Yersinia pestis: Dose Response Models

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Yersinia pestis

(Plague)
Author: Yin Huang


General overview of Yersinia pestis and plague

Yersinia pestis, the causative agent of plague, is a Gram-negative facultative anaerobic bipolar-staining bacillus bacterium belonging to the family Enterobacteriaceae. It has been classified as a Category A bioterrorism agent for public health preparedness by U.S. Centers for Disease Control and Prevention.

Plague is a dreadful disease of long standing. It has been the cause of three pandemics, and has led to the deaths of millions of people, the devastation of cities and villages, and the collapse of governments and civilizations. Small outbreaks of plague continue to occur throughout the world, and at least 2000 cases of plague are reported annually. At the present time, plague remains a serious problem for international public health, and its risk has been assessed using quantitative modeling approaches.Plague may be manifested in one of three forms: bubonic, pneumonic and septicemic.[1] Among the three forms of plague, pneumonic plague is particularly dangerous, with incubation period of 3 to 5 days and mortality rate approaching 100% unless antibiotic treatment is initiated within 24 hours of the onset of symptoms.

Plague is transmitted to humans from infected flees and rodents are reservoirs of the disease. While over 200 mammalian species have been reported to be naturally infected with Y. pestis, rodents are the most important hosts for plague.[2] Currently, most human plague cases in the world are classified as sylvatic plague, namely infection from rural wild animals such as mice, chipmunks, squirrels, gerbils, marmots, voles and rabbits.[3] Transmission between rodents is achieved by their associated fleas from the infected blood of the host. The organism is not transovarially transmitted from flea-to-flea, and artificially infected larvae clear the organism within 24 hours. Therefore, maintenance of plague in environment is dependent upon cyclic transmission between fleas and mammals.[2]


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



Summary Data

Lathem et al. (2005)[1] and Parent et al. (2005)[4] respectively inoculated C57BL/6 mice intranasally with the Y. pestis virulent wild-type CO92 strain and with the KIM D27 strain. Rogers et al. (2007)[5] administered the Y. pestis CO92 strain to BALB/c mice via intraperitoneal route.


Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
1* [1] mice CO92 intranasal 4 CFU death exponential k = 1.63E-03 4.26E+02
2 [4] mice KIM D27 intranasal 4 CFU death exponential k = 1.07E-04 6.47E+03
3 [5] mice CO92 intraperitoneal 5 CFU death exponential k = 3.45E-02 2.01E+01
*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 1 should be used as the best dose-response model. Compared to experiment 2, a more virulent strain in experiment 1 can be more meaningful for emergency preparedness and public health intervention. Also, the exposure route was intranasal which is a better representation of an actual release scenario over the Intraperitoneal.

Exponential and betapoisson model.jpg

Optimization Output for experiment 1 (Yersinia pestis)

Mouse/ CO92 model data [1]
Dose Dead Survived Total
100 1 3 4
1000 3 1 4
1E+04 4 0 4
1E+05 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 0.338 0.195 3 3.84
0.658
7.81
0.953
Beta Poisson 0.142 2 5.99
0.931
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 1.63E-03 3.62E-04 5.50E-04 6.22E-04 7.02E-03 7.02E-03 7.02E-03
ID50/LD50/ETC* 4.26E+02 9.87E+01 9.87E+01 9.87E+01 1.11E+03 1.26E+03 1.92E+03
*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 2 (Yersinia pestis)

Mouse/ KIM D27 model data [4]
Dose Dead Survived Total
100 0 10 10
1000 2 8 10
1E+04 6 4 10
1E+05 10 0 10


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 1.21 0.138 3 3.84
0.711
7.81
0.75
Beta Poisson 1.07 2 5.99
0.585
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 1.07E-04 3.85E-05 4.70E-05 5.57E-05 1.93E-04 2.22E-04 3.29E-04
ID50/LD50/ETC* 6.47E+03 2.11E+03 3.12E+03 3.59E+03 1.24E+04 1.48E+04 1.80E+04
*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 3 (Yersinia pestis)

Mouse/ CO92 model data [5]
Dose Dead Survived Total
2 0 20 20
8 5 15 20
26 13 7 20
74 9 1 10
257 10 0 10


Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
χ20.95,1
p-value
χ20.95,m-k
p-value
Exponential 3.12 -9.43e-05 4 3.84
1
9.49
0.539
Beta Poisson 3.12 3 7.81
0.374
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 3.45E-02 2.01E-02 2.28E-02 2.44E-02 4.89E-02 5.18E-02 5.79E-02
ID50/LD50/ETC* 2.01E+01 1.20E+01 1.34E+01 1.42E+01 2.84E+01 3.04E+01 3.44E+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



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 1-3. The exponential TDR model (equation 1) incorporating the inverse-Weibull distribution (equation 3) provided the best fit to the data. The best TDR models are plotted to compare with the observed mortalities are shown in the figures below. As shown, the clear difference between the different times postinoculation gives a visible representation to the quantified results that the modification added to the classical models has a substantial effect on the dose response.


The cumulative mortality on each day (curves, from the first day to the last as the direction shown by the arrow) estimated by time-dose-response model compared to the observed mortality (points) against dose of Yersinia pestis. (a) experiment 1, (b) experiment 2, (c) experiment 3.
Equation Yersinia pestis.png




References

  1. 1.0 1.1 1.2 1.3 Lathem WW, et al. (2005) Progression of Primary Pneumonic Plague: A Mouse Model of Infection, Pathology, and Bacterial Transcriptional Activity. Proceedings of the National Academy of Sciences of the United States of America 102(49): 17786-17791.
  2. 2.0 2.1 Perry RD, Fetherston JD (1997) Yersinia pestis-Etiologic Agent of Plague. Clinical Microbiology Reviews 10(1): 35-66.
  3. Christie AB, (1982) Plague: review of ecology. Ecol. Dis. 1: 111-115.
  4. 4.0 4.1 4.2 Parent MA, et al. (2005) Cell-Mediated Protection against Pulmonary Yersinia pestis Infection. Infection and Immunity 73(11): 7304-7310.
  5. 5.0 5.1 5.2 Rogers JV, et al. (2007) Transcriptional Responses in Spleens from Mice Exposed to Yersinia pestis CO92. Microbial Pathogenesis 43: 67-77.

Christie AB (1982) Plague: review of ecology. Ecology of disease 1(2-3), 111-115.

Lathem WW, Crosby SD, Miller VL and Goldman WE (2005) Progression of primary pneumonic plague: A mouse model of infection, pathology, and bacterial transcriptional activity. Proceedings of the National Academy of Sciences of the United States of America 102(49), 17786-17791.

Parent MA, Berggren KN, Kummer LW, Wilhelm LB, Szaba FM, Mullarky IK and Smiley ST (2005) Cell-Mediated Protection against Pulmonary Yersinia pestis Infection. Infection and Immunity 73(11), 7304-7310.

Perry RD and Fetherston JD (1997) Yersinia pestis--etiologic agent of plague. Clinical Microbiology Reviews 10(1), 35-66.

Rogers JV, Choi YW, Giannunzio LF, Sabourin PJ, Bornman DM, Blosser EG and Sabourin CLK (2007) Transcriptional responses in spleens from mice exposed to Yersinia pestis CO92. Microbial Pathogenesis 43(2–3), 67-77.