Modeling Cholera Outbreak In South Africa ( ) 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 ll 1/DayRate of contact with untreated water b Cells/mlConcentration of cholera in water that yields 50% of catching cholera didi 1/DayDisease-related death rate drdr 1/DayRecovery rate dwdw 1/DayLoss 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 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 l Control k

When to implement? The plan was in place around February 14, 2001 Better timing? Stay with us…

Competitive models Model 1: S’= - l SW/(b+W) I’= l SW/(b+W)-d i I-d r I R’=d r I W’=kI-d W W Model 2: K= k, for t≤to k 1, for t>to For control: k 1 <k Model 3: L=  l for t≤to  l  for t>to  For control : l  <l Model 4: K= k, for t≤to k 1, for t>to L= l for t≤to l  for t>to l  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 nbrLog-likelihoodAIC BIC (non- informative priors) E E

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 days of epidemic.

Acknowledgments Our mentors: Dr. David Earn and Dr. Fred Adler PCMI participants and organizers

Thank you!