose Disease No disease Total
1000 0 14 14
1E+05 32 84 116
1E+07 16 16 32
1E+08 8 1 9
1E+09 40 2 42

 

Goodness of fit and model selection
Model Deviance Δ Degrees 
of freedom		 χ20.95,1 
p-value 		χ20.95,m-k 
p-value
Exponential 293 284 4 3.84 
0 		9.49 
0
Beta Poisson 8.63 3 7.81 
0.0346
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

 

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 2.03E-01 1.33E-01 1.49E-01 1.57E-01 2.74E-01 2.89E-01 3.27E-01
N50 8.53E+05 3.38E+05 4.28E+05 4.80E+05 1.62E+06 1.85E+06 2.49E+06

 

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

References

  • Crump, J. A., & Mintz, E. D. (2010). Global trends in typhoid and paratyphoid Fever. Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America, 50, 241-246. Retrieved from http://cid.oxfordjournals.org/content/50/2/241.full.pdf+html
  • Miliotis, M. D., & Bier, J. W. (2003). International handbook of foodborne pathogens (Vol. 125). CRC Press.
  • Hornick, R. B., Woodward, T. E., McCrumb, F. R., Snyder, M. J., Dawkins, A. T., & Bulkeley, J. T. De la Macorra F and Corozza FA (1966) Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness. Transactions of the Association of American Physicians, 79, 361.
  • Hornick, R. B., Greisman, S. ., Woodward, T. E., DuPont, H. L., Dawkins, A. T., & Snyder, M. J. (1970). Typhoid fever: pathogenesis and immunologic control. The New England Journal of Medicine, 283, 13.
  • Haas, C. N., Rose, J. B., & Gerba, C. P. (2014). Quantitative Microbial Risk Assessment, Second Edition. New York, NY: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118910030