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!