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Modeling Cholera Outbreak In South Africa (2000-2001)
Olga Krakovska**, Raluca Eftimie*
Eunha (Alicia) Shim***,
*University of Alberta, **The University of Western Ontario, ***Arizona State University
Outline
• Background Information• Available Data• Model Derivation• Candidate Models• Model Selection• Control• Conclusions
Cholera facts
• Transmission: ingestion of food or water contaminated with the bacterium Vibrio cholerae.
• Symptom: copious, painless, watery diarrhea, (severe) dehydration, vomiting and even death. Only 20% of infected show signs.
• Infection period: 7-14 days• Death rate: ~0.2%• Treatment: re-hydration
Enough Data?WHO reports +SA National Disaster management center + Numerical interpolation
Mathematical Model
WdkIW
IdR
IdIdWb
WSI
Wb
WSS
w
r
ri
1/Day Rate of contact with untreated water
b Cells/ml
Concentration of cholera in water that yields 50% of catching cholera
di 1/Day Disease-related death rate
dr 1/Day Recovery rate
dw 1/Day Loss rate of V. Cholerae
k Cells/ml day-
1
person-
1
Contribution of each infective to the population of V.Cholerae in the aquatic environment
Basic Reproductive Rate
wir dddB
kSR
)(0
0
Stable disease-free equilibrium
Stable endemic equilibrium
Model fitting
Can this be explained by control measures?
Control Measures Proposed by WHO:
• Hygienic disposal of human feces• Adequate supply of safe drinking
water• Good food hygiene and cooking• Washing hands after defecation
and before meals
Control measures
Control Control k
When to implement?
• The plan was in place around February 14, 2001
• Better timing?
Stay with us…
Competitive modelsModel 1:S’= -SW/(b+W)I’= SW/(b+W)-diI-drIR’=dr IW’=kI-dW W
Model 2:k , for t≤to k1, for t>to
For control: k1<k
Model 3: for t≤tofor t>to
For control:
Model 4:k , for t≤to k1, for t>to
for t≤tofor t>to
Proper disposal of human feces Washing hands before meals Adequate supply of safe drinking water Good food hygiene and cooking
k
Curve fitting
Results
Model Selection
Model nbr
Log-likelihood AICBIC (non-
informative priors)
1 430.9046 -849.809 3.67E-12
2 446.0595 -878.119 1.4E-05
3 456.5416 -899.083 0.499993
4 456.5416 -897.083 0.499993
When to Initiate the Control Measures?
Conclusions• The curve fitting to data supports the idea that
control was in effect during the second part of the epidemic.
• Hygienic disposal of feces was not effectively practiced during the epidemic.
• The control measure is always good to be implemented ASAP but the critical timing is around the first 100-150 days of epidemic.
Acknowledgments
• Our mentors: Dr. David Earn and Dr. Fred Adler
• PCMI participants and organizers
Thank you!