Chapter 14 Salmonella
14.1 General overview of Salmonella and Salmonellosis
Salmonella, a genus of rod-shaped, Gram-negative, non-spore forming, predominantly motile
enterobacteria, cause more than 104 cases of infections per year in United States. Salmonellosis is
an important medical problem, as while infection with non- typhi Salmonella often causes mild
self-limited ill- ness, severe sequelae including death may occur, particularly in
immunocompromised hosts. It has been reported that the incidence of salmonellosis is higher in
developing than in developed countries and in developing countries food handlers may be a
reservoir for further transmission of infection (Chalker and Blaser 1988).
14.2 Summary Data
Meynell G.G. and Meynell E.W. (1958) inoculated albino (PGMS) mice intraperitoneally with
the Salmonella typhimurium strain 216 and 219 and challenged albino (Tuck) mice with
Salmonella typhimurium strain 533 via intraperitoneal route.
Table 14.1. Summary of the Salmonella data and best fits
Host Best-fit LD50
Experiment Route / number Best-fit parameters
Reference type/pathoge Dose unit Response
number of doses model
n strain
mice/ α = 0.21 50
Meynell and
Salmonella intraperitoneal No of Beta- N50 = 49.78
1 Meynell,195 death
strain 216 /10 organism Poisson
8
and 219
Meynell and mice/ α = 0.062 3E+07
intraperitoneal No of Beta-
2 Meynell,195 Salmonella death N50 =
/11 organism Poisson
8 strain 533 34566908
Meynell and mice/ α = 0.11 1E+07
intraperitoneal No of Beta-
3 Meynell,195 Salmonella death N50 =
/7 organism Poisson
8 strain 533 9661745
The data from different experiments were not able to be statistically pooled.
14.3 Optimized Models and Uncertainty and Fitting Analyses
14.3.1. Output for experiment 1.
Table 14.2: Dose response data Table 14.3: Goodness of fit and model selection
Dose ( No of Model Deviance ∆ DF χ 02.95,df χ 02.95,1
death survival Total
organism ) 9 16.92
5 7 8 15 Exponential 133.15
112.
3.84
25 4 11 15 Beta- 60 8 15.51
20.55
125 7 8 15 Poisson*
630 9 6 15 *Conclusion: Both models do not provide goodness
3160 8 7 15 of fit, but the beta-Poisson model is better than the
exponential. The inconsistent response pattern in
16000 13 2 15
the lowest dose group (dose=5) have contributed to
80000 15 0 15 this unsuccessful fitting, as the fit to the data
400000 15 0 15 excluding this outliner group provided goodness of
2000000 15 0 15 fit (data not shown).
10000000 15 0 15
Meynell and Meynell,1958.
Table 14.4: Parameters for the best-fit model (beta-Poisson), obtained from 1E4 bootstrap
iterations
Parameter MLE Percentiles
or value estimate 0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.21 0.15 0.158 0.164 0.29 0.31 0.36
N50 49.78 8.01 14.00 17.76 136.28 170.89 250.85
(a) (b)
Fig 14.1. Models plot for experiment 1. (a) Uncertainty plot of beta-Poisson model; (b) Plot of
beta-Poisson model with upper and lower 95% and 99% confidence.
14.3.2. Output for experiment 2.
Table 14.5: Dose response data Table 14.6: Goodness of fit and model selection
Dose ( No of Model Deviance ∆ DF χ 02.95,df χ 02.95,1
death survival Total
organism ) 10 18.31
6.03E+02 6 36 42 Exponential 193.16
145.
3.84
1.91E+03 3 39 42 Beta- 70 9 16.92
47.46
6.03E+03 7 35 42 Poisson*
1.91E+04 5 42 47 *Conclusion: Both models do not provide goodness
6.03E+04 6 34 40 of fit, but the beta-Poisson model is better than the
exponential. The inconsistent response pattern in
1.91E+05 3 29 32
the low dose groups (dose=6.03E+02 to 6.03E+04 )
6.03E+05 6 20 26 have contributed to this unsuccessful fitting, as the
1.91E+06 7 7 14 fit to the data excluding these outliner groups
6.03E+06 7 5 12 provided goodness of fit (data not shown).
1.91E+07 10 2 12
6.03E+07 13 0 13
Meynell and Meynell,1958.
Table 14.7: Parameters for the best-fit model (beta-Poisson), obtained from 1E4 bootstrap
iterations
Parameter MLE Percentiles
or value estimate 0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.062 0.034 0.040 0.043 0.11 0.12 0.18
N50 34566908 9.38e+05 1.71e+06 2.50e+06 9.46e+08 2.12e+09 1.63e+10
(a) (b)
Fig 14.2. Models plot for experiment 2. (a) Uncertainty plot of beta-Poisson model; (b) Plot of
beta-Poisson model with upper and lower 95% and 99% confidence.
14.3.3. Output for experiment 3.
Table 14.8: Dose response data Table 14.9: Goodness of fit and model selection
Dose ( No of Model Deviance ∆ DF χ 02.95,df χ 02.95,1
death survival Total
organism ) 6 12.59
1.00E+04 20 180 200 Exponential 214.14
165.
3.84
1.00E+05 17 153 170 Beta- 44 5 11.07
48.70
1.00E+06 11 29 40 Poisson*
3.16E+06 6 24 30 *Conclusion: Both models do not provide goodness
1.00E+07 12 8 20 of fit, but the beta-Poisson model is better than the
exponential. The inconsistent response pattern in
3.16E+07 17 3 20
the low dose groups (dose=1E+04 to 1E+05) have
1.00E+08 19 1 20 contributed to this unsuccessful fitting, as the fit to
Meynell and Meynell,1958. the data excluding these outliner groups provided
goodness of fit (data not shown).
Table 14.10: Parameters for the best-fit model (beta-Poisson), obtained from 1E4 bootstrap
iterations
Parameter MLE Percentiles
or value estimate 0.50% 2.5% 5% 95% 97.5% 99.5%
α 0.11 0.062 0.070 0.075 0.18 0.20 0.24
N50 9661745 1918314 2444076 2806068 58891804 89307034 211097461
(a) (b)
Fig 14.3. Models plot for experiment 3. (a) Uncertainty plot of beta-Poisson model; (b) Plot of
beta-Poisson model with upper and lower 95% and 99% confidence.
14.4. Summary
Noting the very different LD50 for different strains of host and pathogen, substantial variation of
susceptibility is manifestly presented. The inconsistencies of dose response pattern have
identified in the low-dose groups at all three experiments. The failure of pooling between
experiment 2 and 3 might be due to such variation and/or the experimental errors. The mechanism
behind this observation is desirable for future study.
References
Chalker, R. B. and M. J. Blaser (1988). "A review of human salmonellosis: III. Magnitude of
Salmonella infection in the United States." Reviews of Infectious Diseases 10(1): 111-124.
Meynell, G. G. and E. W. Meynell (1958). "The Growth of Micro-Organisms in vivo with Particular
Reference to the Relation between Dose and Latent Period " Journal of Hygiene 56(3): 323-346